Yury Kabanov
email: ykabanov@hse.ru

Andrei V Chugunov
email: chugunov@egov-center.ru

Electronic "Pockets of Effectiveness": E-Governance and Institutional Change in St. Petersburg, Russia

Keywords: E-government, e-governance, institutional change, pockets of effectiveness 1

The paper explores the patterns and factors of e-governance development in ineffective institutional settings. Although it is assumed that most of e-projects in such countries failed, we argue that in some contexts such initiatives can survive in the hostile environment and achieve relatively positive results, leading to limited institutional changes. We adapt the pockets of effectiveness framework in order to analyze the Our Petersburg portal (St. Petersburg, Russia). Our findings suggest that such electronic "pockets" may emerge as a deliberate policy of the political elite in an attempt to make institutions work properly. The key factors of such projects' success relate to agency, namely the political patronage and control, policy entrepreneurship, as well as organization autonomy and the power of the initiative.

Introduction

A substantial part of e-governance research aims at revealing when, how and if ICTs lead to institutional changes in public administration or citizen-government relations [3; 15]. In fact, a plethora of works has found little impact of the e-mechanisms on democratization and the quality of governance, especially in ineffective institutional contexts, developing, neopatrimonial 1 or authoritarian countries [24; 27; 30], limiting the role of such instruments to legitimation and PR [2; 34]. But is this always the case? If incumbents may be interested in malfunctioning institutions to gain rents [START_REF] Gel'man | The vicious circle of post-Soviet neopatrimonialism in Russia[END_REF], can they eventually make use of e-government as a working tool? Although ICTs can consolidate the regime and empower autocrats [START_REF] Göbel | The information dilemma: How ICT strengthen or weaken authoritarian rule[END_REF], can they in fact strengthen the state capacity [START_REF] He | Authoritarian deliberation: The deliberative turn in Chinese political development[END_REF]? For instance, some empirical findings suggest that such relatively successful examples can be found on the subnational level [START_REF] Johnson | e-Government and transparency in authoritarian regimes: comparison of national-and city-level e-government web sites in Central Asia[END_REF].

The research goal is hence to reveal the factors such effective e-governance instruments emerge in the potentially hostile (authoritarian or neopatrimonial) institu-tional environment. To do this, we apply the pocket of effectiveness (PoE) concept [START_REF]The Politics of Public Sector Performance: Pockets of effectiveness in developing countries[END_REF] to the case of the Nash Peterburg (Our Petersburg, OP) portal, St. Petersburg, Russia,2 a government -initiated platform, launched in 2014, showing relative viability and effectiveness particularly against the overall ambiguous performance of the national initiatives [19; 5; 9], and in the context of the Russian political regime [START_REF] Gel'man | The rise and decline of electoral authoritarianism in Russia[END_REF]. We investigate if the OP portal is an example of PoE, and why.

Factors of ICT-Enabled Institutional Change: "Pockets of Effectiveness Framework"

The concepts like e-government, e-participation, e-democracy etc. have always been surrounded by myths and normative implications on better government and democracy. But challenged by reality, they often fail [START_REF] Bekkers | The myths of e-government: Looking beyond the assumptions of a new and better government[END_REF]. Potentially, the directions of ICT-led institutional change are different and overwhelming [START_REF] Nograšek | E-government and organisational transformation of government: Black box revisited?[END_REF]. For instance, e-mechanisms can affect bureaucracy by reducing administrative discretion via the automated information systems [32:223-224; 40; 41], eliminating corruption [46; 11], cutting the red tape [START_REF] Welch | E-government and bureaucracy: Toward a better understanding of intranet implementation and its effect on red tape[END_REF], improving public services' delivery or enhancing participation [28; 31]. All improvements do not follow immediately and with necessity, though [13: 88-89; 12]. The factors influencing the success of e-government are conceptualized differently. An important aspect is agency, or entrepreneurship [START_REF] Garud | Institutional entrepreneurship as embedded agency: An introduction to the special issue[END_REF], and its interaction with structures, i.e. institutions and organizational settings [3; 15; 35; 50]. Leadership and political power are crucial when bureaucracy is reluctant to changes and hinders the reform [1; 44]. Other possible factors include stakeholders' engagement, communication and feedback [START_REF] Luna-Reyes | Digital government transformation and internet portals: The co-evolution of technology, organizations, and institutions[END_REF], public value and trust [START_REF] Bertot | Using ICTs to create a culture of transparency: Egovernment and social media as openness and anti-corruption tools for societies[END_REF], institutional design [49; 6]. Plenty of research has been conducted so far to systemize all factors in one framework [START_REF] Panopoulou | Success factors in designing eParticipation initiatives[END_REF].

The problem is that ICT-enabled institutional change, as previous research shows, often emerges in polities with already sufficient institutional quality and democracy. Developing, neopatrimonial and authoritarian countries usually lag behind in terms of e-participation development [START_REF] Jho | Institutional and technological determinants of civil e-Participation: Solo or duet?[END_REF]. Even when they have enough capacity to introduce technological advancements [START_REF] Stier | Political determinants of e-government performance revisited: Comparing democracies and autocracies[END_REF], new instruments serve other goals: to be a façade for legitimation, international socialization or investment [1; 34]. Even if a strong political will for reforms is observed, they usually fail due to the informal norms and rent-seeking behavior of public officials [START_REF] Gel'man | The vicious circle of post-Soviet neopatrimonialism in Russia[END_REF].

In such context, a full-scale reform cannot be accomplished successfully. However, in some cases scholars observe that new institutions and organizations can resist the hostile environment and show relatively effective performance. Such organizations are called pockets of effectiveness, or PoE -"public organizations that deliver public goods and services relatively effectively in contexts of largely ineffective governments" and "operate in politico-administrative systems that are primarily based on personal networks instead of … impartiality and formal, law -based rules" [START_REF]The Politics of Public Sector Performance: Pockets of effectiveness in developing countries[END_REF]. Roll distinguishes several characteristics of the PoE: "relative effectiveness", contribution to public good and "persistence as PoE for at least three years" [START_REF] Roll | The state that works. Pockets of effectiveness as a perspective on stateness in developing countries[END_REF]. There is a ques-tion why a PoE emerges, and several frameworks were proposed. The discussion is basically focused on what factors are necessary and sufficient. Based on Leonard and Roll [29;[START_REF]The Politics of Public Sector Performance: Pockets of effectiveness in developing countries[END_REF][START_REF] Roll | The state that works. Pockets of effectiveness as a perspective on stateness in developing countries[END_REF], we may discern the following variables:

-political factors, including the strong leadership of the political elite, and its interest in effective institutions. As Leonard argues, the PoE is related to the "benefits and costs … for the politically powerful groups" [29: 97]; -managerial factors, ranging from proper training, commitment and "merit-based recruitment" and "inclusive leadership" and entrepreneurship to the ability of a public organization's leader to get political support and protection, remaining "autonomous of an operational political direction" [29: 95]; -organizational and institutional factors, such as the autonomy and powers of the organization to perform their tasks through legal and enforcement mechanisms; -other factors, distinguished by Roll include, for instance, PR and external pressures.

Although the studies on PoE mostly relate to developing countries in Africa, we suppose that this concept is applicable to any context when institutions do not work properly, such as Post-Soviet countries, including Russia [START_REF] Gel'man | Opportunities and Constraints of Authoritarian Modernisation: Russian Policy Reforms in the 2000s[END_REF]. In some cases, the creation of PoE becomes the final resort to increase governmental performance in time when a more overall reform is hindered by the existing institutions. The key implication of this framework to the e-governance studies is that the ICT -enabled instruments or public organizations may perform the functions of a PoE. The research strategy is to distinguish such successful cases and explain the factors of their success. We can draw several hypotheses from the framework. First, we hypothesize that egovernance initiatives can survive in the hostile institutional environment as a PoE, leading to some limited positive changes (H1). Secondly, we hypothesize that the development of PoE will depend on: 1) political control (H2), meaning the leadership and attention of the chief executive to the development of the policy; 2) institutional entrepreneurship (H3); 3) autonomy (H4) of the key executives in charge of OP.

3

Case of PoE Emergence: Our Petersburg Portal

Research Design

To accomplish the research goal of discovering an electronic PoE and explaining its emergence, we do the case study. We take the Our Petersburg Portal (OP), created by the government of St. Petersburg. The case selection is justified by the fact that St.

Petersburg shows relatively high level of the regional e-government development. On the one hand, it does not have as much resources as another federal city, Moscow. The first task is to discern the characteristics that attribute OP to the PoE. Namely, we need to conceptualize success. As PoE framework suggest, success can be understood as a relatively better service provision, internal efficiency and persistence. To explore if the OP meets these criteria, we explore the development of its institutional design, popularity with citizens and effectiveness in citizens' complaints resolution. The more elaborate the OP becomes, the more complaints it processes and the more spheres it covers, the more successful the OP is supposed to be. The empirical data here is the descriptive statistics on the OP functioning, gathered by the automatic monitoring system developed at the ITMO University [START_REF] Chugunov | E-Participation Portals Automated Monitoring System for Political and Social Research[END_REF] or provided by the city government, as well as official documents that regulate the OP.

The second task of revealing success factors, we have conducted five in-depth semi-structured interviews with public officials, related in various capacities to the OP emergence and operation. We asked them to share their own vision on how the OP had been initiated, on the role of decision-makers and civil servants, on the problems, current state and perspectives of the OP. The thematic and discourse analysis was then used to combine these subjective stories into a general, collective experience on the OP. Along with documental and mass media data, these interviews (some quotes are given) used to explore the formation and success factors.

Our Petersburg Portal as an Emerging PoE

Although the situation in Russia cannot be compared to the situation in some developing countries, it sill faces difficulties in maintaining effective institutions of good governance, mainly due to ineffective bureaucracy and informal ties [START_REF] Gel'man | Opportunities and Constraints of Authoritarian Modernisation: Russian Policy Reforms in the 2000s[END_REF], as well as corruption [START_REF] Goncharov | Public Administration in Russia[END_REF]. In this respect, the real impact of the e-governance is doubted [START_REF] Bershadskaya | e-Government in Russia: is or seems?[END_REF]. Against this picture, St. Petersburg presents a relatively better picture compared to other regions. It is considered to be relatively democratic [START_REF] Petrov | Rating of Democracy by Moscow Carnegie Center: 10 Years in Service[END_REF], having a relatively effective bureaucracy and quality of life. In May 2014 the St. Petersburg Government adopted the ambitious Strategy 2030, 3 aiming at restructuring the city administration, strengthening control and eliminating information asymmetry for better urban planning. In accordance with this, in 2015 the regional administrative reform was launched, to deliver quality service and implement new ICTs into the urban planning. 4The launch of the OP could serve this end.

The Portal was officially launched in early 2014 as a government -led portal, initiated by St. Petersburg Governor Georgy Poltavchenko. It serves to gather online complaints from citizens, devoted to the wide spectrum of urban problems, such as roads and housing etc., and process and solve them through the ICT with minimum delays. 5 In short, to solve a problem related to the urban environment, a citizen needs to register in the OP and submit an application. Each registered complaint is classified and processed through the moderator / coordinator to the executive in charge of its resolution. Then the executive agency should report on the results.

It was neither the first project of that kind in Russia, nor the only platform for urban problems solution in the city. In 2012, a group of civil activists launched the online platform "Beautiful Petersburg" (BP). As a legal basis, the BP uses the federal legislature on citizens' addresses (Law 59 "On Handling Citizens' Appeals"), allowing their transmission in electronic form. 6 Although it was novel for the e-governance practices then, it could have in fact not been called true institutional innovation, as the internal bureaucratic workflow remained pretty much the same [START_REF] Chugunov | Citizen versus Government or Citizen with Government: A Tale of Two e-Participation Portals in One City (A Case of Saint -Petersburg, Russia[END_REF]. On the contrary, the OP provided a brand new and ambitious regional legislation.

The key agencies involved in innovation are the Committee on Information and Communication (CIC), headed by Ivan Gromov, dealing with technological issues, the Gubernatorial Control Board (GCB) in charge of the administrative and legal aspects, and the City Monitoring Center (CMC), as a moderator and information processing unit. The first version of the portal (fig. 1) was limited in scope, but required much effort in order to provide a technological and legal basis. As our interviewee notes, they needed to restructure all administrative workflow from "the Governor to housing offices and road services". Complaints were to reach the exact agency or municipality, and it was crucial to clarify the competence of all divisions and the ownership of each city object, from "roads to trash cans". The portal has been constantly modernizing. In 2015 the Interdepartmental Commission was established in order to resolve possible conflicts between the agencies. In 2016 the public control was introduced, when users could check the completion of a task. 7The recent scheme of the OP is presented in fig. 2. In theory, the OP implies an unprecedented transformation of bureaucratic practices. In comparison to the ordinary procedure, enshrined in Federal Law 59 used by the BP portal, it shortens the time for complaints' processing, and clarifies agencies' responsibilities and control. If Law 59 gives agencies 30 days to respond, in the case of the OP they should do it in 7 days or less. It cuts red tape and sets the interoperability of executive bodies based on ICT. So, the OP has been evolving as a PoE in legal and technological terms.

From the start, the new initiative had to compete with the abovementioned civic initiative, as well as to deal with the internal bureaucratic rigidity. The founder of the BP Krasimir Vransky accused the OP of being a stillborn PR project,8 while shortened time limits and procedures negatively affected the ordinary bureaucratic workflow, making Ivan Gromov "the personal enemy of some districts' administrations". 9Our interviewees emphasize that the implementation was challenged by a "silent rebellion" against the OP and the CIC, especially from the housing services. The latter had to use the portal, but could discredit the portal, attempting to present reports with Photoshop-edited images, or even threaten the applicants. Some services adapted to new regulations by creating separate positions or units to handle complaints, which protect the rest of the structure from changes. Hence, the establishment of a disputeresolving Interdepartmental Commission was a timely measure. The institutional resistance is constant, as new executive agencies are included into the system, being "not eager to help in developing technological routes of applications processing" and "trying to postpone it by any means".

Despite this, the OP seems to have won the competition for efficiency and popularity against the BP by the end of 2015 (fig. 3). Official statistics claim that as of February 2016, about 169 thousand urban problems out of 193,5 thousand reported via the portal were resolved. 10 Our interviewees suggest that the key achievement of the OP is the increase in efficiency and quality of governance. The portal is expanding in terms of problem categories and the agencies involved (Table 1).

While it positively affects the principal -agent problem, discretion and corruption by transparent rules and meaningful control mechanisms, it in unclear if the portal is viable in the long run. The goal of the OP was not to reform the entire system of governance from scratch. All previous legal regulations, such as Federal Law 59, remain in power, with persisting red tape and inefficiency problems. As North argues, formal institutions can be easily altered, but time is needed to change informal rules [START_REF] North | Institutions, institutional change and economic performance[END_REF].

To summarize here, we suppose that OP represents a case of PoE in several respects. It was deliberately excluded from a different legislative basis, creating an alternative system of urban governance beyond the persistent informal norms. It meets the criteria of relative effectiveness, persistence and contribution to public goods, and manages to survive and develop in the potentially hostile institutional environment. It proves the thesis that sometimes the incumbents need working e-governance instruments that function well beyond legitimation, supporting our hypothesis (H1).

Factors of PoE Emergence

Political Control. It's quite clear from the interviews' analysis, that the role of the Governor in success of the OP is crucial. The positioning of the portal as a gubernatorial initiative gave necessary incentives to comply with new rules. The gubernatorial powers and executive domination in Russia have significantly increased since the 2000s [START_REF] Golosov | Gubernatorial Powers in Russia: The Transformation of Regional Institutions Under the Centralizing Control of the Federal Authorities[END_REF]. Supplemented by the so-called power vertical, a hierarchal system of governance and informal rules [START_REF] Gel'man | Local regimes, sub-national governance and the 'power vertical' in contemporary Russia[END_REF], it made governors the key political actors able to concentrate resources in order to implement policies, provided there are incentives. Although the launch of the portal might have been linked to the election campaign, the main rationale, we argue, was to increase the gubernatorial control over bureaucracies at all levels, centralizing the system of governance and strengthening political power. Such goal seems more plausible, as neither the OP was banned after the elections, nor the OP substantially increased the level of citizen engagement in decisionmaking [START_REF] Chugunov | Citizen versus Government or Citizen with Government: A Tale of Two e-Participation Portals in One City (A Case of Saint -Petersburg, Russia[END_REF]. The context is important as well: in 2012 e-government and eparticipation became a national priority, and Moscow was the first to initiate an innovative portal for urban problems reports. Hence, the OP could help St. Petersburg show loyalty to the federal policy and be competitive against other regions.

Such personal political patronage was accompanied by effective control mechanisms. The GCB was empowered to formulate the reports on executive discipline. These documents contain the indicators of agencies' work with the OP. Each executive body should report on a monthly basis. The Governor may take disciplinary measures on the results. As formulated by Ivan Gromov, "… the Governor of St. Petersburg constantly pays attention to it [the OP]. If he didn't systematically check it, the portal wouldn't have raised so high". 11 The transparency of the portal, allowing mass media and citizens to control the work of the executive agencies, has contributed to the gubernatorial control. Falsified images in reports that were found by mass media were met with severe criticism from the Governor. 12 The existing "power vertical" rendered the transmission of gubernatorial incentives through all bureaucratic levels very fast, contributing to the success of the OP. Though it was necessary for the rapid implementation, it seems to be insufficient, as the operative control is needed. Otherwise, when the patronage is over, the initiative will fade with comparable velocity.

Institutional Entrepreneurship. The role of institutional entrepreneurs is crucial in policy changes [START_REF] Garud | Institutional entrepreneurship as embedded agency: An introduction to the special issue[END_REF]. Somebody had to persuade the Governor to implement the policy and level the interests of political actors. Here we can mention the role of Ivan Gromov, a former CIC head, who performed the classical role of an institutional entrepreneur. He was appointed in 2012 when, as he noted, the regional IT system needed more centralization and economic efficiency. 13 His motivation to launch the OP is not clear, but the easy answer obtained from an interview, "he just wanted something working properly to help people". Due to his previous work in Moscow, he might have learnt about the success of a similar project.

Despite his motivation, Gromov possessed sufficient political authority, being a trustee member of the Governor's team. 14 He managed to acquire political support of his initiative, and demonstrated "inclusive leadership" to motivate the employees. To leverage the system of administration, Gromov took the medium position between the Governor, the GCB and the rest of the executive bodies, as he had to sustain the political interest in the OP and ICTs in general, on the one hand, and amortize the possible negative effects on the other. Until 2015, when he was appointed the head of one of St. Petersburg's districts, he had supported (and still does) the project.

Organizational Autonomy. In 2015 Gromov resigned from his position as CIC head, but it did not affect the efficiency of the OP. Is it inertia or regularity? From the framework, we know that the autonomy and sufficient powers are important for the PoE emergence and survival. Furthermore, as literature suggests, the ICT can lead to a reinforcement of the existing power relations [START_REF] Schlaeger | E-Government in China: Technology, Power and Local Government Reform[END_REF], allowing those controlling the ICTs to concentrate more recourses and authority.

This hypothesis is partially confirmed in our case. During the OP establishment, the CIC, led by Gromov, has sufficiently raised its status, mostly informally through the association to the gubernatorial initiative. The importance of ICTs in public administration has also generally increased. In terms of finance allocation, the CIC is the key recipient of funds with an annual average budget of 6 billion rubles, 15 and the regional expenses on IT remain one of the highest in Russia. 16 and patronage have provided the CIC with sufficient autonomy and status to implement the OP and other projects. However, the raise in status was implicit, as no changes in the administrative position of the committee occurred.

Crucial is that the successful implementation of the OP helped to achieve new powers in adjacent spheres, mainly in the administrative reform. First, in 2014 the division in charge for developing new administrative procedures was transferred from the Committee on Executive Agencies under the CIC. The Committee took responsibilities on the administrative reform in the area of electronic services and interdepartmental interaction. As the reform itself was connected to the development of the ICT infrastructure, the CIC acquired new opportunities to influence decision-making on the informatization of government. Second, the CIC became responsible for the Commission on administrative reform (Gromov was appointed its deputy head), raising its steering role. 17 Although the CIC has never been a sanctioning body, the CIC managed to raise its own status and autonomy and secure the development of the OP.

Hence, we can summarize that the case study confirms the hypotheses that the political control (H2), institutional entrepreneurship (H3) and organizational autonomy (H4) became the key factors of the PoE emergence.

Conclusion

Our findings from the case of the OP contribute to the knowledge on e-governance and institutional change in several respects. First, we suggest the PoE can be a valuable research framework to be used in e-governance studies. It helps to grasp an ambiguity of e-governance projects in ineffective institutional settings, and its heuristic value is linked to the variety of hypotheses on why such electronic pockets of effectiveness emerge and persist.

Secondly, the research expands, and to a certain degree challenges the opinion that e-governance projects cannot function properly in ineffective institutional settings.

Although most e-mechanisms are in fact legitimacy tools, in some cases they can serve incumbents better as working instruments, positively affecting the institutional development and public services provision. Here we can refer to one of our interviewees, who said that "no matter whether it were a PR-action, if it achieved real results and benefited the citizens".

The case of the "Our Petersburg" Portal provides an excellent example of such PoE, and proves that such electronic pockets can emerge and survive. Our study shows the crucial importance of agency in creating and maintaining successful e-mechanisms, namely the political control, institutional entrepreneurship and the organizational autonomy.

It is important to continue the analysis to and to compare the OP with other cases in Russia and abroad.

Fig. 1 .

 1 Fig. 1. The OP Portal's Technological and Institutional Ecosystem, Version of 2014. Source: Authors' picture based on open documents.

Fig. 2 .

 2 Fig. 2. The OP Portal's Technological and Institutional Ecosystem, Version of 2016. Source: Authors' picture based on open documents.

Fig. 3 .

 3 Fig. 3. The number of complaints submitted via the BP and OP portals, 2012 -2016. Source: http://analytics.egov.ifmo.ru/

  The official who repaired road with Photoshop is fired,http://www.fontanka.ru/2016/11/29/068/ [in Russian]

		Sufficient resources
	11	Ivan Gromov: "Our Petersburg" Solves Problems Quickly, http://www.spbdnevnik.ru/news/2016-08-30/nash-sankt-
		peterburg--reshaeyt-problemy-bystro/ [in Russian].
	13	St. Petersburg: Informatization, http://www.tadviser.ru/index.php/ [in Russian]; New St. Petersburg IT Director,
		http://www.cnews.ru/news/top/novyj_itdirektor_sanktpeterburga [in Russian]
	14	Persona: Ivan Gromov, http://www.tadviser.ru/index.php/Персона:Громов_Иван_Александрович [in Russian
	15	Committee on Information and Communications of St. Petersburg, http://www.tadviser.ru/index.php/
		Компания:Комитет_по_информатизации_и_связи_Санкт-Петербурга [in Russian]

12

Governor:

Table 1 .

 1 egov.ifmo.ru/ Indicators of OP Growth, 2014-2016

	Number of Coplaints	submitted	0 2000 4000 6000 8000 10000	01.08.20	01.11.20	01.02.20	01.05.20	01.08.20	01.11.20	01.02.20	01.05.20	01.08.20	01.11.20	01.02.20	01.05.20	01.08.20	01.11.20	01.02.20	Our Petersburg Beautiful Petersburg

For discussion on the concept of neopatrimonialism see[START_REF] Erdmann | Neopatrimonialism reconsidered: critical review and elaboration of an elusive concept[END_REF]

Our Petersburg Portal, http://gorod.gov.spb.ru [in Russian]

St. Petersburg 2030 Strategy, http://spbstrategy2030.ru/?page_id=102 [in Russian]

Administrative reform in St. Petersburg, http://gov.spb.ru/gov/otrasl/c_information/adm_ref/ [in Russian]

Our Petersburg Portal, http://gorod.gov.spb.ru [in Russian]

Federal Law 59 On the Order of Consideration of Addresses from Citizens of the Russian Federation. Adopted on 02.05.2006, http://www.consultant.ru/document/cons_doc_LAW_59999/ [in Russian].

Changes in the work of Our Petersburg Portal, http://gorod.gov.spb.ru/content/news/36/ [in Russian]

Portal for Self-Glorification, https://www.zaks.ru/new/archive/view/127361 [in Russian]

Ivan Gromov's speech on the IT Forum, 2015. Authors' notes.

Our Petersburg Portal, http://gorod.gov.spb.ru [in Russian]

Informatization of Regions: Russian Market, http://www.tadviser.ru/index.php/Статья:Информатизация_регионов_(рынок_России) [in Russian]


Linda Veiga

Ibrahim Kholilul

Ibrahim Kholilul Rohman
email: rohman@unu.edu

E-Government and the shadow economy: evidence from across the globe

Keywords: e-Government, shadow economy, growth, developing countries, public administration

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The shadow economy (SE) -unrecorded and unreported economic activities-has been a long problem hampering economic progress in many countries [START_REF] Mai Hassan | Size and development of the shadow economies of 157 countries worldwide: Updated and new measures from 1999 to[END_REF]. Among others, [START_REF] Mazhar | Taxing the unobservable: The impact of the shadow economy on inflation and taxation[END_REF] highlight its impact on tax revenue, [START_REF] González-Fernández | Analysis of the shadow economy in the Spanish regions[END_REF] on regional public debts, and [START_REF] Dell'anno | Analyzing the Determinants of the Shadow Economy With a "Separate Approach". An Application of the Relationship Between Inequality and the Shadow Economy[END_REF][START_REF] Giles | anadian ax oundation Association canadienne d tudes fiscales[END_REF] on the unemployment rate. On the financial sector, SE associates with a higher inflation rate [START_REF] Prinz | In the Shadow of Public Debt: Are there Relations between Public Debt and the Shadow Economy?[END_REF], higher interest rates, a greater probability of sovereign default [START_REF] Elgin | Homeownership, Informality and the Transmission of Monetary Policy[END_REF] and an adverse effect on credit ratings [START_REF] Markellos | Sovereign Debt Markets in Light of the Shadow Economy[END_REF]. At the industry level, [START_REF] Amendolagine | Innovativeness, offshoring and black economy decisions. Evidence from Italian manufacturing firms[END_REF] concluded that firms choosing to enter the SE tend to produce negative spillover effects denoted by lower productivity and the propensity to innovate.

The study by [START_REF] Chong | Inequality, Institutions, and Informality[END_REF] found that the SE is negatively correlated with the wealth of nations. [START_REF] Schneider | Shadow economies around the world: what do we really know?[END_REF] corroborated this result with a finding that a 1%, increase in the SE lowers the growth rate of the "official" GDP by 0.6% in developing countries. [START_REF] Eilat | The Shadow Economy in Transition Countries: Friend or Foe? A Policy Perspective[END_REF] warned that once SE is established, it is hard to remove. The size of the SE is quite enormous especially in the developing regions. Table 1 shows the distribution between regions and the World Bank's income level. 1 shows that the average ratios of the SE on GDP ranges between 43 to 51% in low income countries, and that those in Latin America and the Caribbean are more prone to these activities than those in South Asia, and Sub-Saharan Africa. We also see an indication of spatial effect in Latin America and South Asia based on the values of the standard deviation. Thus, adding to its enormous size, the lower standard deviation indicates a contagion of the SE phenomenon across countries in these regions. In the Sub-Saharan Africa, on the opposite, there is a more clustered outcome due to the disparities of economic progress between countries. Furthermore, the range of the SE in the lower middle income countries is wider (between 30 to 63%) than the low-income group, again showing a higher incidence in Latin America and Caribbean than in any other regions. In the East Asia and Pacific, we see a greater deviation in the Pacific region. The proportion of the SE in the higher middle income countries is somewhat lower (between 20-40%) compared with previous two groups, where countries in (Eastern) Europe and Central Asia have the greatest proportion of SE. The performance of countries is relatively uniform when looking into its standard deviation especially in South Asia where the standard deviation is very low. Moving towards higher income countries the proportion is much smaller (between 17-34%), but the largest incidence is still found in Latin America and the Caribbean also with a greater variation between countries.

Three preliminary conclusions can be drawn from this table. First, that SE is relatively clustered in specific countries (in this case Latin American and Caribbean countries), second, the incidence is significantly larger in low income countries, and third, the phenomenon is contagious across countries in specific regions inferred from the lower standard deviations like those in South Asia and Latin America and the Caribbean.

A study by [START_REF] Larsson | Future-oriented eGovernance: The sustainability concept in eGov research, and ways forward[END_REF] defined e-Government as the use of ICTs in the public sector involving several actors and encompassing various interaction patterns in a continuously changing environment. [START_REF] Boer | What's your favorite blend?: Analyzing source and channel choices in business-to-government service interactions[END_REF] emphasized a need to conduct more studies on the effects of eGov on economic and business activities and s such, our paper aims to contribute to this niche in the literature.

Conceptually, the link between the potential roles of eGov on economic sustainability, and specifically, the SE can be inferred from [START_REF] Eilat | The Shadow Economy in Transition Countries: Friend or Foe? A Policy Perspective[END_REF]. The study mentioned that the primary cause of a shadow activity is an attempt to avoid predatory and obstructive regulations. Thus, if institutional and regulatory problems are addressed, the government might expect a reduction of the shadow activities. The size of the administrative burden can be astounding. [START_REF] Kox | Intra-EU differences in regulation-caused administrative burden for companies[END_REF] estimated that the total administrative burden on businesses within the European Union was around 600 billion euros per year, ranging from 1.5% of GDP in the UK and Sweden to 6.8% of GDP in Hungary, Greece and the Baltic States. Thus, the eGov implementation aimed at reducing the administrative burden on businesses is believed to gauge better policies, better implementation, better compliance and ultimately, better government. Since 2007 Europe has targeted to reduce administrative by 25% in 2012 leading to an increase of 1.4% of EU GDP [START_REF]European Commission: Measuring administrative costs and reducing administrative burdens in the EU[END_REF].

The purpose of the study is to investigate a possible role of digital government in reducing the SE through administrative burden reduction. This paper answers two research questions. First, does the implementation of eGov contribute to a reduction in the size of the SE? Second, is there a threshold point by which eGov development is more effective to reducing the size of the SE? The analysis is carried out at different levels of income and regions, to see the heterogeneity between groups of countries (mainly contrasting the phenomenon in the developed versus developing countries).

On the determinants of the shadow economy

Previous studies (e.g. [START_REF] Smith | Market motives in the informal economy[END_REF]) defined the SE as activities operating outside the principal legal and social structures of the economic system. In the Eastern Europe, the SE primarily concerns with a market sector but operates outside the system of economic planning, and involves the private mobilization of means of production. Contrary, in the Western Europe, the SE is associated with the 'black economy' dealing with the tax evasion, fraudulent claims for unemployment benefit and all nonmarketed productive activities not included in the national accounts.

There are several determinants affecting the size of the SE. In a phenomenon called as a hysteresis, [START_REF] Eilat | The Shadow Economy in Transition Countries: Friend or Foe? A Policy Perspective[END_REF] found a negative association but asymmetric between GDP and SE. To illustrate, a US$1 decrease of GDP is associated with a 31-cent increase in the size of the SE, whereas, a US$1 increase of GDP results in only a 25-cent decrease SE. The study also showed that firms in a more specialized economy have a lower incentive to enter the shadow activities.

Other main determinants concern with the taxation regime and institutional setting. The studies by [START_REF] Blackburn | Tax evasion, the underground economy and financial development[END_REF], [START_REF] Quintano | The shadow economy beyond European public governance[END_REF] and [START_REF] Stankevičius | ax Burden evel everage on Size of the Shadow Economy, Cases of EU Countries 2003-2013[END_REF] found that the burden of taxation is among the main determinants in the EU countries and particularly in Spain ( [START_REF] Markandya | From shadow to green: Linking environmental fiscal reforms and the informal economy[END_REF]). [START_REF] Goel | Shining a light on the shadows: Identifying robust determinants of the shadow economy[END_REF] pointed out that bureaucratic complexity also contributes to the SE. [START_REF] Torgler | The impact of tax morale and institutional quality on the shadow economy[END_REF] stressed the role of institutional factors by which [START_REF] González-Fernández | Analysis of the shadow economy in the Spanish regions[END_REF] exemplified with the degree of the corruption level. [START_REF] Cooray | How Does Corruption Affect Public Debt? An Empirical Analysis[END_REF] backed this argument by analyzing 126 countries over 1996-2012, and found that corruption and the SE are related complementarily.

There are other factors worth addressing. [START_REF] Dell'anno | Analyzing the Determinants of the Shadow Economy With a "Separate Approach". An Application of the Relationship Between Inequality and the Shadow Economy[END_REF] stressed the role of inequality, [START_REF] Chaudhuri | The size and development of the shadow economy: An empirical investigation from states of India[END_REF] on literacy rates and [START_REF] Elgin | Internet usage and the shadow economy: Evidence from panel data[END_REF] on ICT usage (e.g. the Internet). Moreover, while most studies found negative sides of SE, [START_REF] Aristidis | The Absorption of a Shadow Economy in the Greek GDP[END_REF][START_REF] Macias | Modeling the informal economy in Mexico. a structural equation approach[END_REF] found a positive relationship between formal economic activities and SE in Greece and Mexico, respectively.

The role of technology and e-Government

The eGov policy is a complex interaction, [START_REF] Azad | E-Government institutionalizing practices of a land registration mapping system[END_REF][START_REF] Rowley | e-Government stakeholders-Who are they and what do they want[END_REF] showed that implementing workable e-Government systems requires bringing together different perspectives of stakeholders during implementation. [START_REF] Bharosa | Tapping into existing information flows: The transformation to compliance by design in business-to-government information exchange[END_REF] found that transforming Business-to-Government information exchange might result in more efficiency and reduction of redundant controls. [START_REF] Guttman | Real-life MDA: solving business problems with model driven architecture[END_REF] summed that implementing eGov in the U.S. Government's General Services Administration (GSA) helps federal agencies to better serve the public by offering superior workplaces, expert solutions, and management policies.

Moreover, as the main vein in eGov implementation is ICT devices, we argue that the nature of network externality as it exhibits in ICT also applies in eGov. The value of ICT services depends on its network: if there are enough adopters, the good becomes valuable. The point of critical mass is mentioned in many ICT studies (e.g. [START_REF] Meade | Modelling and forecasting the diffusion of innovation -A 25-year review[END_REF][START_REF] Röller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF]). Details of the study by [START_REF] Röller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF][START_REF] Torero | Information and communication technologies for development and poverty reduction: The potential for development and poverty reduction[END_REF] ascertained the need to achieve a critical mass in order to obtain increased economic growth. Based on these studies, we also assume that a critical mass is also required in the eGov implementation.

Methodology and Data

On collection of the data on the shadow economy

There are two possible avenues which can be employed to estimate SE: the direct and indirect approaches [START_REF] Schneider | Estimating the size of the shadow economy methods, problems and open questions[END_REF]. The direct approach is operationalized by assigning a well-designed surveys or samples based on voluntary replies, or tax auditing and other compliance methods. The main disadvantages of this method are the flaws inherent in all surveys hence the results depend greatly on the respondent's willingness to cooperate.

The second avenue is to use indirect approaches or indicator approach. Among these, six main strategies can be implemented. First, by measuring the discrepancy between national expenditure and income statistics, second, between the official and actual labor force, third, between the volume of transaction and GNP (see [START_REF] Feige | Defining and estimating underground and informal economies: The new institutional economics approach[END_REF] for detail), fourth, by assuming that the SE increases the demand for currency, fifth, by estimating the physical inputs (for instance electricity (see [50] for details), and sixth by using econometric modeling. The main weakness of indirect approaches concerns with the double accounting issue. Thus, comparing the direct and indirect approaches, [START_REF] Feige | Defining and estimating underground and informal economies: The new institutional economics approach[END_REF] suggested that the later should be used as the upper-bound.

In this study, the data on the size of the SE was obtained from [START_REF] Mai Hassan | Size and development of the shadow economies of 157 countries worldwide: Updated and new measures from 1999 to[END_REF] which uses the multiple indicators multiple causes (MIMIC) approach to estimate the SE. The concept of the MIMIC model is to examine the relationships between a latent variable "sizes of SE" with a number of observable variables by using their information of covariance. The detail of MIMIC model is thoroughly explained in [START_REF] Schneider | Estimating the size of the shadow economy methods, problems and open questions[END_REF].

The estimated SE used in this study covers all market-based legal production of goods and services that are hidden from public authorities for one or combinations of the following reasons: to avoid payment of taxes, to avoid payment of social security contributions, to avoid certain legal labor market standards and to avoid complying with certain administrative procedures, such as completing statistical questionnaires [START_REF] Mai Hassan | Size and development of the shadow economies of 157 countries worldwide: Updated and new measures from 1999 to[END_REF].

On the e-Government index

Taking into account the analysis implemented by [START_REF] Berntzen | Benchmarking e-Government -A Comparative Review of Three International Benchmarking Studies[END_REF] we decided to use the UNDESA index [START_REF]E-government surveys (various years of datasets[END_REF] in this study. The study [START_REF] Berntzen | Benchmarking e-Government -A Comparative Review of Three International Benchmarking Studies[END_REF] compared the following three indices published internationally based on the reproducibility, coverage of observation, qualitative assessments, and national scope  The index constructed by Accenture, which assesses, on a yearly basis, egovernment efforts in 20+ countries since 2000;  The Brown University's (Prof. West and his research team) index which is released annually since 2001;  And [START_REF] Mai Hassan | Size and development of the shadow economies of 157 countries worldwide: Updated and new measures from 1999 to[END_REF], which assesses the e-government readiness among UN's members, since 2002. The UNDESA eGov development index (EGDI) is reported based on a comprehensive survey of the online presence of all 193 United Nations Member States, which assesses national websites and how e-government policies and strategies are applied in general and in specific sectors for delivery of essential services. The EGDI is not designed to capture e-government development in an absolute sense; but to give a performance rating of national governments relative to one another. Although the basic model has remained consistent, the precise meaning of these values varies from time to time. Moreover, the index is a simple average of the normalized scores of the three most important dimensions of e-government, namely: (1) scope and quality of online services (Online Service Index, OSI), (2) development status of telecommunication infrastructure (Telecommunication Infrastructure Index, TII), and (3) inherent human capital (Human Capital Index, HCI).

Other data and econometric model

Our main variable of interest to explain the level of the SE is the eGov index. However, to avoid the omitted variable bias problem, other control variables commonly used in the literature are also considered. These include the GDP per capita at purchasing power parity in thousands of 2011 US dollars (GDPpc), the general government final consumption expenditure as a percentage of GDP (Gov%GDP), the degree of openness of the economy measured by the sum of exports and imports over GDP (Openness), and the inflation rate (Inflation). All variables were obtained from the World Bank dataset. These variables were also chosen because they exist for 145 of the 147 countries for which data on the SE and the EGDI is available. 1 The estimated baseline model was the following:

Where i stands for country, t for year, SE for shadow economy, EGDI for the egovernment development index, Control for a vector of control variables, Region for a vector of dummies for the World Bank's regions, and e for the error term.  and represent coefficients, and and  vectors of coefficients to be estimated. The EGDI and all control variables were lagged one year because it takes time for them to have an impact on the SE and to mitigate endogeneity problems.

Since the EGDI is only available for specific years (2003,2004,2005,2008, and every two years thereafter), the index was not built to capture e-government development in an absolute sense but rather to assess the diffusion of e-government through a comparison of national governments relative to one another. Moreover, as the index's methodology changed over time [START_REF]E-government surveys (various years of datasets[END_REF], we decided to work with crosssections of countries for each year that the index is available. The model was first estimated by OLS, using heterokedasticity-consistant error terms. Since the estimated SE never yields values below zero or above 100, the data is censored, which implies that performing a Tobit estimation is a more appropriate estimation method.

In addition, as a robustness test, and taking into account that the size of the informal sector is always between zero and one (or one hundred), the model was also estimated with the Fractional Probit model [START_REF] Papke | Econometric Methods for Fractional Response Variables With an Application to 401 (K) Plan Participation Rates[END_REF].

Results

The econometric results for the three methods mentioned above are presented in 1 Several other variables, for which less data is available, were also used in preliminary analysis but results remained essentially the same. Among others, we used the share of taxes on GDP, the share of part-time/long-term employment on total employment, and the real interest rate from the World Bank dataset; a dummy for democracies from POLITY IV; the human capital index from the World Economic Forum; the economic freedom of the world index and the black-market exchange rates index from the Fraser Institute; and finally, the index of socioeconomic conditions from the International Country Risk Guide. Table 2. Columns 1 to 3 are for a cross-section of countries in 2013, and column 4 for 2004. These two years are, respectively, the most recent and first year for which we were able to run the cross-section. As can be seen from the table, results are very similar regardless of the estimation procedure used, or the year analyzed. 2 The estimated coefficient for the EGDI is negative and statistically significant in all specifications indicating that countries with a better performance in the EGDI tend to have a lower SE. As expected, countries with a higher GDP per capita have a smaller informal sector. This result is consistent with previous studies, even though [START_REF] Elgin | Homeownership, Informality and the Transmission of Monetary Policy[END_REF] found a non linear relationship between the two variables. The dummies for the World Bank's regions reveal that the share of the SE in GDP is significantly larger in Latin American and Caribbean countries (Region 3). For OLS and fractional probit estimations, in 2013, there is evidence that it is lower in the Middle East & North Africa (Region 4) and South Asia (Region 6). Finally, the control variables Gov, Open and Inflation did not turn out as statistically significant in any regression. Given that results are similar across the three methods, and the nature of our dependent variable, results for subsequent estimations are reported only for the Tobit estimation. In order to test which component of the EGDI is most influential on the size of the SE, we included each of them in the same regression. Results reported in column 1 of Table 3 3 , suggest that only the telecommunication infrastructure index (TII) is a significant determinant of the SE. 4 The estimated coefficient is negatively signed and highly statistically significant. However, since the three components of the EGDI are strongly correlated, we decided to include each of them separately in the estimations. Results indicate that they are all statistically significant and negatively signed. Therefore, there is also evidence that progress in the Online Service Index (OSI) and Human Capital index (HC) reduce the size of the informal sector though TII shows the biggest magnitude among three sub-indices. Notes: Results for a cross-section of countries for the year 2013 using the Tobit estimation method. Estimations include the same controls as those of Table 3. Robust t-statistics in parentheses. ***p<0.001, **p<0.05, *p<0.1.

The following step of the analysis was to split the sample according to the World Bank's income groups and regions. Results are presented in Table 4. In order to economize space we only show the estimated coefficients for the EGDI, but all estimations include the same controls as those of equation 1, except for the regions' dummies. Table 4 reveals that EGDI seems to exert a bigger influence on the size of the SE in high income countries, suggesting that the ability of e-government to reduce the SE can only be expected after countries reach certain levels of economic and egovernment development. The mean value of the EGDI in the high-income countries is 0.68, much higher than for the other income groups. We also estimated the same analysis by region and found that the largest coefficient (in absolute terms) was obtained for the East Asian and Pacific countries, and the smallest for the Middle East, North African and Sub-Saharan countries. Only for the countries in the Latin America and Caribbean region did the EGDI turn out not to be statistically significant.

Discussion

As the Digital Government landscape is continuously and dynamically evolving, it is important that policymakers and government executives evaluate the Digital Government decisions and foresee its impact on society. The purpose of this study is to investigate a possible role of digital government in reducing the SE activities -a long problem which has hampered many countries, especially the developing ones. We investigate whether the implementation of eGov has contributed to a reduction in the size of the SE and if a minimum level of eGov development is required for it to effectively decrease the size of the informal sector.

The contribution of this study is twofold: (1) we provide empirical evidence, based on a large sample of countries, on the potential impact of eGov (proxied by EGDI-UNDESA) to mitigate the problem of the SE, (2) we show that the impact differs across income and geographic groups of countries, which suggests that it is necessary to achieve a minimum level of economic and eGov infrastructure before a country can reap the benefits from the initiative. Decomposing the sample by income groups, we found the impact of the EGDI on the reduction of the SE is statistically significant in the high-income group. The result is consistent when the analysis is performed at the region level showing the greater impact at the regions entailing a greater economic progress. Our findings are consistent with previous studies on the need to achieve critical mass of ICT (telecommunications and broadband) before expecting a wider spill of the impacts on the economy and society. By disentangling the sub-indices, we can interpret these results as follow: unless a country has achieved at least 26% fixed broadband subscribers and 70% internet users, they might not be able to expect the spillover effect of the eGov development. These figures are obtained from the mean values of both variables in the high-income countries.

The paper also stresses the need to implement a more concrete and thorough eGov road map, especially in developing countries, to reduce the administrative burden and the size of the SE. We acknowledge there is room for improvement on methodological aspects and econometric modeling. We are also aware that, given the complexity of the problems associated with these phenomena, our recommendation should not be seen as a sole panacea. However, we believe that improvements in egovernment may represent a more efficient and socially acceptable strategy to control SE activities than the adoption of punitive measures.

Table 1 .

 1 The size of shadow economy (% to GDP) between region and income, average 2003-2013 and the standard deviation

	Regions	The World Bank income classifications
		High income Higher Middle	Lower Middle	Low income
			income	income
	East Asia & Pacific	17.63 (7.22)	38.25 (13.19) 31.11 (14.87)
	Europe & Central Asia	21.65 (7.83)	41.02 (8.84)	50.64 (9.55)
	Latin America & Caribbean 33.59 (14.20) 38.70 (10.51) 62.96 (10.98) 51.11 (3.53)
	Middle East & North Africa 17.46 (6.22)	24.46 (7.91)	36.44 (5.20)
	North America	21.97 (13.84)
	South Asia		21.32 (2.65) 35.09 (11.54) 42.98 (5.99)
	Sub-Saharan Africa		29.36 (11.20) 36.39 (11.56) 45.14 (14.82)
	Table

Table 2 .

 2 Results using different econometric methods and years Notes: The estimation method used in each regression and the year is indicated in the title of the respective column. Marginal effects (in percentage points) are reported for the Fractional Probit method. Robust t-statistics in parentheses. ***p<0.001, **p<0.05, *p<0.1.

	VARIABLES	OLS 2013	Tobit 2013	Frac. Probit 2013	Tobit 2004
	EGDI	-0.263***	-0.263***	-0.21**	-0.237***
		(-2.967)	(-3.432)	(-2.35)	(-3.965)
	GDPpc	-0.246***	-0.246***	-0.0035***	-0.175**
		(-3.073)	(-2.855)	(-3.67)	(-2.606)
	Gov	0.170	0.170	0.18	0.072
		(0.680)	(0.636)	(0.76)	(0.348)
	Open	-0.032	-0.032	-0.017	-0.089
		(-0.506)	(-0.514)	(-0.27)	(-1.246)
	Inflation	-0.015	-0.015	-0.026	-0.084
		(-0.0882)	(-0.0807)	(-0.17)	(-0.582)
	Region3	9.934***	9.934***	0.093***	7.747***
		(3.144)	(3.331)	(3.37)	(2.911)
	Region4	-5.239**	-5.239	-0.051**	-3.819
		(-2.098)	(-1.482)	(-1.99)	(-1.198)
	Region6	-8.231*	-8.231	-0.077*	-3.323
		(-1.832)	(-1.508)	(-1.82)	(-0.765)
	Constant	50.02***	50.02***	-0.21**	43.84***
		(9.709)	(11.33)	(-2.35)	(11.75)
	N. observations	145	145	145	145
	R-squared	0.433
	Log-likelihood		-571.0	-90.2	-543.5

Table 3 .

 3 EGDI

			and its components
	VARIABLES	(1)	(2)	(3)	(4)
	TII	-0.277***	-0.296***
		(-2.715)	(-4.120)
	OSI	0.0402		-0.141**
		(0.505)		(-2.218)
	HCI	-0.0705			-0.203***
		(-0.840)			(-3.054)
	N. observations	145	145	145	145
	Log-likelihood	-568.2	-568.6	-574.3	-572.2

Table 4 .

 4 Results Notes: Results for a cross-section of countries for the year 2013 using the Tobit estimation method. Robust t-statistics in parentheses. ***p<0.001, **p<0.05, *p<0.1.

				by income class
	VARIABLES	High income Low income Lower middle income Upper middle income
	EGDI	-0.306**	-0.325	0.357	0.240
		(-2.359)	(-1.102)	(1.144)	(1.352)
	N. observations	47	23	35	40
	Log-likelihood	-162.3	-85.1	-143.4	-149.8

Estimations were also performed for each year for which the EGDI is available. Results are available from the authors upon request.

To economize space, in Table3we only report the estimated coefficients associated with the e-indices but the estimated regressions included the same controls as those of Table3(equation 1).

TII currently takes into account the number of: internet users, fixed-broad band subscriptions, wireless broadband subscriptions, fixed-telephone subscriptions and mobile-cellular subscriptions.

Acknowledgements

The authors are very grateful to Friedrich Schneider for providing the data on the estimates for the SE. This research was supported by the Programa Operacional da Região Norte, NORTE2020, in the context of project NORTE-01-0145-FEDER-000037 (SmartEGOV). This work was also carried out within the funding of COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ ECO/03182/ 2013), with the FCT/MECs (Fundação para a Ciência e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Program on Competitiveness and Internationalization -COMPETE 2020 under the PT2020 Partnership Agreement.


Carmen Buchrieser
email: cbuch@pasteur.fr

when the first Chlamydia was discovered (now named Chlamydia trachomatis), they were described as borderline organisms and only much later recognized as a bacterial phylum [START_REF] Moulder | The relation of the psittacosis group (Chlamydiae) to bacteria and viruses[END_REF]. All the presently known Chlamydiae are associated with eukaryotic hosts and are obligate intracellular bacteria that undergo a distinctive biphasic life cycle inside cytoplasmic membrane-bound vacuole inclusions [START_REF] Abdelrahman | The chlamydial developmental cycle[END_REF][START_REF] Kuo | Chlamydia. In, Bergey's Manual of Systematics of Archaea and Bacteria[END_REF]. The developmental cycle is characterized by the alternation between two physiologically and morphologically distinct forms, elementary bodies (EBs) and reticulate bodies (RBs). The bacteria are transmitted as inert but highly infectious EBs that, once inside the inclusions, differentiate to metabolically active RBs. The latter undertake several division cycles and transform back to EBs, capable of evading the host cell and infecting others. The cycle is not synchronized i.e., although a young inclusion will consist only of elementary bodies, mature inclusions will most of the time display the different forms [START_REF] Kuo | Chlamydia. In, Bergey's Manual of Systematics of Archaea and Bacteria[END_REF]. Physical changes in the nucleoid structure and in the outer membrane allow the distinction between EBs and RBs but the trigger causing the switch remains a conundrum [START_REF] Abdelrahman | The chlamydial developmental cycle[END_REF][START_REF] Kuo | Chlamydia. In, Bergey's Manual of Systematics of Archaea and Bacteria[END_REF]. Until recently, EBs were believed to be metabolically inactive and their characteristically highly condensed chromatin was thought to cause a complete shutdown of transcription [START_REF] Barry | Hc1-mediated effects on DNA structure: a potential regulator of chlamydial development[END_REF]. However, this dogma has been challenged by recent findings that have shown that transcription and protein biosynthesis takes place in host-free EBs and that major metabolic routes are active in these particles [START_REF] Haider | Raman microspectroscopy reveals long-term extracellular activity of Chlamydiae[END_REF][START_REF] Sixt | Metabolic features of Protochlamydia amoebophila elementary bodies--a link between activity and infectivity in Chlamydiae[END_REF][START_REF] Omsland | Chlamydial metabolism revisited: interspecies metabolic variability and developmental stage-specific physiologic activities[END_REF].

For a long time, Chlamydiae were considered a small bacterial phylum composed of one single family, the Chlamydiaceae, which included diverse well-known human and animal pathogens such as the previously mentioned C. trachomatis, the causative agent of trachoma and of the worldwide most common sexually-transmitted disease [START_REF] Everett | Emended description of the order Chlamydiales, proposal of Parachlamydiaceae fam. nov. and Simkaniaceae fam. nov., each containing one monotypic genus, revised taxonomy of the family Chlamydiaceae, including a new genus and five new species, and standards for the identification of organisms[END_REF]. But in recent years researchers have shown that Chlamydiae are a much more diverse group of bacteria than previously thought as eight new families (Parachlamydiaceae, Waddliaceae, Simkaniaceae, Rhabdochlamydiaceae, Criblamydiaceae, Piscichlamydiaceae, Clavichlamydiaceae, Parilichlamydiaceae) have been added to the phylum Chlamydiae, radically changing our perception of these organisms [START_REF] Horn | Chlamydiae as symbionts in eukaryotes[END_REF][START_REF] Taylor-Brown | Twenty years of research into Chlamydia-like organisms: a revolution in our understanding of the biology and pathogenicity of members of the phylum Chlamydiae[END_REF]. Furthermore, these findings show that Chlamydiae are not only human or animal pathogens but that they encompass also diverse symbionts of a myriad of hosts such as protists, marine worms and arthropods.

These newly discovered chlamydial families are often named "environmental chlamydia" given the range of habitats from where the isolates have been obtained from [START_REF] Horn | Chlamydiae as symbionts in eukaryotes[END_REF][START_REF] Taylor-Brown | Twenty years of research into Chlamydia-like organisms: a revolution in our understanding of the biology and pathogenicity of members of the phylum Chlamydiae[END_REF]. However, our current knowledge might be just the tip of the iceberg: a recent analysis of metagenomic and amplicon data suggested the existence of up to 181 putative Chlamydiae families comprising a large number of yet unidentified members and also of potential hosts and ecological niches [START_REF] Lagkouvardos | Integrating metagenomic and amplicon databases to resolve the phylogenetic and ecological diversity of the Chlamydiae[END_REF]. The majority of the newly identified lineages derived from marine habitats, a commonly overlooked environment in the quest for new members of this phylum.

Environmental Chlamydiae are more closely related to their pathogenic counterparts than to any other bacteria but, in contrast to what is observed for the Chlamydiaceae, the genomes of these environmental bacteria are diverse and display a large repertoire of genes likely associated with host-adaptation and ecology [START_REF] Collingro | Unity in variety--the pan-genome of the Chlamydiae[END_REF][START_REF] Domman | Following the Footsteps of Chlamydial Gene Regulation[END_REF]. Interestingly, strains of environmental Chlamydiae have been shown to infect and thrive in human cells, suggesting a possible pathogenic role for some environmental chlamydia [START_REF] Greub | Parachlamydia acanthamoeba enters and multiplies within human macrophages and induces their apoptosis[END_REF][START_REF] Casson | Parachlamydia acanthamoebae enters and multiplies within pneumocytes and lung fibroblasts[END_REF].

Chlamydiae have been the focus of several studies but the knowledge about this phylum remains limited, particularly for the environmental representatives. Their strict host-dependency has often hindered isolation and detection approaches, and the resulting impossibility to culture them in the laboratory hampered further studies on these bacteria. In this issue of EMI, Pizzetti and coworkers analyzed the chlamydial seasonal dynamics of the coastal lake Lago di Paola and used a new isolation approach that allowed the first co-isolation of a marine chlamydia (tentatively named Neptunochlamydia vexilliferae)

with its natural host, an amoeba of the family Vexillifera. Remarkably, using a combination of a new high-throughput limited dilution approach that strongly limits the competition between protists [START_REF] Schulz | Marine amoebae with cytoplasmic and perinuclear symbionts deeply branching in the Gammaproteobacteria[END_REF] and super resolution microscopy, the authors directly observed and identified chlamydia-host associations (Figure 1). Besides the successful isolation of N. vexilliferae and its host, this procedure lead also to a much more accurate quantification of the chlamydial diversity and dynamics in this environment compared to a previous report [START_REF] Pizzetti | High abundance of novel environmental chlamydiae in a Tyrrhenian coastal lake (Lago di Paola, Italy)[END_REF]. Curiously, this new isolate had not been detected in a polymerase chain reaction based study performed on Lago di Paola samples, perhaps because it does not belong to any of the major clusters of Chlamydiae previously identified in this lake [START_REF] Pizzetti | High abundance of novel environmental chlamydiae in a Tyrrhenian coastal lake (Lago di Paola, Italy)[END_REF]. This method brings therefore not only significant advances for the isolation of new

Chlamydiae and other amoeba-associated bacteria, but also for future quantification studies as it allows researchers to identify and study previously overlooked host-associated bacteria.

Bearing in mind the strict obligate intracellular lifestyle of Chlamydiae and their low abundance in environmental samples compared to other free-living bacteria, analyzing host-associated bacteria will be of major importance for future studies of these organisms, particularly in previously unexploited environments and putative hosts. As highlighted by this study, the seasonality of chlamydia matched the dynamics of host abundance, showing once more the tight connection between the two partners. This work brings also attention to the fact that the observed peak of amoeba abundance matched the time of highest anthropogenic activity in the lake, which might have sanitary implications considering the putative pathogenic potential of some environmental chlamydia.

Noteworthy also, is the fact that Pizzetti and coworkers succeeded to routinely maintain the here identified environmental chlamydia species N. vexilliferae and its amoeba host in a laboratory culture. Most of the known Chlamydiae families are represented by only a few isolates and the lack of laboratory cultures poses a serious drawback for further studies. In contrast, the fact that Pizzetti and coworkers managed to culture both partners in the lab allows further studies and comparisons to be undertaken between chlamydia having different lifestyles and hosts. Such research is of key importance for in depth understanding of how this group of bacteria evolved, adapted to different hosts and surrounding environments, and emerged as pathogens for animals and humans.

Figure 1 .

 1 Figure 1.

Acknowledgements

Research in CBs group is funded by the Institut Pasteur, ANR-10-LABX-62-IBEID and the Fondation pour la Recherche Médicale grant N° DEQ20120323697. FV was supported by the Infect-ERA project EUGENPATH (ANR-13-IFEC-0003-02).


Gabriele Perozzi

Denis Efimov

Jean-Marc M Biannic

Laurent Planckaert

Patricia Coton

Wind estimation algorithm for quadrotors using detailed aerodynamic coefficients

In the context of safe control of quadrotors, wind velocity estimation and compensation have a key-role. For this reason, assuming the lack of airspeed sensors and considering sensors noise, in this paper three time-varying parameter estimation algorithms are introduced, studied and merged to estimate the varying wind velocity, using only on-board quadrotor sensors and an inertial tracking position system (e.g. Optitrack camera, GPS). To this end, a detailed quadrotor flight dynamics model is presented using identified aerodynamic coefficients and wind velocity components along the three axes. Then, a decomposition of dynamical equations is performed in known and unknown terms to be estimated. Thanks to this decomposition, the estimation algorithms are built and finally tested and validated in numerical experiments, against the introduced sensors' noise.

I. INTRODUCTION

Quadrotors are usually required to move in environments where wind velocity is unknown. To improve their stability, a good control must ensure a good robustness against the disturbance caused by this wind. The problem is that, nowadays the pressure sensors, such as aeroclinometer, Pitot tube and LIDAR based sensors, are too heavy to be mounted on a mini drone. For this reason, an estimation software scheme (or an intelligent sensor) has to be designed based on measurements available on quadrotors and on inertial tracking position system. Then, the objective of this work is to develop an on-board algorithm for estimation of time-varying wind parameters by taking into account a detailed physical model. The design objectives include the time convergence optimization and robustness to measurement noises and model uncertainties improvement. The estimation is performed using IMU (accelerometer, gyroscope) sensors augmented with ground based camera system and rotors angular velocities sensors.

According to the aerodynamic science, a nonlinear dependence of the UAV by the wind speed comes out, while the disturbances (external forces and moments) enter linearly in the drone equations. To estimate constant and time-varying parameters, many algorithms were proposed recently in the literature, and two main groups can be identified:

The following works estimate the wind velocity using airspeed sensors. In [START_REF] Benallegue | High-order slidingmode observer for a quadrotor UAV[END_REF], the high-order sliding mode observer is constructed as an estimator of the effect of the external disturbances in quadrotors such as wind and noise. Another algorithm is provided by [START_REF] Palanthandalam-Madapusi | Windfield reconstruction using flight data[END_REF] which develops an extension of the Kalman filter that provides an estimate of the unknown wind disturbance in micro-UAV scenario. The paper [START_REF] Johansen | On estimation of wind velocity, angle-of-attack and sideslip angle of small UAVs using standard sensors[END_REF] estimates the wind velocity, angle-of-attack and sideslip angle of a fixed-wing UAV using kinematic relationships with a Kalman Filter, avoiding the need to know aerodynamic models or other aircraft parameters. The paper [START_REF] Langelaan | Wind Field Estimation for Small Unmanned Aerial Vehicles[END_REF] describes a method for estimating wind velocity, rate of change of wind velocity, and wind gradient for small and mini UAVs. In the work [START_REF] Rysdyk | Unmanned Aerial Vehicle Path Following for Target Observation in Wind[END_REF] an observer estimates wind data, which is used in the case where the UAV subjected to wind perturbation has to follow an object on the ground.

The following articles propose wind and disturbance estimations without the use of additional airspeed sensors. The paper [START_REF] Yüksel | A nonlinear force observer for quadrotors and application to physical interactive tasks[END_REF] presents Lyapunov method for external forces and moments in flying robots. The article [START_REF] Tomić | A unified framework for external wrench estimation, interaction control and collision reflexes for flying robots[END_REF] presents a modelbased method for external wrench estimation in flying robots based on proprioceptive sensors and the robot's dynamics model. The article [START_REF] Waslander | Wind Disturbance Estimation and Rejection for Quadrotor Position Control[END_REF] develops an estimation algorithm for the wind velocity using the inversion of the equations that define the components of the accelerometer measurements.

The paper outline is as follows. In Section II the considered UAV drone is described and the flight dynamics model is derived. A preliminary study of the dynamics is carried out in Section III. The wind estimation algorithms are presented in Section IV. The results of numeric experiments are shown in Section V. The remarks and discussion conclude the paper in Section VI.

II. FLIGHT DYNAMICS

This section presents the model of the UAV dynamics, which has configuration as it is shown in Fig. 1.

Fig. 1. UAV configuration

According to the identification work at low/medium velocity in [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF] using the Parrot AR Drone 2.0 and similar, rotors gyroscopic effects and inertial counter torques are neglected since they are rather small. The translational dynamics of the drone in the body frame yield

m u + mϖ × u = F aero + mR T g, (1)
where m is the mass of the UAV, u = [u v w] T is its linear velocity expressed in body frame, ϖ = [p q r] T is its angular velocity in body frame, F aero = [F Xaero F Yaero F Zaero ] T is the vector of the external aerodynamic forces in body frame, g = [0 0 g] T is the gravity acceleration in inertial frame, R is the rotational matrix defining the passage between the inertial and body frames. The rotational dynamics of the drone with respect to inertial earth frame are

I π = -ϖ × Iϖ + τ aero , ( 2
)
where I is the inertia matrix of the UAV, and τ aero = [L aero M aero N aero ] T is the external aerodynamic moments in the body frame. The relation between angular velocities and Euler angles φ = p + tan θ (q sin φ + r cos φ ),

θ = q cos φ -r sin φ , ψ = q sin φ + r cos φ cos θ , (3)
are considered avoiding the singularities θ π 2 , which is a reasonable assumption in our case since the topic of this article is not to achieve aggressive maneuvers. The full model of the system is presented by the equations (1), (2), [START_REF] Benallegue | High-order slidingmode observer for a quadrotor UAV[END_REF].

The aerodynamic forces, moments, and coefficients are derived using a combination of momentum and blade element theory in helicopters, explained by [START_REF] Leishman | Principles of Helicopter Aerodynamics with CD Extra[END_REF], [START_REF] Johnson | Helicopter Theory[END_REF], [START_REF] Bramwell | Bramwell's Helicopter Dynamics[END_REF]. Aerodynamic forces and moments for each rotor, where subscript j indicates the j th rotor, are derived as

F X j = -ρAR 2 u j -u w (u j -u w ) 2 + (v j -v w ) 2 C H j ω 2 j , F Y j = -ρAR 2 v j -v w (u j -u w ) 2 + (v j -v w ) 2 C H j ω 2 j , F Z j = -ρAR 2 C T j ω 2 j , L j = -sign ω j ρAR 3 u j -u w (u j -u w ) 2 + (v j -v w ) 2 C Rm j ω 2 j , M j = -sign ω j ρAR 3 v j -v w (u j -u w ) 2 + (v j -v w ) 2 C Rm j ω 2 j , N j = -sign ω j ρAR 3 C Q j ω 2 j ,
where ρ is the air density, A is the rotor area, R is the rotor radius, [u w v w w w ] is the wind velocity with respect to the earth in body frame, C H is the hub force coefficient, C T is rotor thrust coefficient, ω is the rotor angular speed, C Q is the rotor drag moment coefficient, C Rm is the rotor rolling moment coefficient. Total aerodynamic forces are

F Xaero = 4 ∑ j=1 F X j , F Yaero = 4 ∑ j=1 F Y j , F Zaero = 4 ∑ j=1 F Z j . (4)
Total aerodynamic moments are

L aero = 4 ∑ j=1 (L j + F Z j ls j -hF Y j ), M aero = 4 ∑ j=1 (M j -F Z j lc j + hF X j ) N aero = 4 ∑ j=1 (N j + F Y j lc j -F X j ls j ), (5)
where h is the distance between rotors plane and the center of gravity of the UAV, l is the arm length, and with c j = cos π 2 ( j -1) + ε , s j = sin π 2 ( j -1) + ε . In our UAV configuration we have ε = π 4 , thus for vectors c j and s j we have cosines and sinus of the angles [ π 4 , 3 4 π, 5 4 π, 7 4 π]. According to [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF] thanks to in-door experiments on Parrot drone, in moderate velocity and in climbing phase, the aerodynamic coefficients are identified as follows

C T j = C T stat + K z w j -w w R|ω j | , C T stat > 0, λ j = λ stat - 4 σ a K z w j -w w R|ω j | , K z ≥ 0, λ stat > 0, µ j = 1 |ω j |R (u j -u w ) 2 + (v j -v w ) 2 , C Rm j = σ a µ j 8 (λ j - 4 3
),

C Q j = σC D0 8 (1 + µ 2 j ) + σ aλ j ( θ 0 6 - λ j 4
),

C H j = K D µ j , K D ≥ 0 ( 6
)
where σ is the rotor solidity ratio, a is the lift curve slope of the blade section, C D0 is the drag coefficient of the blade section, θ 0 is the angle of attack of the root profile, λ is the inflow ratio, µ is the advance ratio, subscript stat indicates the value in hover phase. The above UAV coefficients can be explained recalling aerodynamic science.

III. PRELIMINARIES Substituting ( 6), ( 4) and ( 5) in ( 1), (2), the UAV dynamics equations can be rewritten in state-space form

Ẋ = f (X,U, ω, d w ),
where f is expressed in (1), (2), d w = [u w v w w w ] T is the vector of time-varying wind velocities to be estimated, ω is the vector of rotors angular rotational velocities and they are directly measured by sensors, the control vector U contains the terms proportional to the squares of rotors velocities ω 2 j , and the state X = [u v w p q r] T is represented by the linear and angular velocities of the UAV in the body frame. Explicit mathematical computations are illustrated in [START_REF] Perozzi | On sliding mode control design for UAV using realistic aerodynamic coefficients[END_REF], [START_REF] Perozzi | Wind rejection via quasi-continuous sliding mode technique to control safely a mini drone[END_REF]. Linear velocities u, v, w together with their derivatives (accelerations) are provided by the on-board accelerometer, which measures directly ∆a

(X) = ∆ a (X) + ε a , ∆ a (X) =   ∆ au (X) ∆ av (X) ∆ aw (X)   =   u v ẇ  +   p q r   ×   u v w   -   -g sin θ g cos θ sin φ g cos θ cos φ   ,
where ε a is a bounded measurement noise of the accelerometer. From the gyroscope, which measures the rotational velocity in body frame with respect to the earth, the rest state coordinates are measured

∆g (X) = ∆ g (X) + ε g , ∆ g (X) = p q r T ,
where ε g is the measurement noise generated by gyroscope. IMU sensor is augmented with ground based cameras, used to estimate u, v, w, φ , θ in coupling with gyroscope and accelerometer and making the drone observable with respect to the inertial frame.

Following the structure of measured information, another decomposition can be performed by splitting the dynamic equations in two parts

∆ a (X) ∆g (X) = f 0 (X,U, ω) + Ω(ω)d w , (7)
where f 0 : R 14 → R 6 is supposed to be known, and Ω : R 4 → R 6×3 is a time-varying regressor matrix related to the wind speed d w , which has to be estimated. In order to derive the expressions of f 0 and Ω, the translational rotor velocities in the body frame are computed as

  u j (X) v j (X) w j (X)   =   p q r   ×   lc j ls j h   +   u v w   .
Remark 1: Nonlinear terms, which represent a small part of rotor rolling torque R m for roll +sign (ω j ) 1 2 ρARK z (u ju w ) (w jw w ) , and for pitch

+sign (ω j ) 1 2 ρARK z (v j -v w ) (w j -w w ) ,
and a small part of rotor torque Q for yaw dynamics

-signω j ρAR × 1 8 σC D0 (u j -u w ) 2 + (v j -v w ) 2 - 4K 2 z σ a (w j -w w ) 2
are neglected. These restrictions can be accepted for low UAV and wind velocities.

It is worth noting that the provided UAV model allows the wind estimation using only three translational dynamics with a simple inversion. Rotational dynamics adds three equations to improve the estimation, since inside the translational dynamics we already have terms proportional to θ , φ that consider the rotational behavior of the UAV subjected to external wind. Moreover the rotational dynamics include also the inertia matrix which is rather complicated to precisely estimate.

IV. ESTIMATION ALGORITHM

In the following, the argument dependence of the functions f 0 and Ω is avoided to make the presentation more compact. To design the algorithm let us decompose the system [START_REF] Waslander | Wind Disturbance Estimation and Rejection for Quadrotor Position Control[END_REF] as follows

∆ a ∆g = f 0a f 0g + Ω a Ω g d w , ∆a ∆g = ∆ a + ε a ∆ g + ε g ,
where the variables ∆a and ∆g are available from measurements, f 0a , Ω a , f 0g , Ω g are the vector and matrix variables, respectively for translational (subscript a) and rotational (subscript g), whose values are functions of measured variables X, U, ω. The presented algorithms are designed assuming that u, v, w, and φ , θ with their derivatives are available from measurements (trajectography, optical flow, GPS). For simplicity, in theoretical analysis we supposed that these values are reconstructed exactly, but for simulation a state measurement noise has been added modeling this effect. To avoid unnecessary state differentiation, three sub-algorithms can be considered: one suitable for translational dynamics, the others for rotational dynamics. The algorithms presented in this section are based on the following hypothesis (we will switch between them depending on applied approach): Assumption 1: The measurement noises are absent (ε a = 0 and ε g = 0) and the wind velocity is constant ( ḋw = 0).

Assumption 2: The measurement noises ε a , ε g and the wind acceleration ḋw are bounded signals Assumption 3: The matrix Ω g is bounded and persistently excited for all t ≥ 0 (see [START_REF] Efimov | Design of impulsive adaptive observers for improvement of persistency of excitation[END_REF] for definition of this property1 ).

A. Translational dynamics

Define the predicted acceleration:

∆a = f 0a + Ω a dw ,
which is based on the estimate dw of the wind velocity derived below; and introduce the error between the measured state acceleration ∆a and predicted one as follows

e a = ∆a -∆a = Ω a (d w -dw ) + ε a , (8)
with ε a the bounded sensors noise for the accelerometer. According to [START_REF] Ríos | Finite-Time Identification Algorithm based on Time-Varying Homogeneity and Lyapunov Approach[END_REF], the following finite-time estimation algorithm can be introduced ḋw = γ a Ω T a e a α , 0 < α < 1, γ a 0, [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF] where

• α = | • | α sign(•) is understood element-wise.
The following results can be proven (the proofs are excluded due to space limitations).

Theorem 1: Let Assumption 1 be satisfied, then the value d w can be estimated in a finite time by [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF].

Theorem 2: Let Assumption 2 be satisfied, then for (9) there exist T ( dw , ε) > 0 and ν a2 > 0 such that |d w (t) -dw (t)| ≤ ν a2 max{ dw , ε} ∀t ≥ T ( dw , ε). Therefore, the system ( 9) is globally finite-time stable, and the parameter identification error converges to a neighborhood of the origin that depends on the upper bound of the noise ε, maximal amplitude of acceleration of the wind dw , the choice of the gain γ a and the parameter α.

B. Rotational dynamics

Wind estimation problem for rotational dynamics is slightly different from the linear one because the state vector is measured and not its derivative is provided by the sensor, hence an adaptive observer, which estimates the state and the wind simultaneously, has to be also designed. To this end, first, the adaptive observer equations can be written as follows ∆g = f 0g + Ω g dw + sign( ∆g -∆g ),

ḋw = γ g Ω T g ( ∆g -∆g ), ( 10
)
where ∆g is an estimate of the state vector ∆ g , dw is again an estimate of the vector of wind velocities d w ; > 0 and γ g 0 are tuning parameters. The following result can be obtained (the induced norm of a matrix Ω g is denoted by Ω g 2 ): Theorem 3: Let assumptions 1 and 3 be satisfied, and there is a known bound dw > 0 such that |d w | ≤ dw , then for > 2 Ω g 2 dw the estimate dw in [START_REF] Leishman | Principles of Helicopter Aerodynamics with CD Extra[END_REF] converges to the value of d w in a finite time.

The main issue with the algorithm [START_REF] Leishman | Principles of Helicopter Aerodynamics with CD Extra[END_REF] is hidden in rather strong restrictions imposed in Assumption 1, which we need to substantiate the convergence. Less restricted estimation algorithm can be obtained by the price of an augmented computational complexity as the following one:

∆g = f 0g + Ω g dw + ( ∆g -∆g ) + Ξ ḋw , Ξ = -Ξ + Ω g , ḋw = γ g Ξ T ∆g -∆g α , (11)
where ∆g and dw as before are the estimates of ∆ g and d w , respectively; > 0, α ∈ (0, 1) and γ g 0 are design parameters; Ξ is an auxiliary matrix variable having the dimension of Ω g (obviously it is always bounded for bounded Ω g and > 0) and having its initialization in Ξ(0) = 0. In order to clarify the stability and robustness properties of this estimation scheme let us introduce three estimation errors

e ∆ = ∆ g -∆g , e d = d w -dw , δ = e ∆ -Ξe d ,
which have the following dynamics:

ė∆ = -(e ∆ + ε g ) + Ω g e d -γ g ΞΞ T e ∆ + ε g α , ėd = -γ g Ξ T Ξe d + δ + ε g α + ḋw , δ = -(δ + ε g ) -Ξ ḋw .
Introduce the following hypothesis: Assumption 4: The minimum singular value of the matrix variable Ξ(t) ∈ R 3×3 is bigger than σ Ξ for all t ≥ 0. The last condition on Ξ can be ensured by a proper initialization and the same property of Ω g (Assumption 3). The following result can be substantiated:

Theorem 4: Let assumptions 2 and 4 be satisfied, then in (11) there exists T > 0 such that

|e d (t)| ≤ ρ(ε, dw ), |e ∆ (t)| ≤ max{σ -1 Ξ ε, √ 2 ( Ω g 2 ρ(ε, dw ) + ε)},
for all t ≥ T , where

ρ(ε, dw ) = σ -1 Ξ max{ 2 Ξ 2 dw + 3ε, α +1 c d1+α -1 w }, c = 2α α + 1 c -2-α -1 σ -1-α -1 Ξ .
If δ = ε = dw = 0, then a finite-time convergence of dw to d w is substantiated.

As we can conclude, the restrictions used for the estimation algorithms are not the same. Algorithm [START_REF] Leishman | Principles of Helicopter Aerodynamics with CD Extra[END_REF] is obtained in the noise-free and constant wind conditions, despite the theoretical result this algorithm also possesses some noise filtering abilities. The estimation schemes ( 9), [START_REF] Johnson | Helicopter Theory[END_REF] assume both that the noise and wind derivative are bounded signals. Thus, some fusion of these last solutions is desirable to improve the accuracy of the wind estimates. To this end, let us define the estimates of d w generated by the algorithms [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF], and (11), as di w for i = 1, 2 respectively. Denote the errors as υ 1 (t) = e a (t) for (9) and υ 2 (t) = ∆g (t) -∆g (t) for [START_REF] Johnson | Helicopter Theory[END_REF]. Then dfusion

w (t) = ∑ 2 i=1 e -κ i υ 2 i (t) di w (t) ∑ 2 i=1 e -κ i υ 2 i (t) (12)
is the united estimate of d w from all the estimation algorithms developed in this paper, and κ i > 0 for i = 1, 2 are tuning parameters. The proposed estimation algorithms, ( 9), ( 10) and [START_REF] Johnson | Helicopter Theory[END_REF], require as input an estimate of u, v, w, θ , φ , which are generally obtained fusing the accelerometric and gyroscopic measurements available on board, and ground measurements such as camera tracking.

V. NUMERICAL EXPERIMENTS

To show the performance of the proposed estimation algorithms, we are going to consider the Parrot Drone which has mass m = 0.47 kg, rotors velocities 200 rad/s ≤ ω j ≤ 400 rad/s, and we are going to compare the wind velocities in the earth frame. It means that the wind estimates dw in the body frame, are then transposed to the earth frame. Gaussian noises with 2.5 deg /s, and 0.052 m/s 2 standard deviations for gyroscope and accelerometer respectively, are added to simulate the augmented-IMU sensors noise. Additional Gaussian noises of 1 cm/s standard deviation for linear velocities, and 1 deg standard deviation for angles are added because state measurement (u, v, w, φ , θ ) are not reconstructed exactly. Wind signals in earth frame are simulated as sinusoids, which is a reasonable assumption since the gust generator at ONERA lab allows to create a sinusoidal wind gust profile, hence the sinusoidal wind effect over time is correlated to the motion of the drone through the turbulent area. Wind signals have maximal amplitude of 3, 3, 0.5, since the UAV identification work by [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF] is valid for ≈ ±5, ±5, ±1 translational velocities respectively in x, y, z axes. A flight case is illustrated where the mini drone is forced to follow the position reference in forward, lateral and vertical flights (coupling together movements on x, y, z axes) in Figures 2,3 Figures 4,5 show the performance of the algorithm (9) using the three translational dynamic equations. Many varyingwind velocities, having different frequencies, are tested.

Figures 6,7 show the performance of the algorithm (10) using the three rotational dynamic equations. The assumed noise-free and constant wind velocity conditions influence very much the quality of the result: the wind velocity with higher frequency gets the worst estimation. The tested wind velocities are the ones used for the algorithm [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF].

Figures 8,9 show that the problem of these restrictive hypotheses is solved introducing the algorithm (11), using the three rotational dynamic equations. The tested wind velocities are the ones used for the algorithm [START_REF] Planckaert | Quadrotor UAV aerodynamic model identification using indoor flight experiment and feasibility of UAV as wind gust sensor[END_REF]. Fig. 10 show the performance of the algorithm [START_REF] Bramwell | Bramwell's Helicopter Dynamics[END_REF], which allows to estimate correctly the wind velocity using a fusion of algorithms ( 9), [START_REF] Johnson | Helicopter Theory[END_REF] along the x, y axes, and using only (9) for z axis. even with the introduction of sensors' noise. Future indoor experiments will validate the proposed algorithm and further investigations can be performed by coupling this wind estimator to a robust controller ( [START_REF] Perozzi | Wind rejection via quasi-continuous sliding mode technique to control safely a mini drone[END_REF], [START_REF] Perozzi | On sliding mode control design for UAV using realistic aerodynamic coefficients[END_REF]) to extend the domain of flight, and reducing in real-time the control effort on the rotors, when it is not necessary. 12) and ( 9). (-: real; -: estimation).

  sup t≥0 max{|ε a (t)|, |ε g (t)|} ≤ ε, sup t≥0 | ḋw (t)| ≤ dw , for some ε > 0 and dw > 0.

  , and using PID control. Algorithms[START_REF] Leishman | Principles of Helicopter Aerodynamics with CD Extra[END_REF],[START_REF] Johnson | Helicopter Theory[END_REF] cannot estimate correctly the z component of the wind because w w (wind velocity along z axis in body frame) is not present in the equations of moments. Parameters of the presented algorithms are tuned by trial and errors (γ a = 40, α a = 0.9, γ g = 60, l = 40, γ g = 40, α = 0.4, l = 20), and kept equals for all the simulations.

Fig. 2 .

 2 Fig. 2. Reference trajectory position in 2D.

Fig. 3 .

 3 Fig. 3. Reference trajectory position in 3D.

Fig. 4 .

 4 Fig. 4. Wind estimation using (9). (-: real; -: estimation).

Fig. 5 .

 5 Fig. 5. Wind estimation using (9) and a reference wind velocity with higher frequency. (-: real; -: estimation).

Fig. 6 .

 6 Fig. 6. Wind estimation using (10). (-: real; -: estimation).

Fig. 7 .

 7 Fig. 7. Wind estimation using (10) and a reference wind velocity with higher frequency. (-: real; -: estimation).

Fig. 8 .

 8 Fig. 8. Wind estimation using (11). (-: real; -: estimation).

Fig. 9 .

 9 Fig. 9. Wind estimation using (11) and a reference wind velocity with higher frequency. (-: real; -: estimation).

Fig. 10 .

 10 Fig. 10. Wind estimation using (12) and (9). (-: real; -: estimation).

The Lebesgue measurable and square integrable matrix function R is PE if there are > 0, ξ > 0 such that t+ t R(s)R(s) T ds ≥ ξ I , where I is an identity square matrix of dimension .

This work was funded by Hauts-de-France region and ONERA.