Walid Oueslati
email: walid.oueslati@agrocampus-ouest.fr

Seraphim Alvanides
email: s.alvanides@gmail.com

Guy Garrod
email: guy.garrod@ncl.ac.uk

Determinants of urban sprawl in European cities

Keywords: étalement urbain, villes européennes, échelle spatiale, modèle de ville monocentrique, fragmentation urbaine urban sprawl, European cities, spatial scale, monocentric city model, urban scattering Urban sprawl, European cities, spatial scale, monocentric city model, urban scattering JEL Classification : H4, Q15, R1, R2, R5

Ce papier étudie les causes de l'étalement urbain dans le contexte européen. Sur la base d'un modèle de ville monocentrique, nous exploitons plusieurs sources de données portant sur 282 aires urbaines et trois périodes de références 1990, 2000 et 2006. Deux indicateurs de l'étalement ont été utilisés : la superficie artificialisée et fragmentation urbaine. Ces deux indicateurs ont été confrontés à un ensemble de variables économiques et géographiques. Afin de contrôler les corrélations possibles entre les variables explicatives et l'hétérogénéité des observations individuelles, nous avons utilisé à la fois une régression à la Hausman Taylor et une régression aléatoire. Bien que les principales conclusions du modèle monocentrique aient été confirmées, son pouvoir explicatif de la fragmentation est relativement faible.

Introduction

Europe has one of the world's highest densities of urban settlement, with over 75% of the population living in urban areas. Despite Europe's relatively low rate of population growth, there continues to be an uneven growth of urban areas across the continent. The size of many European cities is increasing at a much faster rate than their populations. This trend towards reduced population densities began in the early 1970s, most prominantly in medium-sized European cities. There is no sign that this trend is slowing down and as a result, the demand for land around cities is becoming a critical issue in many areas (EEA, 2006).

The phenonenon of increasingly large urban areas taking up a greater proportion of the available land area is often termed urban sprawl. Studies such as Czech et al. (2000), Johnson (2001) and Robinson et al. (2005) have documented the negative environmental impacts that can be associated with urban sprawl, while other studies (e.g. Hasse and Lathrop, 2003) have also documented the increased social costs involved in the provision of public infrastructure as cities increase in size. Such impacts can directly affect the quality of life for people living in European cities. For this reason, it is essential to gain a better understanding of urban sprawl and to gain some insights into what causes it. This paper, therefore, sets out to explore the determinants of urban sprawl in European cities and to compare its findings with those of the existing literature on this topic.

The literature on urban sprawl incorporates the work of economists, geographers and planners.

Surveys of important issues underlying this research can be found in, among others, [START_REF] Anas | Urban Spatial Structure[END_REF], [START_REF] Brueckner | Urban Sprawl: Diagnosis and Remedies[END_REF], [START_REF] Nechyba | Urban Sprawl[END_REF], [START_REF] Couch | Urban Sprawl in Europe: Landscapes. Land-Use Change and Policy[END_REF], and [START_REF] Anas | Anti-sprawl policies in a system of congested cities[END_REF].

Although there is some debate over the precise definition of urban sprawl, a general consensus seems to be emerging that characterises urban sprawl as a multidimensional phenomenon, typified by an unplanned and uneven pattern of urban development that is driven by a multitude of processes and which leads to inefficient utilisation of land resources. Urban sprawl is observed globally, though its characteristics and impacts vary. While early research in this area tended to focus on North American, several recent studies have discussed the accelleration of urban sprawl across Europe (e.g. EEA, 2006;[START_REF] Couch | Urban Sprawl in Europe: Landscapes. Land-Use Change and Policy[END_REF][START_REF] Christiansen | Drivers behind urban sprawl in Europe[END_REF]. Although differences in the nature and pattern of spawl have been observed between Europe and North America, there are also intra-European variations in urban sprawl reflecting the former's greater diversity in geography, land-use policy, economic conditions and urban culture.

Despite the increasing interest in urban sprawl in Europe, relatively few empirical studies have been undertaken at the continental scale. The heterogeneity of the European urban context and limits to the availability of data are probably the main reasons for this lack of interest. That is not to say that there has not been an effort to study the process of urban sprawl in Europe. Various studies, including [START_REF] Batty | Traffic. urban growth and suburban sprawl[END_REF], [START_REF] Phelps | Edge Urban Geographies: Notes from the Margins of Europe's Capital Cities[END_REF], [START_REF] Holden | Three Challenges for the Compact City as a Sustainable Urban Form: Household Consumption of Energy and Transport in Eight Residential Areas in the Greater Oslo Region[END_REF], [START_REF] Couch | Urban Sprawl in Europe: Landscapes. Land-Use Change and Policy[END_REF]), Travisi et al. (2010) and [START_REF] Pirotte | Determinants of urban sprawl in France : An analysis using a hierarchical Bayes approach on panel data[END_REF], focus on urban sprawl within particular regions or cities.

However, to the best of our knowledge, only Pattichani and Zenou (2009) and [START_REF] Arribas-Bel | Multidimensional urban sprawl in Europe: a selforganizing map approach[END_REF] consider a range of cities with the aim of giving a general overview of the phenomenon for Europe as a whole. Pattichani and Zenou (2009) sought to contrast urban patterns in Europe and the United States, using data on a sample of European Cities2 . They noted the lack of a standard definition of the city or metropolitan area in Europe and highlighted the difficulties inherent in attempting a systematic crossnational comparison of European cities owing to the limited availability of data. Despite these limitations, their study provided some evidence on the extent of urban sprawl in cities in the European Union. However, their study does not address the measurement of urbanized areas and instead concentrates on identifying the factors that influence population density. In their study, [START_REF] Arribas-Bel | Multidimensional urban sprawl in Europe: a selforganizing map approach[END_REF] used spatial data derived from the European Corine Land Cover database to consider the issue of urban sprawl from a multidimensional viewpoint. Using six dimensions to define the concept (i.e. connectivity, decentralisation, density, scattering, availability of open space, and land-use mix), they developed various indices of sprawl that were then calculated for a sample of 209 European cities for year 2000. Even though the study offered a new methodological approach using rich data sets to measure urban sprawl, it did not explicitly address the determinants of the phenomenon.

In this paper, we identify and gather existing data that can be used to identify the key determinants of urban sprawl across a large sample of European cities. We base our analysis on the well-known monocentric city model, which identifies population, income, transportation cost and the value of agricultural land as essential drivers of sprawl. In addition to these economic variables, other geographical, socio-cultural and climatic factors, highlighted by the literature, are also considered.

Our study makes two main contributions to the literature on urban sprawl. The first concerns the measurement of sprawl and makes some observations about the data that is available for this purpose.

Two complementary indices of sprawl are used, the first reflecting the change in spatial scale and the second the fragmentation processes that are observed when large urban areas grow. By considering these two indices, we seek to ascertain whether the factors that lead to the expansion of urban areas are also responsible for discontinuities in its spatial configuration. Both indices are calculated using Corine Land Cover data sets for three reference years (1990, 2000 and 2006). Moreover, we use a range of data sources to build a complete and consistent set of explanatory variables for a sample of 282 European cities. To our knowledge this is the first time that a study of this magnitude and scope has been conducted in the European context.

The second important contribution of this study is related to the econometric techniques used in the estimation of the indices. Unlike previous studies, a comprehensive analysis of panel data is conducted to account for unobservable individual heterogeneity and to determine the best estimation method for each index. Several tests were used to choose between alternative panel data estimators. Specifically, a modified random effects-type model (the Hausman-Taylor method) is used, which allows us to control for endogeneity bias while, simultaneously, identifying the estimates for the time-invariant regressor.

The remainder of this paper is structured as follows. Section 2 reviews the theoretical and empirical literature on sprawl and identifies its main determinants. Section 3 presents some methodological issues related to the measurement of sprawl and the associated data requirements, and goes on to discuss some characteristics of urban sprawl in Europe based on our indices. Section 4 presents the empirical model and results from a regression analysis. The final section concludes and makes some observations relevant to urban planning policy.

Determinants of urban sprawl

Theoretical background

The fundamental theory in urban economics relevant to urban expansion is the monocentric city model (Alonso 1994;Mills 1967;Muth 1969;[START_REF] Wheaton | A Comparative Static Analysis of Urban Spatial Structure[END_REF]. Within this model it is assumed that all employment in the city takes place within a single Central Business District (CBD). The pattern of urban development is then shaped by the trade-off between afforable housing further away from the CBD and the associated commuting costs. Thus, to offset higher commuting costs, housing prices decline with distance away from the CBD. In the monocentric city framework, space is represented by a real line with the CBD at its origin. Let be the boundary of the city, denotes urban land rent and is the agricultural land rent. Land being rented to the highest bidder, the city can then be represented by the set:

(1)

where and are the household income and the commuting cost respectively. is a common utility level enjoyed by all households in the metropolitan area. The urban area must be sufficient to provide housing for all households who chosen to settle in the city. To formalize this condition, let be the population density and θ equal the number of radians of land available for housing at each , with 0<θ≤2π (This means that the remaining land will be consumed by topographical irregularities).

Multiplying the density by θ gives the number of people fitting in a narrow ring and integrating out to then yields the n households living in the city. The condition that the urban population n fits inside may then be written :

(2)

The interpretation of the urban equilibrium conditions (1) and ( 2) depends on whether the city is closed or open to migration. In a closed city, where n is fixed, the equilibrium conditions are given by ( 1) and ( 2), determining the utility level (u) in the urban area. In an open-city, where migration in and out is costless, urban residents are neither better of nor worse of than the rest of the population. In this case, the urban utility level is fixed exogenously, and population n becomes endogenous, adjusting to whatever value is consistent with the prevailing utility level.

The influence of these parameters on the city's spatial size can be derived by comparative static analysis of ( 1) and ( 2), as presented by [START_REF] Wheaton | A Comparative Static Analysis of Urban Spatial Structure[END_REF] and [START_REF] Brueckner | The Structure of Urban Equilibria: A Unified Treatment of the Muth-Mills model[END_REF]. In the closed-city model, the exogenous parameters are n, y, t and . Results of the comparative static analysis for and ρ can be expressed as:

(3) (4)

These results highlight the main predictions of the monocentric city model. First an increase in the urban population should increase the distance to the edge of the city and raise the population density since more people must be housed. Second, an increase in income increases housing demand and leads to an extended city with a lower population density. Third, an increase in commuting cost lowers disposable income at all locations, reducing housing demand and leading to a compact city with high population density. Fourth, increasing the agricultural rent raises the opportunity cost of urban land and makes the city smaller and denser.

In the open-city model, where the population (n) is endogenous and the utility level is exogenous the impact of changes in y, t and on x and ρ follow immediately from (1) and (2). The results predict that a high-income city will have a larger and denser area than a low-income city. Moreover, high transportation costs in an open city leads to a smaller and less dense city. The comparative static analysis also predicts that a high agricultural rent leads to a smaller city with a lower population, but at a given distance from the CBD the cities will be identical. More complicated comparative static analyses that includes multiple resident classes have been presented by [START_REF] Miyao | Dynamics and Comparative Statics in the Theory of Residential Location[END_REF] and [START_REF] Hartwick | Comparative Statics of a Residential Economy with Several Classes[END_REF].

The question that arises is whether cities in the real world are best viewed according to the open-or closed-city model. Several empirical studies suggest that the predictions of both models are partly borne out in reality. While the case of a closed city seems to be considered typical of advanced countries, the open city situation is more likely in developing country contexts (Wheaton,1974).

The basic version of the monocentric city model cannot explain scattered development, where parcels of land are left undeveloped while others farther away are built up. One direction that urban economists have followed to account for scattered development is to assign an amenity value to public open space so that individuals may be willing to incur the additional commuting costs associated with locating farther away from the city center in order to have open space near their home (Wu and Plantinga, 2003;[START_REF] Turner | Landscape preferences and patterns of residential development[END_REF][START_REF] Wu | Environmental amenities. urban sprawl. and community characteristics[END_REF][START_REF] Tajibaeva | A discrete-space urban model with environmental amenities[END_REF]Newbern and Berck, 2011). This is mainly due to the fact that the household bid-function is not necessarily monotonous with regards to the distance from the CBD. Following this line of research, [START_REF] Cavailhès | The periurban city: why to live between the suburbs and the countryside[END_REF] and [START_REF] Coisnon | Urban sprawl occurrence under spatially varying agricultural amenities[END_REF] show that the spatial heterogeneity of agricultural amenities can also lead to leapfrog development within a suburban area.

Empirical approaches

Several empirical studies have been undertaken to test the empirical validity of the monocentric city model. [START_REF] Brueckner | The economics of urban sprawl: Theory and evidence on the spatial sizes of cities[END_REF] utilised cross-sectional data from 40 small metropolitan regions in the United States using linear and non-linear Box-Cox regressions. They found that income, population and agricultural rent were statistically significant determinants of urban land area.

However, the coefficients of the variables measuring commuting costs were not significant. They used two proxies to measure the commuting cost: percentage of commuters using public transit and percentage of households owning one or more automobiles.

Using a panel data set for 33 United States metropolitan statistical areas, [START_REF] Mcgrath | More evidence on the spatial scale of cities[END_REF] found similar results to [START_REF] Brueckner | The economics of urban sprawl: Theory and evidence on the spatial sizes of cities[END_REF], except for the coefficient on the commuting costs variable3 , which was statistically significant. Both studies used different proxies for commuting costs.

In order to capture the time-variant unobservable factors, [START_REF] Mcgrath | More evidence on the spatial scale of cities[END_REF] included a time trend variable to control for the fact that the data covered five decades. [START_REF] Song | Property tax and urban sprawl: Theory and implications for US cities[END_REF], estimated a model relating an urbanized area's size to the property tax rate and other control variables such as population, income, agricultural rent, and transportation expenditure. Their study covered 448 urban areas in the US. They found that higher property taxes result in smaller cities. For the other variable, they confirmed the predictions of the monocentric city model, except for the coefficient of the agricultural rent variable which was not significant. They explained this result by arguing that the constructed weighted average of agricultural land rent for the urbanized area did not reflect the actual agricultural land rent at the periphery of the urbanized area.

In addition to the key variables of the monocentric city model, [START_REF] Burchfield | Cause of sprawl: A portrait from space[END_REF] included different environmental and geographical variables to account for differences between cities. Sprawl in their study is measured as the amount of undeveloped land surrounding an average urban dwelling.

This involves capturing the extent to which urban development is scattered across undeveloped land.

They concluded that sprawl in the United States between 1976 and 1992 was positively related to ground water availability, temperate climate, rugged terrain, decentralized employment, early public transport infrastructure, uncertainty about metropolitan growth, and low impact of public service financing on local taxpayers.

In the context of developing countries, [START_REF] Deng | Growth. population and industrialization and urban land expansion in China[END_REF][START_REF] Shanzi | Determinants of Urban Spatial Scale: Chinese Cities in Transition[END_REF] investigate the determinants of the spatial scale of Chinese cities using a consolidated monocentric city model.

Consistent with a number of the key hypotheses generated by that model, their results demonstrate the crucial role that income growth has played in China's urban expansion. Similarly, while [START_REF] Deng | Growth. population and industrialization and urban land expansion in China[END_REF] find that industrialisation and the rise of the service sector both appear to have influenced the growth of urban development, they conclude that the role of these factors was relatively minor compared to the direct effect of economic growth. In addition, [START_REF] Shanzi | Determinants of Urban Spatial Scale: Chinese Cities in Transition[END_REF] illustrate that the urban spatial scale of Chinese cities is better understood by using a model that consolidates features of both closed and open city models. In another paper, [START_REF] Deng | Economic Growth and the Expansion of Urban Land in China[END_REF] estimated the elasticity of economic growth on urban land expansion in China by using spatial statistics. Using these techniques they filter out the effects associated with spatial dependencies that can distort the relationship between GDP growth and the size of the urban core.

All of these studies confirm that the monocentric city model is empirically robust. The economic variables identified by this literature explain the majority of spatial variation in the sizes of cities in different contexts. Moreover, many other geographical variables have also been found to play an important role in explaining urban expansion.

It should also be noted that some models have included variables that measure the ethnic composition of the population (e.g. [START_REF] Selod | City Structure. Job Search and Labour Discrimination: Theory and Policy Implications[END_REF] and crime rates (e.g. Freeman et al., 1996). In the American context, it was established that increases in the percentage of ethnic minority populations within cities and rising city centre crime rates both led to a growth in urban sprawl. The latter has been explained by the desire of many residents to improve their personal security by moving further away the central area of the city. In a European context, Patachini and Zenou (2009) confirm the positive impact of higher crime rates on sprawl, but observe the opposite effect for the impact of ethnic minority populations.

Although there is evidence that urban sprawl is a multidimensional issue that should be measured in a particular way [START_REF] Arribas-Bel | Multidimensional urban sprawl in Europe: a selforganizing map approach[END_REF], each of the previous empirical studies examines only a single dimension of sprawl, i.e. the urbanised area or population density. Chin ( 2002), however, identified four definitions of urban sprawl based upon: urban form; land use; impacts; and density. In definitions based around urban form, sprawl is positioned against the ideal of the compact city, any deviation away from which may be regarded as sprawl. By contrast, the land-use perspective tends to associate sprawl with spatial segregation and with the extensive mono-functional use of land. An alternative definition is based on the impacts of sprawl. Here it is suggested that sprawl can be defined as any development pattern leading to poor accessibility among related land uses (Ewing, 1994). Finally, the density approach considers the relationship between sprawl and the number of people living in a given land area and concentrates on the intensity of land use, i.e. where a decrease in the population density of an urban area can be an indicator of urban sprawl.

Chin (2002) also identifies three main dimensions of urban sprawl, respectively based around: urban spatial scale; population density decline; and scattered urbanisation. These are used to provide the rationale for the indicators used in this study.

Data

Based on the theoretical and empirical literature, we seek to explain differences in urban sprawl in Europe across space and time. Our approach is mainly based on the monocentric city framework and conceptually our empirical model is given by:

Sprawl index = f( income, population, agricultural land value, transportation costs, other socioeconomic, climatic and geographic variables)

We consider the two indices of sprawl that best reflect both the spatial scale of cities and urban morphology. By considering these indices, we examine the extent to which the determinants of urban expansion can explain the fragmentation of urban areas. As independent variables, both indices will be estimated using the same explanatory variables. In this section we specify the sources and extent of the data used in this study before discussing the methodological features of sprawl measurements and the choice of explanatory variables.

Data on urbanisation and sprawl measures

We focus on a sample of European cities obtained by combining various existing data sources. Our starting point was the complete set of 320 cities used in the Urban Audit database 4 . Here, all cities are defined at three scales: the Core city, which encompasses the administrative boundaries of the city; the Large Urban Zone (LUZ), which is an approximation of the functional urban region centred around the Core city; and the Sub-City District, which is a subdivision of the LUZ (Eurostat, 2004). We concentrate on the LUZ, because sprawl is observed around the fringes of cities from where it spreads out across the whole urban region. Therefore, the boundary of each LUZ defines the spatial units upon which this study is based.

Urban Audit provides rather limited information on land-use, with poor coverage for many cities. As an alternative to this data set, we use data on Urban Morphological Zones (UMZ), compiled by the European Environment Agency (EEA), which contains spatial information for three years (1990, 2000 and 2006) 5 . Derived from Corine Land Cover, UMZ data covers the whole EU-27 at a 200m resolution for those urban areas that considered to contribute to urban tissue and function (Guerois et al., 2012). Geospatial data on land-use for each city is obtained by superimposing the LUZ boundaries and the UMZ spatial data, using a Geographical Information System (GIS). To illustrate this process and the nature of the spatial data, maps are provided created for four selected cities.

Figure 1 shows the example of the urban regions of Kielce and Radom (Poland), Eindhoven (Netherlands) and Murcia (Spain), observed for the three reference years (1990, 2000 and 2006). As shown in Figure 1, the external boundary (in grey) representing each LUZ remains stationary through time. However, the fragments of urbanised land represented by the black patches vary in both their size and numbers. The cities in Figure 1 were selected to illustrate different urban dynamics. For Kielce and Radom, both the number of fragments and the artificial area increased significantly in a relatively short period of time (between 2000 and 2006). In Eindhoven the artificial area increased while the number of fragments decreased over the three reference years. Finally, Murcia experienced a major urban development (as evidenced by the increase in artificial area), but the number of fragments remained relatively steady over time, for example compared to Kielce and Radom. 4 The Urban audit database arises from a project coordinated by Eurostat that aims to provide a wide range of indicators of socio-economic and environmental issues. These indicators are measured across four periods: 1989-1993, 1994-1998, 1999-2002, 2003-2006. For futher details, refer to : http://epp.eurostat.ec.europa.eu/portal/page/portal/region_cities/city_urban 5 For further details, refer to : http://eea.europa.eu/ The second index reflects urban morphology, and the spatial patterns of residential land development, in particular, whether residential development is scattered or compact. A simple scattering index is adopted, measuring the degree to which urban development is spread across land in different fragments. We use the following expression:

(5)

where Frag represents the number of urban fragments (i.e. individual patches) within a specific LUZ.

This index reflects how scattered the urban development is across the whole urban region. Sprawl is then identified as a high number of different fragments. We divide here by the artificial area within each LUZ to correct for the size effect, since we expect that larger urbanised areas will have more fragments.

Data on explanatory variables

The Urban audit database provides a wide range of variables, including those used in the monocentric city model (urban area, population, revenue, transport). However, data are missing for different cities The ESPON database provides comprehensive data for each LUZ on Gross Domestic Product (GDP) adjusted for Purchasing Power Standards 8 and total population (POP) 9 . We use GDP per capita (GDPcap) as a proxy for income. All of these variables are defined for the three reference years (1990, 2000 and 2006) for 282 cities across Europe. However, no direct measures of transport costs or agricultural land rents exist for the whole of Europe over the relevant time periods. Similarly, there are no European data sets relating to agricultral land markets or transport costs at the city level. Based on the empirical studies cited earlier, proxies are identified that provide adequate measurements of these variables. First, to account for agricultural land rent, we calculate the ratio of agricultural land value to the area of agricultural land (Agriprox). Data on agricultural added value was available from ESPON, and the relevant data for agricultural land area for each LUZ was calculated from the other available data sets. The rationale for including this proxy is that the ratio could explain different levels of agricultural productivity. Normally, higher agricultural productivity should be capitalised into land rent. Similarly, highway density (Highway) data from the Eurostat regional data set was used as a 7 ESPON is a European research programme, which provides pan-European evidence and knowledge about European territorial structures, trends, perspectives and policy impacts which enables comparisons amongst regions and cities. For further details, see : http://database.espon.eu/ 8 Purchasing Power Standards (PPS) reflect the price ratios between the countries and are at the same time expressed in a single currency. They thus eliminate from gross domestic products both the differences in currency expression and the differences in the prices levels between the countries. 9 Total population represents all residents who have their residence within the LUZ proxy for transport costs. The implicit assumption here, is that investments in highways make traveling faster and more convenient, which reduces the time and the costs of commuting.

Following [START_REF] Burchfield | Cause of sprawl: A portrait from space[END_REF] and [START_REF] Deng | Growth. population and industrialization and urban land expansion in China[END_REF], a set of climatic and environmental data was collected from the Urban Audit. The former include the number of days of rain per year (Rain)

and the average temperature of the warmest months on the year (Temperature). The latter includes the annual average concentration of NO2 (NO2) as a good indicator of air pollution in the cities. A terrain variable, median city centre altitude above sea level (MedAlt), is also included. This variable is a partial indicator for the ruggednes of the LUZ's terrain which may have an impact on the potential for urban growth.

In addition to the economic and geographical variables of interest, various other social and cultural variables are considered. First, data on recorded crime (Crime) from the Urban Audit is used to account for the security situation in the central city. As mentioned previously, Patachini and Zenou (2009) find that higher crime rates increase sprawl. Second, we include the number of cinema seats (Cinema) as a proxy for the cultural attractiveness of the central city. A vibrant central city would be expected to discourage decentralisation, thus reducing sprawl and resulting in more compact urban areas. Despite some of these variables having missing data for certain cities, they were used to estimate the differentiating factors between different LUZs our sample. Table 1 provides a statistical summary of the panel data used in this study.

Table 1 : Statistical summary of explanatory variables

Variables unit /( source) (c) Obs. (a) Missing Obs.

Variations in urban sprawl across Europe

Preliminary analysis of the data shows that on average over the period 1990-2000, the urbanized area increased by 18.4%, while population density fell by 9.07 % and the Scattering index decreased by 9.43% (Table 3). In general, European cities became larger, less dense and more compact over this period. Obviously these averages conceal a wide variation across countries and regions. To observe the evolution of sprawl indices at the regional level, we subdivide the sample into four supra-national regions that are close geographically, as shown in Figure 2. Table 3 shows that the Southern European cities achieve the highest urban growth (32.02 %), but with less fragmentation of urban areas (-4.53%). Despite low growth in urban areas, the Eastern cities are denser and more scattered. The Western European cities experience a high urban growth (15.29%), a small decrease in density (-3.8%) and a decrease in scattering close to the sample mean. Northern European cities show a low urban growth (7.98%) but a sharp decline in density (-11.91%) and scattering (-8.08).

In summary, sprawl shows different trends depending on the index used and the region within which cities are located. Southern cities have the fastest growth of urbanization and the highest decrease in density, but their morphology tends to be more compact. Despite their relatively low levels of urban growth, northern cities experienced a relatively large decline in both density and scattering. From this it can be deduced that rapid urbanisation is not necessarily accompanied by a decrease in density. Also urban areas within cities with declining density are not necessarily more scattered. To illustrate the interdependence between these three indices of urban sprawl and the time-varying explanatory variables (Population and GDP per capita), we divide our sample of LUZ into two groups depending on the growth rate of each index. The first group corresponds to the bottom quartile (relatively slow growth). The second group corresponds to the top quartile (relatively high growth).

Table 2 summarises changes across these groups. Inspection of Table 2 shows that GDP per capita growth is lower for cities where growth is relatively slow, compared to those that were growing at a much faster rate. However, GDP per capita growth is inversely related to density and the growth of scattering. It should also be noted that population growth is lower for cities having a slow growth of urbanisation and density, but is higher for cities with a slow growth of scattering. All changes in urban areas and density are moving in the direction that is predicted by the monocentric city model. Furthermore, the growth of population and GDP per capita are negatively corrolated to the evolution of scattering.

Empirical model and regression results

Estimation strategy

The panel data analysis is adopted to deal with observations from multiple cities over three periods.

Given the variables discused above, the estimating equation of sprawl indices is given by ( 5)

where i and t stand for cities and time periods respectively. The dependant variable represents urban sprawl indices (ArtifArea or Scatt) 10 . We have two time-varying regressors including Population (POP) and GDP per capita (GDPcap). is a vector of time-invariant variables. is specified as random or fixed effects. is the error term.

Eq. ( 5) may be estimated using OLS, pooling observations across cities and over time. However, OLS does not take into account the panel nature of the data and can yield invalid inferences [START_REF] Baltagi | Econometric analysis of panel data[END_REF].

Instead of OLS, the more relevant models are the random effects and the fixed effects models, which are the two estimators most commonly applied to panel data. Unobservable individual heterogeneity is taken into account by both models. The distinction between the two models is whether the individualspecific time-invariant effects are correlated with the regressors or not. The fixed effects model offers consistent estimators but does not allow us to estimate time-invariant variables since it is based on the within operator (it subtracts from the variables their mean over time, so time-invariant variables have a mean equal to their value and the within estimator leads to a null value of the within transformation of these variables). The random-effects model increases the efficiency of estimations but imposes a strong assumption that individual effects are not correlated with explanatory variables.

Furthermore, in order to improve on some of the shortcomings of these two models, the Hausman-Taylor instrumental variable estimator might also be applied [START_REF] Hausman | Panel data and unobservable individual effects[END_REF]). The Hausman-Taylor model combines the fixed and random effects models to deal with the null correlation between the specific effects and the covariates by allowing some variables to be considered as endogenous, i.e. correlated with individual effects. The variance matrix of the composite errors maintains the random structure but the variables suspected of being correlated with the individual effects are instrumented by their within transformation (Wooldrige. 2002).

Our model selection process follows [START_REF] Baltagi | Fixed effects. random effects or Hausman-Taylor? A pretest estimator[END_REF] in using the Hausman test to select between alternative panel data estimators [START_REF] Hausman | Specification tests in econometrics[END_REF]. First, we perform a Hausman test comparing the fixed and random effects estimators. If the null hypothesis of no systematic differences is not rejected, the random effects model is preferred since it yields the most efficient estimator under the assumption of no correlation between the explanatory variables and the errors. However, if the Hausman test between fixed and random effects is rejected, then a second Hausman test is performed comparing the Hausman-Taylor estimator and the fixed effects estimator. Failure to reject this second Hausman test implies the use of the more-efficient Hausman-Taylor estimator, while rejection implies the use of the fixed model 11 .

The Hausman and Taylor method can be represented in its most general form as follows:

(6) 11 For more details see [START_REF] Hausman | Panel data and unobservable individual effects[END_REF], [START_REF] Wooldridge | Econometric Analysis of Cross-Section and Panel Data[END_REF] and [START_REF] Baltagi | Fixed effects. random effects or Hausman-Taylor? A pretest estimator[END_REF].

where and are time-varying variables, whereas and are individual time-invariant regressors. is iid(0. is idd(0. and both are independent of each other. The and are assumed to be exogenous and not correlated with and . while the and are endogenous due to their correction with but not with . Thus, the endogeneity arises from the potential correlation with individual fixed effects. [START_REF] Hausman | Panel data and unobservable individual effects[END_REF] suggest an instrumental variables estimator which premultiplies expression ( 6) by (where is the variance-covariance term of the error component + ) and then performs 2SLS using as instruments [Q.

Results

We performed a Hausman test to discriminate between fixed and random effects approaches. Under the null hypothesis of the Hausman test, the estimators from the random effects model are not systematically different from those from the fixed effects model. If the null hypothesis cannot be rejected (probability of the test higher than 10%), we consider the estimators from the random effects model to be consistent. Otherwise, if the null hypothesis is rejected (probability lower than 10%). only the fixed-effects model is consistent and unbiased. In the case of our model, Hausman test results

show that the random effects hypothesis is rejected in favour of the fixed effect estimator when ArtifArea idex is the dependent variable. However, when the Scatt index is considered as the dependent variable, the random effect regressor is consistent. The results of the Hausman test are reported in the bottom of tables 4 and 512 .

Some qualifications need to be made regarding the use of the Hausman-Taylor estimator, in the case of the ArtifArea index. Although the fixed effects estimator is not an option in our study, since it does not allow the estimation of the coefficients of the time-invariant regressors, it is still useful in order to test the strict exogeneity of the regressors that are used as instruments in the Hausman-Taylor estimation.

Thus, when strict exogeneity for a set of regressors is rejected, others must be considered in the estimation to act as instruments. Once the second Hausman test has identified which regressors are strictly exogenous, they are subsequently used as instruments in the Hausman-Taylor estimation.

After testing several configurations, we retain POP as endogenous, while GDPcap and all timeinvariant variables are exogenous. Only this configuration allowed us to obtain estimates close to the fixed-effects for time-varying variables. In addition, the Hausman test confirms the consistency of the Hausman-Taylor estimator (see the bottom of Table 4).

Table 4 reports the results of a regression for the ArtifArea index obtained using the Hausman-Taylor estimator. We present two configurations of our model. The first includes only the main variables of the monocentric city model, i.e. populatio, GDP per capita, agricultral rent proxy and transportation costs proxy (columns (1) and ( 2)). The second configuration adds all the explanatory variables selected in our study (columns (3) and ( 4)). Furthermore, year dummies are used to control for time-specific changes in the sprawl indices caused by other factors. Notes : Absolute values of t-statistics in parentheses. * significant at 10 per cent; ** significant at 5 percent; *** significant at 1 percent. Hausman FE-RE is the Chi-squared of the Hausman test comparing the fixed effects and random effects estimator. Hausman FE-HT is the Chi-squared of the Hausman test comparing the fixed effects and Hausman-Taylor estimator. p-value is the p-value of this test.

All the coefficients of the main independent variables emerge as significant with the expected signs (columns (1) and ( 2)). Population coefficient is significant and positive, ranging between 0.223 and 0.272. GDP per capita coefficient is also significant with a positive sign, varying between 0.134 and 0.243. The sign on the coefficient of the Agriprox, our proxy for agricultural land values, is negative and is in accordance with the monocentric model prediction. The higher the agricultural land value, the slower the expansion of artificial area. The coefficient on transportation cost proxy (Highway) is positive which is also as expected. When transportation networks are dense, the cost of transportation is low and the artificial area is relatively large. As we add other explanatory variables, the main variables of the monocentric model remain significant with the expected signs. This is still true with or without the dummies for years.

Interstingly, this study highlights the importance of agricultural productivity in limiting the expansion of urban areas. Unlike previous studies, a relatively high coefficient is observed for the agricultral rent proxy, ranging from -0.302 to -0.971. This means that agricultural productivity can be a genuine barrier to urban sprawl in Europe. This reflects the fact that in Europe, agriculture at the urban fringe is often highly intensive and offering relatively high yields and profits.

The coefficient on the variable Crime is significant and positive varying between 0.273 and 0.261. A high crime rate in the central city would promote urban expansion, encouraging households to settle in suburban areas. The climatic variables (Rain and Temperature) have a significant and negative effect, which reflects the tendency towards urban sprawl in temperate climates. The connectivity of cities to the rest of world, measured through the relative importance of the nearest airport (AccessAir), is also significant and positive. Generally, cities with a major airport attract significant economic activity and therefore grow. The cultural attractiveness of the city, approximated by the number of cinema seats, is significant and negative, suggesting that attractive cultural amenities in the centre of the urban area discourage outward sprawl that makes those amenities less accessible. The coefficients of the variables NO2 and MedAlt are not significant, but show the expected signs. Thus, pollution recorded in the central city tends to encourage households to move to suburban areas, promoting sprawl. We also note that, as might be expected, increasing altitude acts as a brake to the expansion of cities.

Returning to the Scatt index, where the Hausman test rejects the fixed effects estimator in favour of the random effects model. Table 5 reports the results of the regression and various statistical tests.

Again, two configurations, with and without year dummies, are considered. Columns (1) and ( 2) includes the main variables of the monocentric city model, while Columns (3) and (4) add the other explanatory variables.

The Breusch-Pagan test (Lagrange-Multiplier test) is used to test for the existence of individual heterogeneity, i.e. testing whether or not the pooled OLS is an appropriate model (Breusch and Pagan, 1980). The OLS hypothesis is unsurprisingly rejected in favour of the random effects estimator for all configurations. Moreover, the Hausman test clearly rejects the fixed effects model in favour of a random effects estimator. Results reported in columns ( 5) to (8) are consistent. The low adjusted R-squared values and nonsignificance of several variables, shows that fragmentation is not necessarily influenced by the same set of variables that determines spatial scale. In all cases, we observe that the coefficients for Population and GDP per capita, are negative and significant. suggesting that larger populations and higher income levels in an urban area are associated with lower rates of fragmentation. Therefore increases in population and per capita income are likely to result in cities that are both larger and more compact. This reflects the strong demand for land in more affluent LUZs and the associated levels of population growth. Such demand may lead to a reduction in the number of urban fragments, as discrete settlements start to expand and merge with each other, or with the central city. Such phenomena can be influenced by urban planning policies, which may be designed to encourage development within these interstitial spaces rather than around the fringes of the LUZ.

Furthermore, the coefficient of the agricultural land value proxy is also negative but not always significant. As might be expected, high agricultural land productiviy should constrain urban fragmentation by limiting the amount of land available for development. The opposite might be expected for less productive land provided that other factors (e.g. topography, drainage) are favourable to development. The results reported here, suggest some level of heterogeneity in the agricultural activities within each LUZ, resulting in complex land use patterns specific to each area. The transport cost proxy also had a negative coefficent, and again this was not always significant. Of the other explanatory variables, only NO2 and MedAlt were significant in the models. The pollution proxy has a negative impact on scattering, reflecting a tendency towards greater fragmentation in cities experiencing higher levels of air pollution. However, the effect of altitude is positive; cities located in urban areas at higher altitudes are likely to be more fragmented, possibly as a result of the local terrain.

Investigating the effects of variables that vary over time

The relative importance of variables that vary over time (Population and GDP per capita) in explaining changes in the sprawl index, can be ranked according to the magnitude of their elasticities.

However, this criteria can be misleading, because the total effect of one factor on another over time, depends on both the magnitude of the elasticity and the change in the variable. Decomposition analysis is used to help understand the effect of these time-varying variables on the dependent variables. This approach accounts for both the size of the marginal effects and the magnitude of the change in the explanatory variables. Table 6 reports the results of the decomposition analysis for both ArtifArea and Scatt index 13 . GDP per capita is the most important factor affecting change in artificial area. Nearly 70% of the growth of urban areas between 1990 and 2006 is explained by increases in income per capita. However, population growth explains only 4.45% of urban area growth. Other explanatory variables explain another 24.9% of variation in the expansion of urban ares. By contrast, 13.3% of the decline in scattering is explained by population growth and 23% by growth in income per capita.

The significance of this decomposition analysis is twofold. First, we show that income growth is by far the most important cause of urban expansion. Second, we find that other factors are more important than changes in income and population in explaining the fragmentation of urban areas within LUZs. (a) The decomposition analysis follows three steps. First. the percentage change of each variable between 1990 and 2000 is calculated (column 1). Then column 1 is multiplied by parameters estimated for each index (columns 2 and 5) to obtain the impact of each time-varying variable on both indices respectively (column 3 and 6).

Finally. the impact of each variable is divided by the percentage change in ArtifArea (18.4%) and Scatt (-9.07%) to obtain the contribution of each variable to changes in ArtifArea (column 4) and Scatt (colimn 7).

Conclusions

Using the framework of the monocentric city model, this paper has empirically investigated the determinants that influence urban sprawl across a large set of European cities. The phenomenon of sprawl was examined both as an increase in the spatial scale of urban areas and as a process of fragmentation, where the urban area is shown to be characterised by a number of discrete parcels of urban settlement scattered around the central city. For each city in our sample, data on these two dimensions of urban sprawl were accurately measured using GIS software. Based on the literature on the causes of urban sprawl, a set of potential explanatory variables was drawn up and appropriate data collected from a range of existing sources (e.g. Eurostat, Urban Audit, ESPON). Where data on potential explanatory variables was not available, a suitable proxy variable was constructed.

Data was obtained for these variables over three reference years. The use of panel data allows unobservable individual heterogeneity to be controlled but also means that a simple OLS estimator is unlikely to be suitable, as this would not account for such unobservable heterogeneity across cities.

Several different estimators were considered and statistical tests were performed to determine the ability of each to account for the specific structure of the panel data for the two aspects of sprawl measured by the study. The Hausman-Taylor estimator was used in the case where sprawl is measured in terms of changes to the urban (artificial) area, but where the dependent variable is an index of fragmentation (i.e. scattering) a random effects estimator was adopted.

Our results are robust and when urban sprawl is approximated by the spatial scale, i.e. changes to the artificial area within the LUZ, they clearly confirm the predictions of the monocentric city model.

Thus, the coefficients of the main explanatory variables in the model are significant, with the expected signs. In addition, the significance of these variables does not change when other explanatory variables are introduced. While increasing income per capita and population growth are clear drivers of the expansion of urban areas, the models reported in this paper highlight the importance of the productivity of adjacent agricultural land as a factor discouraging the outward growth of cities. High productivity maintains or increases land values and makes development on the urban fringe more expensive and therefore less atractive. This economic restriction to the supply of available land may be supported by planning regulations, which limit the availability of land in the urban fringe for development.

In terms of explaining the fragmentation of urban areas, the growth of income and population are far Some limits of our study must be acknowledged, such as our current inability to include variables relating to important political and institutional factors, such as land supply and zoning, that are likely to affect both urban scale and fragmentation. The model also omits information on some specific geographical features therefore limiting our ability to explore the variation in urban sprawl indices more deeply. It is also possible that there may be complex interactions between some environmental factors (such as coastal and mountain amenities) and urban sprawl, that are not accounted for in our model.

Although we have not accounted explicitly for the role of land use policies (mainly due to the lack of data), our study can provide some insights into the design of policies seeking to control sprawl. While environmental and landscape protection are important aims, such policies should not ignore the important economic mechanisms that can drive urban sprawl. This research confirms that in many cities, urban sprawl is associated with increasing wealth. Therefore policies that limit the expansion of urban areas may risk restricting economic growth, as house prices within the LUZ increase, development land becomes scarce and individuals and businesses decide to relocate to cities where there is still room for new development on the periphary.

Policy makers reluctant to place regulatory restrictions on sprawl but who are concerned about the loss of environmental quality or amenity from the development of the urban fringe, may wish to consider other policies that use the market to discourage the outward expansion of cities. Our results suggest that agricultural productivity, and by extension profits, can restrict development by driving up land prices around cities. Therefore the adoption of policies that have a positive impact on farm incomes on the urban periphary can have a direct impact on reducing the likelihood of outward sprawl, while at the same time potentially encouraging the development of non-urban areas within the LUZ boundary, therefore reducing urban fragmentation and making the city more compact. Within such compact cities, achieving low crime rates and maintaining a vibrant cultural life appear to be key considerations when encouraging residents to live close to the city centre rather than in the outer suburbs. These conclusions appear to offer some support for those who argue that planners should implement policies that encourage an urban morphology that maximises the quality of life for residents, while at the same time minimizing the environmental impacts of urban growth.

Figure 1 :

 1 Figure 1: UMZ boundaries (in grey) and Artificial urban areas (in black) for selected cities

Figure 2 :

 2 Figure 2: Study area with Urban Atlas Cities for supra-national regions

  and at different periods, which makes their use unfeasible. Therefore, the Urban Audit data is supplemented using data obtained from the European Observation Network, Territorial Development and Cohesion (ESPON) 7 . When combined, these data sources provide a set of explanatory variables covering a broad sample of European cities for three periods1990, 2000 and 2006.

  X 1 . Z 1 ], where Q is the within transformation matrix with = and the individual mean. Thus we run 2SLS with [ ] as the set of instruments (Baltage et al..2003). If the model is identified in the sense that there are at least as many time-varying exogenous regressors as there are individual timeinvariant endogenous regressors then this Hausman-Taylor estimator is more efficient than the fixed effects estimator. How should the endogenous and exogenous variables be defined? The Hausman-Taylor estimator should produce estimations close to the fixed-effect estimator for timevarying variables. Thus, a Hausman test between the fixed-effects model and the Hausman-Taylor model allows the best specification to be chosen.

  less important. A few other factors, such as altitude or terrain, are shown in the model to increase the tendency towards fragmentation but much of the variation is left unexplained. It is suggested that urban planning policies and land availabity may be particularly influential in determining the level of fragmentation, along with any other factors that reduce the outward growth of cities and therefore encourage in-fill development in the interstices between fragments.

  The sample is consisted of 282 cities observed in1990, 2000 and 2006. (b) Missing data includes cities in the UK and Greece for 1990, and Cyprus, Finland, Greece, Sweden for 2006. (c). Data sources : ER: Eurosatat Regional data; ES: ESPON; U: UMZ and UA:Urban Audit.

	CineSeats	250	32	17.3	0.8	51.9	9.8
	per1000 inhabitants (UA)
	MedAlt	282	0	132.2	2	746	142.5
	m (UA)
	(a)
			(b)	Mean	Min	Max	St. dev.
	ArtifArea	801	45	211.41	9.64	2876.50	293.54
	Km2(UMZ)
	Scatt	801	45	0.472 0.017	1.438	0.275
	fragmenst/Km (UMZ)
	POP (a)	846	0	939.8	26.7	12961	1255.7
	1000 inhabitants (ES)
	GDPcap (a)	846	0	19935.6	1152	149681	12288.2
	Euros (ES)
	Agriprox	240	42	5761.9	36.2	90364.2	10415.2
	Euros per ha (ES and U)
	Highway	282	0	28.6	0.1	289.0	36.4
	km per km2(ER)
	Crime	228	54	79.1	0.9	233.0	45.4
	per 1000 inhabitants (UA)
	Rain	282	0	157.3	32.0	266.0	49.6
	Number of days of rain per year
	(UA)
	Temperature	282	0	21.2	14.6	35.5	4.0
	°C (UA)
	AccessAir	248	34	94.6	26.0	187.0	34.4
	EU=100(U A)
	NO2	210	72	27.6	8.7	64.8	10.3
	Annual average concentration
	(UA)

Table 2 : Growth rates of sprawl indices, population and GDP between 1990 and 2006 according to different supra-national region groups

 2

	Sprawl indices in growth rate	Obs. a	ArtifArea	Scatt	Density
	1990-2006 (percent)
	All cities	237	18.40	-9.07	-9.43
	Southern European cities	65	32.02	-13.98	-14.53
	Western European cities	85	15.29	-9.62	-3.80
	Eastern European cities	77	11.68	-4.36	-11.01
	Northern European cities	10	7.98	-8.08	-11.91

(a)

. We consider only the cities for which we have urbanization data for 1990 and 2006.

Table 3 : The growth rate of sprawl indices between 1990 and 2006 according to the change of population and GDP per capita

 3

	Items	Population Growth (percent)	GDPcap Growth (percent)
	Relatively slow ArtifArea growth a	-0.50	10.26
	Relatively high ArtifArea growth b	70.92	77.11
	Relatively slow density growth a	2.05	77.55
	Relatively high density growth b	8.77	56.06
	Relatively slow scatt growth a	7.44	78.44
	Relatively high scatt growth b	1.20	68.16

(a) Relatively slow growth is associated with the cities that are in the lowest quartile. (b) Relatively high growth is associated with cities that are in the highest quartile.

Table 4 :

 4 Estimation of the determinants of ArtifArea index(Hausman-Taylor)

		Dependent variable : Ln(ArtifArea)
		(1)	(2)	(3)	(4)
	Constant	7.051	8.264	6.9171	6.231
		(4.40)***	(3.05)***	(2.99)**	(2.80)**
	Ln(POP)	0.223	0.272	0.153	0.184
		(5.01)***	(5.46)***	(2.63)**	(3.24)***
	Ln(GDPcap)	0.134	0.243	0.191	0.277
		(4.71)***	(17.30)***	(4.32)***	(15.08)***
	Ln(Agriprox)	-0.655	-0.971	-0.302	-0.302
		(3.45)***	(2.89)**	(6.16)***	(6.37)***
	Ln(Highway)	0.105	0.077	0.059	0.054
		(2.93)**	(2.44)**	(1.79)*	(1.69)*
	Ln(Crime)			0.273	0.261
				(2.46)**	(2.44)**
	Ln(Rain)			-0.586	-0.583
				(2.91)**	(2.99)**
	Ln(Temperature)			-1.306	-1.284
				(2.94)**	(2.98)**
	L(AccessAir)			0.714	0.662
				(3.39)***	(3.27)***
	Ln(NO2)			0.229	0.200
				(1.45)	(1.31)
	Ln(CineSeats)			-0.199	-0.215
				(2.14)**	(2.40)**
	Ln(MedAlt)			-0.04	-0.039
				(1.06)	(0.99)
	Year dummies	Yes	No	Yes	No
	Obs.	677	677	466	466
	Hausman FE-RE	171.91	95.85	93.35	91.08
	(p-value)	(0..000)	(0.000)	(0.000)	(0.000)
	Hausman FE-HT	0.207	0.101	2.128	1.085
	(p-value)	(0.999)	(0.999)	(0.712)	(0.581)

Table 5 :

 5 Estimation of the determinants of Urban sprawl indices (GLS Random effects) LM test is the Chi-squared of the Breusch-Pagan test comparing the pooling and random effects estimators. Hausman FE-RE is the Chi-squared of the Hausman test comparing the fixed effects and random effects estimator. p-value is the p-value of tests.

		Dependent variables : Ln(Scatt)
		(1)	(2)	(3)	(4)
	Constant	3.300	3.640	1.490	2.224
		(6.03)***	(8.97)***	(0.66)	(0.94)
	Ln(POP)	-0.307	-0.309	-0.226	-0.243
		(7.54)***	(7.54)***	(4.80)***	(5.20)***
	Ln(GDPcap)	-0.158	-0.194	-0.031	-0.164
		(3.96)***	(11.02)***	(8.20)***	(8.20)***
	Ln(Agriprox)	-0.093	-0.094	-0.059	-0.059
		(2.96)**	(2.85)**	(2.17)**	(2.17)**
	Ln(Highway)	-0.017	-0.011	-0.056	-0.049
		(1.85)*	(1.58)*	(1.75)*	(1.73)*
	Ln(Crime)			0.149	0.175
				(1.39)	(1.43)
	Ln(Rain)			-0.19	-0.183
				(0.98)	(0.85)
	Ln(Temperature)			0.464	0.486
				(1.08)	(1.02)
	L(AccessAir)			-0.157	-0.103
				(0.78)	(0.48)
	Ln(NO2)			-0.428	-0.398
				(2.79)**	(2.45)**
	Ln(CineSeats)			0.003	0.027
				(0.035)	(0.28)
	Ln(MedAlt)			0.229	0.226
				(5.72)***	(5.30)***
	Year dummies	Yes	No	Yes	No
	Obs.	654	654	433	433
	Adj. R-squard	0.38	0.30	0.38	0.36
	LM test	455.31	453.75	293.89	287.03
	(p-value)	(0.000)	(0.000)	(0.000)	(0.000)
	Hausman FE-RE	1.748	0.518	11.61	1.259
	(p-value)	(0.782)	(0.771)	(0.020)	(0.532)
	Notes : Absolute values of t-statistics in parentheses. * significant at 10 per cent; ** significant at 5 percent;
	*** significant at 1 percent.

Table 6 :

 6 Decomposition analysis of sources of urban sprawl indices(a)

	Variables		Ln(ArtifArea)			Ln(Scatt)
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
		Changes	Estimatied	Impact on	Contribution	Estimatied	Impact on	Contribution
		in variables	parameter	ArtifArea	(percent)	parameter	Scatt	(percent)
		(percent)
	Ln(POP)	5.36	0.153	0.82	4.45	-0.226	-1.21	13.34
	Ln(GDPcap)	68.00	0.191	12.98	70.58	-0.031	-2.10	23.24
	Residual				24.96			63.41
	ArtifArea	18.40			100
	Scatt	-9.07						100

Corresponding author: walid.oueslati@agrocampus-ouest.fr

Pattichani and Zenou (2009) used data provided by the Urban Audit database.

[START_REF] Mcgrath | More evidence on the spatial scale of cities[END_REF] used average annual Consumer Price Index (CPI) for private transportation for each year, rescaled to each region using private transportation cost data.

The supra-national regions are defined as follows : Southern European cities (Cyprus, Portugal, Spain, Italy, Malte, Slovenia), West European cities (Austria, Germany, Belguim, France, Ireland, Luxembourg, Netherlands, UK). Northern European cities (Danmark, Sweden, Finland, Estonia, Latvia, Lithuania) and Eastern European cities(Poland, Romania, Slovakia, Hungary, Czech Republic, Bulgaria).

As there is a strong correlation between ArtiArea and density, we get similar results for both dependent variables (except for the sign of some coefficient, see equations (3) and (4)).

All estimates presented in this paper are obtained using the Plm package of R . For details see[START_REF] Croissant | Panel Data Econometrics in R: The plm Package[END_REF].

Estimated parameters for ArtifArea correspond to those obtained in Table 4 column 3. Estimated parameters for Scatt correspond to those reported in Table 5 column 3. Considering estimated parameters without year dummies does not change the conclusions drawn from the decomposition analysis.


Khairol Amali
email: khairol-amali.ahmad@etu.isae.fr

Bin Ahmad

Mohamed Sahmoudi
email: mohamed.sahmoudi@isae.fr

Christophe Macabiau

Aude Bourdeau

Grégory Moura

Reliable GNSS Positioning in Mixed LOS/NLOS Environments Using a 3D Model

Reliable GNSS positioning is a very challenging task in harsh urban environment. The main source of error is due to non-line-of-sight (NLOS) reception and multipath phenomena. The effect of assuming a direct path in a NLOS propagation environment leads to serious degradation in accuracy. Instead of discarding all measurements which are found to be in NLOS conditions, we propose to properly use these observations to improve the positioning accuracy and integrity in harsh environments. In this paper, we combine the sigma-ε variance model with a mean jump (i.e. NLOS bias) to model the pseudorange (PR) errors. First, we use a 3D model of the environment to detect the NLOS state of reception and to predict the NLOS bias related to the excess delay phenomenon. For reliable positioning, we use a C/No-based variance adjustment for the LOS PRs, and we subtract the bias from the NLOS PRs during the trilateration step of position computation. The performance of the proposed scheme is assessed using real data and compared to a standard Kalman filter without predicted information from the 3D simulator.

positioning. In December 2009, he became an associate professor at the French Institute of Aeronautics and Space (ISAE), Toulouse, France. His research interest includes weak multi-GNSS signals processing, multipath mitigation and multi-sensor fusion.

Aude Bourdeau received an engineer degree in mathematics and numerical modeling from INSA Toulouse in 2010. Since October 2010, she is preparing PhD at the French Institute of Aeronautics and Space (ISAE). Her research interest includes signal processing, GNSS navigation in challenging environment and GNSS signal tracking.

Christophe Macabiau graduated as an electronics engineer in 1992 from the ENAC in Toulouse, France. Since 1994, he has been working on the application of satellite navigation techniques to civil aviation. He received his PhD in 1997 and has been in charge of the signal processing lab of ENAC from 2000 to 2012. He is currently the head of the TELECOM lab of ENAC.

Grégory Moura graduated from the French Institute of Aeronautics and Space (ISAE-SUPAERO, Toulouse, France) in 2004. Since 2005, he has been working as a software engineer in the field of GNSS propagation simulation. He is currently SE-NAV product manager at OKTAL Synthetic Environment.

I. INTRODUCTION

Reliable navigation entails quality of service in terms of accuracy, continuity, availability and also integrity especially for safety and liability critical applications. Even for the majority of comfort applications, while few meters of accuracy is sufficient, the positioning quality cannot be guaranteed in general when traversing a deep urban environment. The reason is that GNSS signal reception in harsh urban settings is notoriously challenging. Buildings and other objects surrounding the receiving antenna may block the direct line-of-sight (LOS) to many satellites, hence reducing the visibility. Often, the remaining signals have poor geometry and therefore degrade the position accuracy.

Apart from being blocked, the signals are also reflected and diffracted from the buildings and other objects. These signals distort measurements and bias the calculated position. If the signal is received only through reflections, the situation is known as non-line-of-sight (NLOS) reception. Multipath interference is a phenomenon when the signal is received through multiple paths. Even though both the NLOS reception and multipath interference are often grouped together as 'multipath', they are actually separate phenomena that cause very different ranging errors. These degraded reception of multipath-contaminated LOS or NLOS are the dominant causes of reduced consumer grade positioning reliability in the urban environment. The effect of NLOS reception on a pseudorange (PR) measurement is associated to the additional path delay, i.e., the difference between the lengths of the path taken by the reflected signal as compared to the direct path, from satellite to the receiver. Hence, this error is always positive and, while typically tens of meters, is potentially unbounded [START_REF] Cosmen-Schortmann | Integrity in urban and road environments and its use in liability critical applications[END_REF]. Whenever high sensitivity receivers are used, the number of received NLOS signals can increase significantly due to the ability of the receivers to acquire much weaker signals.

Several existing techniques of multipath and NLOS mitigation may be categorized as hardware-based, signal processing in receiver and measurements domain [START_REF] Sahmoudi | Multipath mitigation techniques using maximum-likelihood principle[END_REF][START_REF] Groves | Intelligent Urban Positioning using Multi-Constellation GNSS with 3D Mapping and NLOS Signal Detection[END_REF]. The work in [START_REF] Groves | Intelligent Urban Positioning using Multi-Constellation GNSS with 3D Mapping and NLOS Signal Detection[END_REF] elaborates those techniques which make use of dual-polarization antenna, sky-pointing camera, beam forming antenna arrays, ground planes and choke rings. Their main limitations are usually related to cost, size, weights and power consumption. The common approaches to deal with the multipath problem through receiver-based techniques, such as the narrow correlators, do not bring the best improvement in the case of NLOS situations due to the absent of LOS signal. In postreceiver techniques (i.e., prior to the position calculation), one way to solve the NLOS situation problem is to identify and exclude the associated measurements in the navigation algorithm, by using techniques such as consistency-checking which is similar in concept with RAIM. However, this approach is not well adapted to positioning in harsh environments, when only degraded measurements may be available.

Under the poor conditions of satellites visibility, the positioning algorithms have to take into account the fact that the received signal may reach the antenna from a non-direct path with an additional distance. For this purpose, few works exist in the literature on constructive use of NLOS signals [START_REF] Ke | Mobile Location with NLOS Identification and Mitigation Based on Modified Kalman Filtering[END_REF]. One option is to approximate the PR errors model of NLOS measurements so that the PR may still be usable for positioning. The bias can be treated either as a random variable, if a statistical characterization is available or as a deterministic quantity if it is somehow known or predictable.

Mixing the bias with the additive noise, the resulting term is considered as random error and may be modeled by a Gaussian mixture [START_REF] Viandier | GNSS Performance Enhancement in Urban Environment Based on Pseudo-range Error Model[END_REF] since the NLOS measurements noise has been observed to be non-Gaussian, or by adapting the measurements variance [START_REF] Wieser | Improved positioning accuracy with high sensitivity GNSS receivers and SNR aided integrity monitoring of pseudo-range observation[END_REF]. In addition, authors in [START_REF] Spangenberg | Detection of Variance Changes and Mean Value Jumps in Measurement Noise for Multipath Mitigation in Urban Navigation[END_REF] shows that the measurement errors distributions depend on the observation window size. Over a short observation period, PR errors can be modeled by a Gaussian distribution, with time-varying mean and variance.

In order to adopt such measurements error-model based processing, a reliable decision on the reception state of the received signal (i.e. LOS or NLOS status) is needed. In [START_REF] Viandier | GNSS Performance Enhancement in Urban Environment Based on Pseudo-range Error Model[END_REF], authors use the Jump Markov System as probabilistic model with received signal-to-noiseratio (SNR) as indicator of the LOS/NLOS reception state. However, although it has the potential to be used independently of any heavy environment assumptions, SNR estimation is a critical issue in harsh environments, thus the decision based on contaminated information will affect the result. Furthermore, SNR values which are obtained from PRs collected in one area will not be representative any more for another area since the transition between LOS and NLOS depends greatly on the geometrical structure of the location.

In this paper, we analyze the benefit brought in the comfortable situation where a 3D city model can be used to predict the reception state and the bias of each satellite as a potential alternative. We integrate tightly these simulated information in the Kalman filter computing the PVT (position, velocity, time) and we assess the performance of the proposed approach.

II. PREDICTING LOS/NLOS CONDITION VIA 3D MODEL

As 3D city models becoming more accurate and widely available, there are growing interests in their application to predict satellite reception availability. The works of [START_REF] Wang | Multi-Constellation GNSS Performance Evaluation for Urban Canyons Using Large Virtual Reality City Models[END_REF][START_REF] Bradbury | Prediction of Urban GNSS Availability and Signal Degradation Using Virtual Reality City Models[END_REF] used 3D city model to predict GNSS availability considering LOS, diffracted and re-radiated signals. In [START_REF] Obst | Urban multipath detection and mitigation with dynamic 3D maps for reliable land vehicle localization[END_REF], the authors used 3D digital map in order to detect and mitigate multipath in real-time where a ray tracing algorithm is used to check if satellite signals are reflected or blocked. The suspicious PRs are simply excluded from the observation set. 3D model along with camera image were used in [START_REF] Peyret | Non-Line-Of-Sight GNSS signal detection using an on-board 3D model of buildings[END_REF] to filter out the PR measurements which are considered to be NLOS based on the comparison of the actual satellite elevation angle with the critical elevation angle calculated using the 3D model. In [START_REF] Bourdeau | Tight Integration of GNSS and a 3D City Model for Robust Positioning in Urban Canyons[END_REF] the authors use a 3D model to predict the geometric paths of NLOS signals so that they may be used constructively in order to obtain enough information to compute the user's position in harsh urban environment.

In this work, we use SE-NAV software [START_REF]OKTAL[END_REF] to predict the signal reception of GNSS systems such as GPS into 3D virtual scenes of known urban areas. The propagation of signals is based on a ray-tracing algorithm that computes the shadowing and multipath effects. SE-NAV uses geometric optics to calculate the reflected, diffracted and transmitted rays. Based on these multiple rays that reach the receiver, the LOS or NLOS reception state of a satellite is provided. The position of the satellites and the receiver must be known. The satellite positions are calculated based on the ephemeris data whereas the positions along the trajectory are obtained from the receiver.

A. SE-NAV -Deterministic simulator of GNSS reception in constrained environment

SE-NAV simulates the propagation of GNSS signals in constrained environment (urban area, indoor etc.). This software, developed by the company OKTAL Synthetic Environment, embeds a GPU Raytracing kernel to compute the masks and the multipath (reflections, transmission and diffractions) generated by the objects/buildings near the receiver. A Raytracing algorithm consists in finding the intersections between a ray and a defined geometry as fast as possible. SE-NAV uses geometries made of a large number of triangles. For high frequency asymptotic EM simulation, a large number of such intersections has to be computed. A very naïve approach would require N*M ray-triangle intersections, N being the number of triangles and M the number of rays. Except for very simple situations, this cost is prohibitive, hence the need for acceleration methods. Among these methods, the Bounding Volume Hierarchy (BVH), an object-based subdivision structure is chosen. The principle is to build a tree-structure of a set of triangles. Each triangle is stored in a leaf of the tree. Each internal node stores for each of its children the bounding volume of the descendant triangles. A bounding-volume hierarchy is built according to the location of each triangle of the database, trying to minimize the extent and the number of nodes.

Once the structure is built, the intersection between a ray and the scene is done by traversing the tree recursively from the root. A child is processed only if the ray intersects its bounding volume. If the two children are traversed, the process is repeated first on the children closest to the ray origin. If the child is a leaf, the ray is intersected with all triangles contained in the leaf, potentially updating the intersection data. Traversal is stopped as soon as no intersection closer than the current one can be found. This method decreases drastically the ray-scene intersection computation time, computing only O(log(N)*M) intersections instead of N*M for N triangles and M rays. 2) GPU Resources The Raytracing kernel has been developed in CUDA 4.0 language and uses the GPU resources in order to compute masks and multipath in record times (1000 times quicker in optimal configurations). SE-NAV uses GPU to find rays and CPU to filtrate them according to Geometrical Optics rules. SE-NAV runs on NVIDIA Graphics board series 8 or later. The video memory shall be greater than 512 Mo and the compute capability rate greater than 1.1 (atomic operations shall be allowed)

3) Model Outputs SE-NAV uses Geometrical Optics to model reflections and transmissions and Uniform Theory of Diffraction to detect signal's diffractions on the edges of the objects. As SE-NAV uses a deterministic method, the software can calculate and display the geometry of each ray reaching the receiver and then computes the total link budget and errors needed to forecast the local pseudorange. Thanks to the different DOPs provided as an output and also the visibilities of the constellation (LOS, NLOS, and hidden satellite), the user can assess the availability of the navigation system and its performance within a given area.

SE-NAV computes a link budget and provides in output the received power per multipath and per channel. To do so, SE-NAV assesses the main source of attenuations during the propagation of the signal in the environment. The reliability of the computed position depends on the reliability of the PR measurements model. In this work, distribution of the errors on the final navigation solution depends on the quality of the decision taken on the NLOS and LOS situation as obtained from the 3D model. Hence, it is crucial to determine the quality of the SE-NAV LOS/NLOS identification as well as the impact of this decision on the error modeling.

While there have been several works such as in [START_REF] Wang | Multi-Constellation GNSS Performance Evaluation for Urban Canyons Using Large Virtual Reality City Models[END_REF][START_REF] Bradbury | Prediction of Urban GNSS Availability and Signal Degradation Using Virtual Reality City Models[END_REF] where prediction of satellite availability based on 3D model were studied, there has not been many works studying the LOS/NLOS state of reception based on 3D model. One of the approaches in categorising the LOS/NLOS state of reception is to base on the received C/No [START_REF] Viandier | GNSS Performance Enhancement in Urban Environment Based on Pseudo-range Error Model[END_REF]. In this work, we compare the conformity of state reception prediction provided by the 3D model with that one obtained using the C/No value. An example of conformity is when SE-NAV predicts a received signal as a NLOS and the C/No of that signal is below the set threshold (a value between 40 and 30 dB-Hz).

Apart from predicting the reception state, the 3D model is also utilized to predict the NLOS bias statistic, which is to be used for the PR corrections. In this case, how close the predicted bias to the measured NLOS bias will affect the similarity of the final computed position.

III. POSITIONING APPROACH WITH NLOS SIGNALS A. LOS/NLOS Psudoranges measurements model

Over a relatively long observation window, the NLOS measurements error has been observed to have a non-Gaussian distribution and may be approximated by a Gaussian mixture [START_REF] Viandier | GNSS Performance Enhancement in Urban Environment Based on Pseudo-range Error Model[END_REF], as illustrated in Figure 4. However, for a short observation window, the most common approach consist of modeling the pseudorange error as Gaussian distribution with a timevarying mean and variance [START_REF] Spangenberg | Detection of Variance Changes and Mean Value Jumps in Measurement Noise for Multipath Mitigation in Urban Navigation[END_REF] as illustrated in Figure 5.

Here, the error distributions of the same satellite are shown within different 40 seconds windows where it can be seen their change in the mean and variance. In the NLOS case, the presence of only reflected signals introduce a jump on the mean value as a result of the extra distance. In the case of degraded LOS path, an additional variance is introduced as increase of the uncertainty on the direct path. Accordingly, we model separately these effects of the degraded LOS noise and NLOS bias on the PR measurements error.

For the case of multipath degraded LOS reception, implementing the signal-to-noise ratio based variance model, i.e. the SIGMA-ε model, would improve the positioning accuracy in the urban environment [START_REF] Wieser | Improved positioning accuracy with high sensitivity GNSS receivers and SNR aided integrity monitoring of pseudo-range observation[END_REF][START_REF] Kuusniemi | User-Level Reliability and Quality Monitoring in Satellite-Based Personal Navigation[END_REF]. The covariance matrix of the observation can be constructed as where

(1) and is the variance of the observation. The constant and are determined depending on the environment and user equipment. The PR measurement model is commonly expressed as the true distance between the receiver and satellite, plus with several other types of errors.

For each satellite at k th point in time, the pseudorange ρ can be written as, [START_REF] Sahmoudi | Multipath mitigation techniques using maximum-likelihood principle[END_REF] with represents clock offset (satellite or receiver), represents both the ionospheric and tropospheric delays.

is the multipath delay and is the receiver noise. In harsh urban environment, is the major contributor of error and could consist of the mixed LOS/NLOS conditions.

Once the ionospheric, tropospheric, ephemeris and clock errors are compensated, the model is reduced to the following expression,

(3) To further illustrate the LOS/NLOS conditions in the multipath, we may rewrite the equation as [START_REF] Liao | Robust Mobile Location Estimator with NLOS Mitigation using Interacting Multiple Model Algorithm[END_REF] (4)

where:

{ { √
and is the centralized zero mean white Gaussian noise . Then, in the case of NLOS, the affected measurement becomes , [START_REF] Viandier | GNSS Performance Enhancement in Urban Environment Based on Pseudo-range Error Model[END_REF] and √

B. Integration of the 3D-based Bias Estimation in the PVT Kalman Filter

In this paper, the well-established Extended Kalman Filter (EKF) is chosen as the positioning estimator for post-processing the measured PRs. Based on the measurement model in (4), the state equation can be provided by: (6) where is the state vector, is the state transition matrix and is the process noise with zero mean Gaussian distribution.

̇ ̇ (7) where is the position coordinates, ̇ are the velocities, is the clock bias and ̇ is the clock drift.

[ ] (8)
where is the identity matrix and is the sampling period.

(9) where

[ ] (10)
and

[ ] (11)
The clock bias variance and clock drift variance depend on the quality of the receiver, while the acceleration variance depend the motion of the receiver.

Based on the prediction from the 3D model of the LOS/NLOS reception condition of each satellite, the PR measurement and its variance are treated accordingly. If the measured PR is predicted as a LOS signal, its covariance is adapted to the value using equation (1). However, if the measurement is predicted as a NLOS reception, the NLOS bias is predicted from SE-NAV and subtracted from PR measurement and the NLOS variance is included in the covariance as described by equations ( 4) and ( 5).

The observation equation can be formulated as,

where describes the non-linear dependence of the observations on the state. The observation covariance is, (13) where depends on the LOS/NLOS condition of the reception state.

Usually, the values for the bias and variances of NLOS errors are obtained based on the PR error distributions. In this study, the PR error values are initially calculated based on the difference between the measured PRs vis-à-vis the reference PRs which are acquired by computing the distance from the satellite positions and the reference positions. However, such approach would be limited for positioning applications with a fixed and predetermined route.

In an attempt to make the application to be less restrictive, this work further considers the PR errors values generated from the predictions of the 3D-model. The delays of the PR ray-tracings from the 3D-model are treated as the errors of the PR measurements.

C. Data Collection, Equipment and Software

In this work, the measurements were obtained from a trajectory around Toulouse, France (Figure 6). The area represents a deep urban environment with narrow streets and buildings alongside the streets.

The GPS receiver used for the PR measurements is the u-blox LEA-4T receiver while the NovAtel SPAN system is used for the reference trajectory. The measurement was sampled at 1 Hz. All data processing was accomplished using Matlab and SE-NAV In order to implement the SIGMA-ε variance model as in equation ( 1), the values for parameters and have to be determined. This is achieved by fitting the √ to the plot of absolute pseudorange errors vs. C/No. The standard deviation is simply the square root of the variance in equation ( 1) and the absolute pseudorange errors are the magnitude of the pseudorange errors. Figure 7 shows an example of the plot and Table 1 lists all the determined and values per visible satellite during data collection. These C/No values may also be cross referenced with the elevation angle of the satellites since the signals of the lower elevation satellites are more likely to be received as NLOS in the urban environment as compared to those of the higher elevation ones. In Figure 8, satellites with lower than 26° elevation tend to be the satellites with higher conformity with the SE-NAV LOS/NLOS prediction.

C. Results on Position Estimation

As a base of comparison, the error sequence of position estimation with NLOS bias correction is plotted against the error sequence of position estimation using the variance (C/No) only (i.e., without considering LOS/NLOS reception).

Figure 9 (a) shows the comparison in 3D while Figure 9 (b) and 9 (c) are their respective error plots in ENU format.

From Figure 9 (a), it can be seen that the estimation with NLOS bias correction was generally better than the performance of the position estimation using only the variance (C/No) model. After about the 100 th sample it can be said that both estimators When comparing their performance in the ENU format, it is obvious that both of the error patterns of the two position estimation approaches are strongly influenced by their error estimation in the height direction. If the height error is discounted, their performance can be compared in the XY plane (Figure 10) where their performances are much better. The estimation with bias correction was able to reduce several large error values that exist in the estimation with variance (C/No) around the 37 th , 66 th and 87 th samples.

D. Bias Prediction by SE-NAV

Apart from predicting the LOS/NLOS reception, this study also attempts to use the 3D model to predict the NLOS bias. Figure 11 shows the comparison of the measured bias versus the predicted bias for Sat 5. While there is some similarity in the patterns, the values of the bias are quite different between them. Further research could be pursued in order to improve NLOS bias prediction by the 3D model.

Figure 12 is the position error comparison between the positions estimate using measured bias for PR correction against the positions estimate using bias predicted by SE-NAV for the PR correction. The plot is in the XY plane to discount the effect of the estimation error in the height direction. Despite the difference between their bias values as indicated in Figure 11 before, their positioning performances in XY plane are quite similar in general.

V. CONCLUSIONS

This paper proposed the utilization of 3D model in predicting the LOS/NLOS reception state. In addition, the 3D model is also used to predict the NLOS bias of the measurements. These simulated information is used for correction of the PR error according to the LOS or NLOS case and then processed in the PVT computation algorithm. The ability of the 3D model to predict LOS/NLOS was found to be encouraging when compared with other indicators such as C/No and satellite angle of elevation. The ability of the 3D model to predict the NLOS bias was deemed modest and not concluding for the short processed data. Further research and analysis are required to validate the quality of the predictions by

Figure 1 :

 1 Figure 1: Left: Mask sphere showing the masking impact. Right: Example of multipaths reception in an urban area. -3D Red arrows point to the location of the receiver 1) Raytracing and BVH optimizationA Raytracing algorithm consists in finding the intersections between a ray and a defined geometry as fast as possible. SE-NAV uses geometries made of a large number of triangles. For high frequency asymptotic EM simulation, a large number of such intersections has to be computed. A very naïve approach would require N*M ray-triangle intersections, N being the number of triangles and M the number of rays. Except for very simple situations, this cost is prohibitive, hence the need for acceleration methods. Among these methods, the Bounding Volume Hierarchy (BVH), an object-based subdivision structure is chosen. The principle is to build a tree-structure of a set of triangles. Each triangle is stored in a leaf of the tree. Each internal node stores for each of its children the bounding volume of the descendant triangles. A bounding-volume hierarchy is built according to the location of each triangle of the database, trying to minimize the extent and the number of nodes.Once the structure is built, the intersection between a ray and the scene is done by traversing the tree recursively from the root. A child is processed only if the ray intersects its bounding volume. If the two children are traversed, the process is repeated first on the children closest to the ray origin. If the child is a leaf, the ray is intersected with all triangles contained in the leaf, potentially updating the intersection data. Traversal is stopped as soon as no intersection closer than the current one can be found. This method decreases drastically the ray-scene intersection computation time, computing only O(log(N)*M) intersections instead of N*M for N triangles and M rays.

Figure 2 :

 2 Figure 2: Top: Triangles sorting -Bottom: Boundingvolumes hierarchy

Figure 3 :

 3 Figure 3: Link budget SE-NAV takes into account cabling losses, antenna gain (satellite and receiver), free space losses, tropospheric losses and multipath losses. SE-NAV computes the complete field (modulus and phase) and therefore models interferences and fading effects. SE-NAV also provides Signal-To-Noise Ratio and composite power (i.e. integrated power for a given channel). B. Reliability of 3D model for reception state prediction and NLOS bias prediction.

Figure 4 :

 4 Figure 4: NLOS error distribution

Figure 5 :

 5 Figure 5: PR error distributions in short observations periods.

Figure 6 :

 6 Figure 6: Reference trajectory in Toulouse, France. IV. RESULTS A. Estimation of Variance (C/No) Model Parameters

Figure 7 :

 7 Figure 7: C/No variance model. It is noted that during this early stage of research, the number of sampled measurements is rather small. Nevertheless, they are sufficient at the moment. B. LOS/NLOS Prediction by SE-NAV Determination between LOS/NLOS reception is indeed a challenging task. Here, the LOS/NLOS prediction by SE-NAV is compared to the received C/No values of the PR measurements. Threshold

  on more or less of equal performance at the end.

Figure 8 :

 8 Figure 8: Elevation angle per satellite

Figure 9 :

 9 Figure 9: (a) Error of position estimates in 3D, (b) and (c) Error estimates in East, North and Height.

  In term of the bias prediction, other technics of exploiting better the 3D information may be developed.

Figure 10 :Figure 11 :

 1011 Figure 10: Error of position estimates in XY plane

Figure 12 :

 12 Figure 12: Measured NLOS bias against SE-NAV predicted NLOS bias by

Table 2 .Table 1 :

 21 List of parameters for variance (C/No) model obtained by curve fitting with the absolute PR errors

	Sat
	5	164	-1 x 10 4
	8	115	1 x 10 4
	9	127	3336
	10	171	2 x 10 4
	15	136	-1 x 10 4
	17	325	1339
	18	48	2 x 10 4
	24	982	-4649
	26	55	-1 x 10 4
	27	29	-7603
	28	8	1 x 10 4

Table 2 :

 2 Conformity between SE-NAV LOS/NLOS prediction and the C/No values

	Sat	C/No = 40	C/No = 38	C/No = 30
		dB-Hz	dB-Hz	dB-Hz
	5	61 %	45 %	2 %
	8	98 %	95 %	48 %
	9	89 %	87 %	54 %
	10	86 %	82 %	75 %
	15	64 %	47 %	5 %
	17	100 %	100 %	62 %
	18	100 %	100 %	72 %
	24	100 %	100 %	100 %
	26	91 %	80 %	14 %
	27	94 %	93 %	38 %
	28	93 %	83 %	15 %
	Total	89 %	83 %	44 %

ACKNOWLEDGMENT

The authors would like to thank Benoit Priot for providing some assistance for the experimental work.