domain: sde sdu sdu.ocean

text:
Junmei Zhang

Lingxiao Yang
email: yanglingxiao@sdu.edu.cn

Abdelwahid S Mellouki

Jianmin Chen

Xiangfeng Chen

Ying Gao

Pan Jiang

Yanyan Li

Hao Yu

Wenxing Wang

Diurnal concentrations, sources, and cancer risk assessments of PM 2.5 -bound PAHs, NPAHs, and OPAHs in urban, marine and mountain environments

Keywords: PAHs, NPAHs, OPAHs, marine and mountain sites, diurnal variations

come

Introduction

Increasing levels of ambient particulate matter (PM) pollution from rapid urbanization and economic development in China have drawn worldwide attention and have substantial adverse effect on human health [START_REF] Wang | Assessing the effects of anthropogenic aerosols on Pacific storm track using a multiscale global climate model[END_REF]. The International Agency for Research on Cancer (IARC) classified PM from outdoor air pollution as carcinogenic to humans in 2013 [START_REF] Loomis | The carcinogenicity of outdoor air pollution[END_REF]. The toxicity of PM is dependent on the certain chemical components, such as polycyclic Aromatic Hydrocarbons (PAHs) and their derivatives. PAHs are known to be mutagenic, genotoxic, and carcinogenic persistent organic pollutants [START_REF] Abdel-Shafy | A review on polycyclic aromatic hydrocarbons: Source, environmental impact, effect on human health and remediation[END_REF][START_REF] Łuczyński | Oxidative metabolism, mutagenic and carcinogenic properties of some polycyclic aromatic hydrocarbons[END_REF] and are mainly emitted by incomplete combustion of organic materials, such as from coal and biomass burning, vehicle emissions, and industrial processes. NPAHs and OPAHs are nitrated and oxygenated derivatives of PAHs, respectively.

Many NPAHs and OPAHs are more toxic than their parent PAHs due to their direct-acting mutagenicity and carcinogenicity [START_REF] Albinet | Nitrated and oxygenated derivatives of polycyclic aromatic hydrocarbons in the ambient air of two French alpine valleysPart 1: Concentrations, sources and gas/particle partitioning[END_REF][START_REF] Pedersen | Human Cell Mutagens in Respirable Airborne Particles from the Northeastern United States. 2. Quantification of Mutagens and Other Organic Compounds[END_REF], and high molecular weight NPAHs and OPAHs generally present a greater hazard to health due to their carcinogenic behavior. NPAHs and OPAHs are not only directly co-emitted with PAHs but also formed through atmospheric photochemical reactions of parent PAHs with OH, NO x , and O 3 radicals [START_REF] Reisen | Atmospheric reactions influence seasonal PAH and nitro-PAH concentrations in the Los Angeles basin[END_REF][START_REF] Jariyasopit | Heterogeneous reactions of particulate matter-bound PAHs and NPAHs with NO 3 /N 2 O 5 , OH radicals, and O 3 under simulated long-range atmospheric transport conditions: reactivity and mutagenicity[END_REF]. The relative contributions of primary and secondary sources of NPAHs and OPAHs varies greatly between different sampling sites and periods [START_REF] Kojima | Influence of secondary formation on atmospheric occurrences of oxygenated polycyclic aromatic hydrocarbons in airborne particles[END_REF][START_REF] Li | Concentrations and origins of nitro-polycyclic aromatic hydrocarbons and oxy-polycyclic aromatic hydrocarbons in ambient air in urban and rural areas in northern China[END_REF].

To date, surveys of the concentrations, sources, transformation reactions, and long-distance transport of NPAHs and OPAHs have been carried out in 24 h, monthly, and seasonal sampling periods [START_REF] Albinet | Polycyclic aromatic hydrocarbons (PAHs), nitrated PAHs and oxygenated PAHs in ambient air of the Marseilles area (South of France): concentrations and sources[END_REF][START_REF] Albinet | Nitrated and oxygenated derivatives of polycyclic aromatic hydrocarbons in the ambient air of two French alpine valleysPart 1: Concentrations, sources and gas/particle partitioning[END_REF][START_REF] Zhuo | Estimating relative contributions of primary and secondary sources of ambient nitrated and oxygenated polycyclic aromatic hydrocarbons[END_REF][START_REF] Zimmermann | Isomer distributions of molecular weight 247 and 273 nitro-PAHs in ambient samples, NIST diesel SRM, and from radical-initiated chamber reactions[END_REF], which may be influenced by the sampling artifact mainly including oxidative degradation caused by O 3 within the samplers [START_REF] Balducci | Volatilization and oxidative artifacts of PM bound PAHs collected at low volume sampling (1): Laboratory and field evaluation[END_REF][START_REF] Liu | Investigation on sampling artifacts of particle associated PAHs using ozone denuder systems[END_REF]. Possibly due to the limits of current analytical techniques or the low concentration of NPAHs and OPAHs bounded in PM, shorter temporal sampling resolution measurements studies are scarce. As we know, only a few studies have reported 12 h [START_REF] Ringuet | Diurnal/nocturnal concentrations and sources of particulate-bound PAHs, OPAHs and NPAHs at traffic and suburban sites in the region of Paris (France)[END_REF][START_REF] Souza | Diurnal and nocturnal measurements of PAH, nitro-PAH, and oxy-PAH compounds in atmospheric particulate matter of a sugar cane burning region[END_REF], 3 or 4 h [START_REF] Alam | Diurnal variability of polycyclic aromatic compound (PAC) concentrations: Relationship with meteorological conditions and inferred sources[END_REF][START_REF] Tsapakis | Diurnal Cycle of PAHs, Nitro-PAHs, and oxy-PAHs in a High Oxidation Capacity Marine Background Atmosphere[END_REF], and 3.5 h and 11.5 h time intervals during the daytime and nighttime, respectively [START_REF] Reisen | Atmospheric reactions influence seasonal PAH and nitro-PAH concentrations in the Los Angeles basin[END_REF] measurements to analyze the diurnal variation of NPAHs and OPAHs, which were mainly carried out at one or two sampling sites among traffic site, suburban site, rural site, urban site, urban background site and marine background site, and the molecular compositions of NPAHs and OPAHs were different from those in the paper. No research has been found to study the diurnal variation of NPAHs and OPAHs under mountain atmosphere conditions by short time intervals, let alone the detailed comparison among mountain, marine and urban sampling sites. Less resolved measurements are subjected to substantial disadvantages when attempting to understand the physical and chemical processes (e.g., secondary formation) in the atmosphere [START_REF] Ringuet | Diurnal/nocturnal concentrations and sources of particulate-bound PAHs, OPAHs and NPAHs at traffic and suburban sites in the region of Paris (France)[END_REF]. Shorter sampling periods are more conducive to exploring the fate and governing factors of NPAHs and OPAHs [START_REF] Elorduy | Diurnal variation of particle-bound PAHs in an urban area of Spain using TD-GC/MS: Influence of meteorological parameters and emission sources[END_REF].

The concentrations and physicochemical properties of chemicals present in the atmospheric environment vary by sampling regions due to many factors, such as differences in population density, life style, or meteorological conditions [START_REF] Seinfeld | ACE-Asia: Regional climatic and atmospheric chemical effects of Asian dust and pollution[END_REF][START_REF] Wang | Observation of atmospheric aerosols at Mt. Hua and Mt. Tai in central and east China during spring 2009 -Part 2: Impact of dust storm on organic aerosol composition and size distribution[END_REF]. Therefore, the molecular components and levels of PAHs, NPAHs, and OPAHs in PM may show significant difference between urban and background areas. For example, urban areas in China with greater population, dense traffic, and developed industry emit large amount of pollutants and frequently exhibit haze episodes (Wang et al., 2011b), which leads to high levels of PAHs, NPAHs, and OPAHs. Conversely, background areas are typically characterized by sparse population and less emission sources, and may be significantly impacted by long-distance transport, where the PAHs, NPAHs and OPAHs may be relatively aged. The majority of previous studies on PAHs, NPAHs, and OPAHs were conducted in urban areas, such as Beijing [START_REF] Wu | Characterization and source apportionment of particulate PAHs in the roadside environment in Beijing[END_REF]), Shenyang (Miller-Schulze et al., 2010), Xi'an [START_REF] Wei | Occurrence, gas/particle partitioning and carcinogenic risk of polycyclic aromatic hydrocarbons and their oxygen and nitrogen containing derivatives in Xi'an, central China[END_REF], Guangzhou [START_REF] Tan | Characteristics of particulate PAHs during a typical haze episode in Guangzhou, China[END_REF], Southern European cities [START_REF] Alves | Polycyclic aromatic hydrocarbons and their derivatives (nitro-PAHs, oxygenated PAHs, and azaarenes) in PM 2.5 from Southern European cities[END_REF] and Braga, Portugal [START_REF] Alves | Polycyclic aromatic hydrocarbons (PAHs) and their derivatives (oxygenated-PAHs, nitrated-PAHs and azaarenes) in size-fractionated particles emitted in an urban road tunnel[END_REF], where PAHs, NPAHs, and OPAHs are present in high concentrations.

Limited information has been reported on the sources and properties of PAHs, NPAHs, and OPAHs in background areas in China [START_REF] Liu | Diurnal and nocturnal variations of PAHs in the Lhasa atmosphere, Tibetan Plateau: Implication for local sources and the impact of atmospheric degradation processing[END_REF] and other developing countries [START_REF] Lee | Seasonal trend of particulate PAHs at Gosan, a background site in Korea between 2001 and 2002 and major factors affecting their levels[END_REF], which inhibits the characterization and evaluation of regional pollution, transport, and human exposure risk.

With the rapid economic development, China has the largest emissions of PAHs in the world (annual emission 106 Gg in 2007, accounting for 21% of the global total emission) [START_REF] Shen | Global atmospheric emissions of polycyclic aromatic hydrocarbons from 1960 to 2008 and future predictions[END_REF], the North of China as one of the most polluted areas have more intensive emission [START_REF] Xu | Emission of polycyclic aromatic hydrocarbons in China[END_REF]. In order to investigate the diurnal and spatial variations, sources, secondary formation, long-distance transport, and cancer risk assessments of PAHs, NPAHs, and OPAHs, PM 2.5 samples were collected in three distinct locations (an urban, a mountain, and a marine site) in the North of China at 3.5 h and 11.5 h intervals during the daytime and nighttime, respectively.

Methodology

Study sites and sampling

PM 2.5 samples were collected at three sites in the North of China. Jinan (JN), the highly populated capital of Shandong Province, was selected to represent an urban environment. The area is characterized by poor atmospheric diffusion conditions due to the surrounding mountains on three sides and high pollutant emissions [START_REF] Yang | Influence of meteorological conditions and particulate matter on visual range impairment in Jinan, China[END_REF]. The sampling site in JN (36°40'N, 117°03'E; 50 m above sea level; a.s.l.) (Fig. 1) was on the rooftop of a building at the central campus of Shandong University. It is surrounding by school, residential, and commercial areas, with no significant stationary pollution sources. The mountain site was at the summit of Mount Tai (MT, 36°15'N, 117°06'E 1465 m a.s.l.) in the southeast of Shandong Province in the center of Northern China, which represents the mountain background site. It is strongly influenced by the East Asian monsoon circulation and is an ideal location for investigating atmospheric chemistry processing of air pollutants because the measurement site was located above the nighttime planetary boundary layer. The sampling site for MT was located at the Kongjun Hotel, which is far from the frequently visited zones. So the data obtained in the area can be regional representative due to unique geographical location, climatic conditions and negligible anthropogenic emissions. The marine sampling site Tuoji Island (TJ; 38°11'N, 120°44'E; 153 m a.s.l.) was located in the middle of the Bohai Strait at the distance of about 40 km and 70 km from Penglai and Dalian, which is considered as the marine background site. This site had the lowest elevation among the background monitoring stations and is the sole marine atmospheric background station in Northern China. It is an ideal receptor site for investigating continental outflow pollution. Details of the site has been described in greater detail previously [START_REF] Zhang | Identification and quantification of shipping emissions in Bohai Rim[END_REF][START_REF] Zhang | Chemical characteristics and influence of continental outflow on PM 1.0 , PM 2.5 and PM 10 measured at Tuoji island in the Bohai Sea[END_REF][START_REF] Zhang | Atmospheric PAHs, NPAHs, and OPAHs at an urban, mountainous, and marine sites in Northern China: Molecular composition, sources, and ageing[END_REF]. PM 2.5 samples were collected in TJ from June 12 to 17, in JN from June 22 to July 04, and in MT from July 09 to 23, 2015 by a mid-volume suspended particle sampler (Model TH-150 A; Wuhan Tianhong Corporation, China). Quartz filters with 1 μm pore size and 88 mm diameter were used to collect samples (Pall Gelman Inc., USA,). Each filter was baked for 6 h at 600°C before sampling. The flow rate of the samplers was 100 L min -1 , and each sampler was calibrated before and after sampling. The sampling time periods per day was 7:00-10:30 (morning), 11:00-14:30 (day), 15:00-18:30 (evening), and 19:00-6:30 the next day (night) local time. The concentration during daytime period means the average concentration during morning, day and evening periods. Frequent rainfall events occurred during the sampling periods at the mountain and urban sites, so 20 samples (5 samples from the four sampling time periods) were selected for each site. Rainy sampling days were excluded from the analysis.

Sample analysis

Due to short sampling time and low levels of NPAHs and OPAHs at the background sites, the sample filters (three circles with a diameter of 25 mm from every sample filter) obtained in the same time interval at the same sampling site were combined prior to analysis. The combined samples were analyzed by Soxhlet extraction with 150 mL dichloromethane (DCM) for 8 h. The extracted samples were concentrated to about 1 mL by rotary evaporation and then fractionated by silica/alumina gel columns (1 cm internal diameter × 35 cm length). 12 cm alumina (bottom), 12 cm silica (middle), and 1cm anhydrous sodium sulfate (top). The silica and alumina were baked for 6 h at 400 °C by muffle furnace and then activated at 130 °C for 16 h before use. The purification columns were eluted by 20 mL hexane (discarded) and then by 70 mL mixture of hexane and DCM (1:1, v/v) (collected). The elutes were concentrated by a rotary evaporator to about 1 mL at 30±1°C (water bath), added to 10 mL hexane for solvent displacement, and then evaporated again to 1-2 mL by rotary evaporation. The concentrated elutes were further concentrated to 1 mL under high purity nitrogen stream at 30±1 °C. Internal standards

Quality control and data analysis

The air sampler without a denuder for reactive gaseous species removal may result in sampling artifacts due to the degradation of PAHs and their derivatives [START_REF] Menichini | On-filter degradation of particle-bound benzo[a]pyrene by ozone during air sampling: A review of the experimental evidence of an artefact[END_REF]Liu et al., 2014), but the denuder-based sampling system has not yet been used widely in literature. So the sampling artifacts was not considered too much in the paper, which may lead to underestimation of PAHs and their derivatives, especially BaP.

Prior to sample analysis, surrogate standards, including acenaphthene-d 10 , chrysene-d 12 , 2-nitrofluorene-d 9 and 3-nitrofluoranthene-d 9 , were spiked in 50% randomly loaded filters in order to monitor the complete analysis process. which were extracted and measured by GC-MS/MS using the same protocol above mentioned, were analyzed, and the average variation was 11.2%.

Results and discussion

Diurnal variation of PAHs, NPAHs, and OPAHs concentrations

The concentrations of the individual PAHs, NPAHs, and OPAHs during the four sampling periods are presented in Fig. 2 and TableS. 1. The concentration of total PAHs at the urban site ranged from 12.17 to 26.65 ng m -3 , with a mean of 19.45 ng m -3 , which is much higher than those at the marine (between 3.07 and 6.36 ng m -3 , with a mean value of 4.44 ng m -3 ) and mountain sites (ranged from 3.27 to 6.98 ng m -3 , with an average of 5.39 ng m -3 ). A similar diurnal pattern was observed at the marine and urban site with the highest PAHs concentrations during the morning and night sampling periods. This is different from the result that no obviously diurnal pattern for PAHs at Mediterranean marine background site, Finokalia, Island of Crete was found in [START_REF] Tsapakis | Diurnal Cycle of PAHs, Nitro-PAHs, and oxy-PAHs in a High Oxidation Capacity Marine Background Atmosphere[END_REF]. Direct emissions from vehicular traffic during the morning period, and the lower mixing layer height and heavy truck traffic (yellow-labeled vehicles were not banned in the night) during the night period likely contributed to the high PAHs concentrations observed during these times. The concentration is lower during the evening period likely due to the enhanced photochemical activity during the day period. Most individual components showed a similar diurnal pattern at JN and TJ sites, for example FLU, PHE, BaA, CHY, BbF, BkF, BaP, IcdP and BghiP, which all shows a substantial morning and night rush time peak, which is slightly different from the study in PM 10 in Birmingham UK [START_REF] Alam | Diurnal variability of polycyclic aromatic compound (PAC) concentrations: Relationship with meteorological conditions and inferred sources[END_REF] with maximum level during morning period (7:00-11:00),

and is similar to that in East of France at three urban sites (Strasbourg, Besancon and Spicheren) in PM 10 with highest concentrations during morning (04:00-10:00) and evening (16:00-22:00)

times [START_REF] Delhomme | Characterization of particulate polycyclic aromatic hydrocarbons in the east of France urban areas[END_REF]. [START_REF] Han | Comparison of spatial and temporal variations in p-PAH, BC, and p-PAH/BC ratio in six US counties[END_REF] suggested that the peak of PAHs concentration in five US counties (Maricopa, AZ, Anoka, MN, Harris, TX, Pinellas, FL and Jefferson, KY) occurred during morning rush hour times (6:00), and the peak was also observed during nighttime in Sacramento, CA. However, the PAHs measured at the mountain site exhibited higher concentrations during the morning and day periods and the lowest concentrations during the night period. Every individual species showed higher concentration during the daytime (the average concentration during morning, day and evening periods), compared with that during the nighttime at MT. The high elevation of the sampling location (about 1500 m) may have impeded the transport of air masses from ground level to the top of the mountain during the night period, resulting in the lower concentration.

FLT, CHY, BbF, and BghiP were the dominant PAHs at the urban site, accounting for 43.1%-47.3% of total PAHs, in all measurements, which indicates that the major source was likely coal combustion and vehicle emissions. FLU, PHE, FLT, and CHY were dominate in the samples from the marine and mountain sites, accounting for 50.9%-61.5% and 53.3%-61.0%, respectively. The distinctions in the composition profiles at the urban and background sites were likely due to the difference in their emission sources, photochemical degradation rates, and loss due to condensation and deposition during transport [START_REF] Wang | Size-distributions of n-alkanes, PAHs and hopanes and their sources[END_REF]. PAHs with molecular weights between 252-300 (from BbF to COR) accounted for 33.8%-53.4% of the total PAHs with higher percentages found during morning and night periods at the urban site. This was well correlated with the early and late peaks in traffic emissions. Differently, the contribution of high molecular weights (e.g., 5,6,7-ring PAHs) to the total PAHs was significantly lower at the marine (21.3%-30.7%) and mountain (25.2%-32.7%) sites, which may be attributed to loses during transport and a limited number of motor vehicles at the two sites. Previous studies have also reported that high molecular weight PAHs made a large contribution to the total PAHs in Xi'an, an urban site [START_REF] Okuda | Measurement and source identification of polycyclic aromatic hydrocarbons (PAHs) in the aerosol in Xi'an, China, by using automated column chromatography and applying positive matrix factorization (PMF)[END_REF] and in Malaysia, a semi-urban area [START_REF] Khan | Seasonal effect and source apportionment of polycyclic aromatic hydrocarbons in PM 2.5[END_REF].

The concentration of 12 NPAHs at the urban site ranged from 71.41 to 237.6 pg m -3 , with a mean value of 153.7 pg m -3 . This was 3.61 and 3.27 times higher than in samples from the marine (30.78 -62.31 pg m -3 , average: 42.60 pg m -3 ) and mountain (32.50 -68.07 pg m -3 , average: 47.00 pg m -3 ) sites. The total concentration of 12 NPAHs is almost two orders of magnitude lower than the total average concentration of the 17 PAHs measured at the three sites,

The three most abundant NPAHs at the urban site were 9N-ANT, 2+3N-FLT, and 2N-PYR, accounting for 78.2%-88.1% of total NPAHs. Similar molecular composition patterns were found at the background sites, accounting for 81.5%-92.9% at the marine site and 81.2%-91.5%

at the mountain site. The concentrations of total NPAHs at the marine sites were higher during the morning and night periods compared with those during day and evening periods, which was the same as the observed diurnal variation of PAHs. However, the concentration of NPAH varied considerably at the mountain site, with lowest values observed during the night period and highest during the day period. This was dissimilar to the diurnal cycle of total PAHs.

1N-PYR, which solely originates from direct emissions (mainly from diesel powered engines) [START_REF] Nielsen | Reactivity of polycyclic aromatic hydrocarbons toward nitrating species[END_REF], ranged from 5.09 to 2.22 pg m -3 at the urban site, with the greatest concentrations occurring during periods of increased traffic. 7N-BaA exhibited similar diurnal variation as 1N-PYR at the urban site, which is the most abundant compound in diesel fuel particles [START_REF] Finlayson-Pitts | Chemistry of the Upper and Lower Atmosphere[END_REF]. The concentrations of 7N-BaA were found to be the highest at the urban sites, followed by the mountain site (from 0.76 to 1.81 pg m -3 ), and then the marine site (from 1.03 to 1.12 pg m -3 ). This suggests that local emissions were relatively small contributors at the background sites. The average concentration of 2+3N-FLT in the daytime including morning, day and evening time periods at MT site was much higher than that in the nighttime, but the same level was shown during daytime and nighttime at TJ site, and slightly lower level was found in the daytime at JN than that in nighttime. But 2N-PYR had a peak during morning time and was much higher in the daytime compared with that in the nighttime at the three sites. This is may associated with the daytime formation of 2+3N-FLT and 2N-PYR or 3N-FLT from vehicle emissions possibly had a unexpected role, and the influence of NO 3 is also can't be ignored. [START_REF] Alam | Diurnal variability of polycyclic aromatic compound (PAC) concentrations: Relationship with meteorological conditions and inferred sources[END_REF] and [START_REF] Tsapakis | Diurnal Cycle of PAHs, Nitro-PAHs, and oxy-PAHs in a High Oxidation Capacity Marine Background Atmosphere[END_REF] found that the concentrations of 2+3N-FLT and 2N-PYR were higher in daytime than those in nighttime in UK and Mediterranean.

The concentration of the 6 measured OPAHs was higher at the urban site (an average value of 0.85 ng m -3 ) than at the mountain (0.28 ng m -3 ) and at the marine site (0.22 ng m -3 ). This is almost one order of magnitude lower than concurrent concentration of total PAHs. Our measured OPAHs at the urban site were more concentrated than measurements conducted in than Taiyuan (0.71 ng m -3 ), Dezhou (0.03 ng m -3 ), and Yantai (0.08 ng m -3 ) [START_REF] Li | Concentrations and origins of nitro-polycyclic aromatic hydrocarbons and oxy-polycyclic aromatic hydrocarbons in ambient air in urban and rural areas in northern China[END_REF]. The concentrations of OPAHs was highest in the morning and day periods at all three sites, which is distinct from the diurnal variations of PAHs and NPAHs. This difference may be partly due to the fact that OPAHs are mainly emitted from solid fuel burning such as coal, firewood, and crop residues in Northern China and vehicle emissions contributed relatively little to OPAHs compared with to PAHs and NPAHs [START_REF] Li | Concentrations and origins of nitro-polycyclic aromatic hydrocarbons and oxy-polycyclic aromatic hydrocarbons in ambient air in urban and rural areas in northern China[END_REF]. no obviously diurnal pattern of OPAHs difference in the IcdP/(IcdP+BghiP) ratio at the marine (from 0.37 to 0.42, average: 0.39), mountain (from 0.42 to 0.47, average: 0.45), and urban sites was found. The ratio is lower than those obtained in Florence, a urban background site and Athens, a suburban site (all higher than 0.5) in summer [START_REF] Alves | Polycyclic aromatic hydrocarbons and their derivatives (nitro-PAHs, oxygenated PAHs, and azaarenes) in PM 2.5 from Southern European cities[END_REF]. But the ratios of IcdP/(IcdP+BghiP) at the background sites in this paper were comparable with that previously obtained at the Yellow River Delta National Nature Reserve (YRDNNR) in the summer (0.46) [START_REF] Zhu | Airborne particulate polycyclic aromatic hydrocarbon (PAH) pollution in a background site in the North China Plain: concentration, size distribution, toxicity and sources[END_REF]. The average values of the FLT/(FLT+PYR) ratio at the urban (0.68), marine (0.68), and mountain (0.66) sites were similar, and all were higher than 0.5 indicating that coal or biomass combustion was a main source. The ratios were slightly higher than those at Florence and Athens (all higher than 0.5, but lower than 0.6) in summer, but much higher than that in Oporto, a urban site (lower than 0.3) [START_REF] Alves | Polycyclic aromatic hydrocarbons and their derivatives (nitro-PAHs, oxygenated PAHs, and azaarenes) in PM 2.5 from Southern European cities[END_REF]. No obvious diurnal variations of the ratios were observed at the three sites, indicating that the main source did not change during different sampling intervals. In conclusion, the two diagnostic ratios suggest that fossil fuel and biomass combustion were the main sources at the urban and background sites during the summer.

BaA and BaP degrade faster than their corresponding homologues (CHR and BeP), which may significantly influence diagnostic ratios for source and downwind regions [START_REF] Behymer | Photolysis of polycyclic aromatic hydrocarbons adsorbed on fly ash[END_REF][START_REF] Zhang | Source diagnostics of polycyclicaromatic hydrocarbons based on species ratios: a multimedia approach[END_REF]. By leveraging these isomer pairs (BaA/CHR and BaP/BeP) the residence time of particulate PAHs in the atmosphere can be evaluated. The ratios of BaP/BeP and BaA/CHR were plotted in Fig. 3A and 3B during the four sampling periods for the urban, marine, and mountain sites. The average ratios were the highest at the urban site (BaA/CHR: 0.46 and BaP/BeP: 0.46), and the lowest ratios were observed at the marine site ((BaA/CHR: 0.34 and BaP/BeP: 0.27), implying that the air masses collected at the urban site were relatively fresh and most aged at the marine site. The ratios at the marine and mountain sites during the sampling periods were persistently less than 0.4, suggesting that air masses were strongly influenced by photo-degradation and long distance transport likely played an important role [START_REF] Liu | Diurnal and nocturnal variations of PAHs in the Lhasa atmosphere, Tibetan Plateau: Implication for local sources and the impact of atmospheric degradation processing[END_REF]. In the urban area, the ratios of BaA/CHR and BaP/BeP were relatively low in day and evening periods, indicating the influence of photochemical reaction. The diurnal patterns of BaP/BeP in marine area was the same with that in urban area, but was different from that in mountain areas with higher values in day and night periods.

The ratio of 2N-FLT/1N-PYR has been traditionally applied to differentiate primary emission and secondary formation of NPAHs in the atmosphere. 1N-PYR mainly derived from diesel powered engines [START_REF] Nielsen | Reactivity of polycyclic aromatic hydrocarbons toward nitrating species[END_REF], while 2N-FLT is known to be formed by atmospheric photochemical reactions initiated by OH radicals in the daytime and NO 3 radicals in the nighttime, and has never been observed from direct emissions [START_REF] Arey | The formation of nitro-PAH from the gas-phase reactions of fluoranthene and pyrene with the OH radical in the presence of NOx[END_REF]. A ratio of 2N-FLT/1N-PYR higher than 5 indicates secondary formation of NPAHs, while a ratio lower than 5 indicates the primary emissions [START_REF] Albinet | Polycyclic aromatic hydrocarbons (PAHs), nitrated PAHs and oxygenated PAHs in ambient air of the Marseilles area (South of France): concentrations and sources[END_REF][START_REF] Bandowe | PM 2.5 -bound oxygenated PAHs, nitro-PAHs and parent-PAHs from the atmosphere of a Chinese megacity: seasonal variation, sources and cancer risk assessment[END_REF]. In our study, the isomers of 2N-FLT and 3N-FLT were not separated by our GC-column HP-5MS and analytical procedure. However, many previous studies have reported that 2+3N-FLT/1N-PYR can be used in lieu of to replace the original 2N-FLT/1N-PYR ratio due to negligible abundant of 3N-FLT in the air compared with 2N-FLT [START_REF] Bamford | Nitro-polycyclic aromatic hydrocarbon concentrations and sources in urban and suburban atmospheres of the mid-Atlantic region[END_REF]. Fig. 3C presents the ratios of 2+3N-FLT/1N-PYR from the three sites during the four sampling periods. While the average value at the urban site (17.5) was significant lower than that at the marine (27.3) and mountain (25.8) sites, this diagnostic ratio reveals that atmospheric secondary formation of 2N-FLT dominated at the urban and background sites. The ratio values were comparable to that obtained in the North China in the hot season (23.6) [START_REF] Lin | Concentrations and spatial distribution of polycyclic aromatic hydrocarbons (PAHs) and nitrated PAHs (NPAHs) in the atmosphere of North China, and the transformation from PAHs to NPAHs[END_REF], but much lower than that (89.1) observed during the winter in Wanqingsha, the South of China [START_REF] Huang | Phase distribution, sources and risk assessment of PAHs, NPAHs and OPAHs in a rural site of Pearl River Delta region, China[END_REF]. The greatest ratio (24.9) at the urban site was found in the day samples during periods of highest photochemical activity, which is similar to that at the mountain site. The ratio at the marine site was the highest in the morning period.

The ratio of 2N-FLT/2N-PYR has been widely used to explore the occurrence and relative importance of OH vs NO 3 radical initiated oxidation pathways for the formation of NPAHs in the atmosphere [START_REF] Arey | The formation of nitro-PAH from the gas-phase reactions of fluoranthene and pyrene with the OH radical in the presence of NOx[END_REF]. 2N-PYR is formed from PYR reacting with an OH radical in the presence of NO 2 , but is not formed from the reaction with NO 3 radical [START_REF] Arey | The formation of nitro-PAH from the gas-phase reactions of fluoranthene and pyrene with the OH radical in the presence of NOx[END_REF]. A ratio close to 10 indicates the dominance of the OH radical-initiated reaction, while a ratio close to 100 indicates that the NO 3 radical-initiated reactions dominate NPAHs formation [START_REF] Albinet | Polycyclic aromatic hydrocarbons (PAHs), nitrated PAHs and oxygenated PAHs in ambient air of the Marseilles area (South of France): concentrations and sources[END_REF]Wang et al., 2011a). In our study, the average ratios at the urban (4.0), marine (9.6), and mountain sites (8.8) (Fig. 3D) were all less than 10, indicating the domination of day-time OH radical-initiated formation pathways. This is consistent with previously reported values from the summer season in North China (4.5) [START_REF] Lin | Concentrations and spatial distribution of polycyclic aromatic hydrocarbons (PAHs) and nitrated PAHs (NPAHs) in the atmosphere of North China, and the transformation from PAHs to NPAHs[END_REF] and in Beijing (below 10) (Wang et al., 2011a). The highest ratios were observed during the night period at the urban site, which is similar to trends at the two background sites. The ratios at the background sites were significantly higher than the urban site, which may partly be due to the higher concentration of NO in the urban atmosphere because the reaction of NO 3 with NO leads to low level of NO 3 [START_REF] Huang | Phase distribution, sources and risk assessment of PAHs, NPAHs and OPAHs in a rural site of Pearl River Delta region, China[END_REF].

3.3.Evaluation of excess cancer risk

The lifetime excess cancer risk from inhalation (ECR) of PAH and NPAHs mixtures was applied to assess the carcinogenicity of the samples. This method has been recommended by the Office of Environmental Health Hazard Assessment (OEHHA) of the California Environmental Protection Agency (CalEPA) and has been widely utilized in many previous studies [START_REF] Bandowe | PM 2.5 -bound oxygenated PAHs, nitro-PAHs and parent-PAHs from the atmosphere of a Chinese megacity: seasonal variation, sources and cancer risk assessment[END_REF][START_REF] Wei | Occurrence, gas/particle partitioning and carcinogenic risk of polycyclic aromatic hydrocarbons and their oxygen and nitrogen containing derivatives in Xi'an, central China[END_REF][START_REF] Zhu | Airborne particulate polycyclic aromatic hydrocarbon (PAH) pollution in a background site in the North China Plain: concentration, size distribution, toxicity and sources[END_REF]Ramirez et al., 2011;[START_REF] Alves | Polycyclic aromatic hydrocarbons and their derivatives (nitro-PAHs, oxygenated PAHs, and azaarenes) in PM 2.5 from Southern European cities[END_REF]. The carcinogenic risk of each PAH or NPAH compound was estimated based on its BaP equivalent concentration (BaP eqi ), which is calculated by multiplying individual compound concentration (C i ng m -3 ) by the corresponding toxicity equivalency factor (TEF i ) as Eq (1). The TEF values for 15 PAHs and 6 NPAHs were taken from Collins et al., (1998) and [START_REF] Nisbet | Toxic equivalency factors (TEFs) for polycyclic aromatic hydrocarbons (PAHs)[END_REF], who reported the toxic potency of each PAH or NPAH relative to BaP [START_REF] Petry | The use of toxic equivalency factors in assessing occupational and environmental health risk associated with exposure to airborne mixtures of polycyclic aromatic hydrocarbons (PAHs)[END_REF]. The risk of OPAHs was not evaluated due to the lack of available TEF data. Using Eq (1), the toxic equivalency (TEQ) is the sum of target compound BaP eq .

BaP eqi = C i * TEF i and TEQ =∑(C i * TEF i )

ECR was assessed by employing Eq (2), where UR BaP is the unit inhalation cancer risk factor of BaP. The UR BaP is defined as the number of people who will develop cancer from the inhalation of 1 ng/m 3 BaP eq within a lifetime of 70 years. The UR BaP was suggested to be 8.7 × 10 -5 (ng m -3 ) -1 by the World Health Organization (WHO) and 1.1 × 10 -6 (ng m -3 ) -1 by CalEPA (OEHHA, 1994;WHO, 2000). This means that 8.7 or 0.11 cases per 100,000 people with inhalational exposure to 1 ng/m 3 of BaP over a lifetime of 70 years would have cancer risk.

ECR = TEQ* UR BaP

(2)

The mean TEQ at the urban site was 2.49 ng m -3 for the 21 target compounds, which is substantially higher than for the mountain (0.43 ng m -3 ) and marine (0.33 ng m -3 ) sites. The TEQ at the urban site was much lower than the national standard of 10 ng m -3 , but higher than the WHO standard (1 ng m -3 ) [START_REF] Ventafridda | A validation study of the WHO method for cancer pain relief[END_REF]. The value at the urban location was also much lower than what was previously calculated for Beijing, China [START_REF] Jia | Estimated reduction in cancer risk due to PAH exposures if source control measures during the 2008 Beijing Olympics were sustained[END_REF], Xi'an, China [START_REF] Bandowe | PM 2.5 -bound oxygenated PAHs, nitro-PAHs and parent-PAHs from the atmosphere of a Chinese megacity: seasonal variation, sources and cancer risk assessment[END_REF]Zonguldak,Turkey (Akyuz andCabuk, 2008), but higher than those for western and southern European cities [START_REF] Martellini | One year intensive PM 2.5 -bound polycyclic aromatic hydrocarbons monitoring in the area of Tuscany, Italy. Concentrations, source understanding and implications[END_REF][START_REF] Alves | Polycyclic aromatic hydrocarbons and their derivatives (nitro-PAHs, oxygenated PAHs, and azaarenes) in PM 2.5 from Southern European cities[END_REF]. The values at the marine and mountain locations were comparable with that observed in the YRDNNR in summer (0.45 ng m -3 ) [START_REF] Zhu | Airborne particulate polycyclic aromatic hydrocarbon (PAH) pollution in a background site in the North China Plain: concentration, size distribution, toxicity and sources[END_REF]. BbF, BaP, IcdP, and DahA, especially DahA and BaP, contributed significantly to the TEQ value at the three sites. The actual TEQ may be higher in view of the BaP degradation by O 3 during air sampling on the filters [START_REF] Menichini | On-filter degradation of particle-bound benzo[a]pyrene by ozone during air sampling: A review of the experimental evidence of an artefact[END_REF]. The TEQ diurnal patterns at the three sites were consistent with the daily variation of total PAHs concentration, which was highest during morning and night periods at the urban and marine sites and during morning and day periods at mountain site. The contribution of average TEQ of 6 NPAHs to the total TEQ was larger at the background sites (MT, 1.72% and TJ, 1.34%) than that at the urban site (0.41%), which may due to the influence of secondary formation of NPAHs during long-distance transport and high concentration of PAHs at urban site.

The average ECR for 70 years' life span was 2.17 × 10 -4 (WHO method) and 2.74 × 10 -6 (CalEPA method) at the urban site. Hence, inhalation of the 21 measured compounds could result in 217 or 3 cases of cancer per million adult residents in Jinan, respectively. This was higher than estimates for the marine (29 WHO method and 1 CalEPA method cases per million)

and mountain (38 WHO method and 1 CalEPA method cases per million) sites. The lower ECR at background sites is likely attributable to less direct source emissions, lower population, and favorable diffusion conditions. The acceptable or negligible threshold of ECR using WHO method based on American Environmental Protection Agency is 10 -6 , so the lifetime excess cancer risk should be paid attention for healthy protection in the future in the Chinese cities.

Summary

In this study, PAHs, NPAHs, and OPAHs were investigated during the summer in the Northern China at an urban site and two background sites at 3.5 h and 11.5 h sampling intervals.

The average concentrations of PAHs, NPAHs, and OPAHs at the urban site were 19.45 ng m -3 , 153.7 pg m -3 , and 0.85 ng m -3 , respectively, which were 3.61-4.38 and 3.05-3.61 times higher than those at marine and mountain sites, respectively. The concentrations of PAHs and NPAHs were greatest during morning and night periods at the urban and marine sites and during morning and day periods at the mountain site. The concentration of OPAHs was highest during the morning and day periods at all the three sites. The diurnal variations of high molecular weight PAHs (e.g., 1N-PRY and 7N-BaA) at the urban site was closely linked to vehicle emissions.

On the basis of diagnostic ratios, the main sources of PAHs were found to be fossil fuel and biomass combustion. The air masses at the background sites, especially at the marine site, were more aged compared with those at the urban site. The atmospheric reactions were most efficient at the marine site, followed by the mountain site. The main reaction pathway was OH-initiated radical reactions at the urban and background sites. The contribution of secondary formation to the total PAHs was largest during the day period at the urban and mountain sites and during morning period at the marine site.

The mean toxicity equivalency factor at the urban site was higher than those at marine and mountain sites and greater than the guidelines suggested by the World Health Organization. The average excess cancer risk from inhalation (ECR) for 70 years' life span was highest at the urban site.

  -d 9 , 1-nitropyrene-d 9 , 6-nitrochrysene-d 11 and anthraquinone-d 8 ) were spiked prior to the sample injection into the gas chromatography -mass spectrometer (GC-MS). All used glassware devices were soaked in potassium dichromate lotion, rinsed by purified water and ultrapure water, and then baked at 100 °C until dry.A gas chromatograph coupled (GC, Agilent 7890A) with a triple quadrupole mass spectrometer (MS/MS, Agilent 7000) with a 5% phenyl substituted methylpolysiloxane GC column (HP-5MS, length: 30 m, diameter: 0.25 mm, film thickness: 0.25 μm, Agilent, USA) was used to analyze PAHs. The system was set to use electron impact ionization (EI) in selected ion monitoring (SIM) mode. The oven temperature program was held at 60°C for 1 min, gradually increased to 150 °C at the rate of 40 °C/min where it was held for 5min, and then increased to 300 °C at 4°C/min and held for 15min. 17 different PAHs were detected based on retention time and qualitative and quantitative ions of standard PAHs. The NPAHs and OPAHs was also measured by GC-MS/MS with HP-5MS column using negative chemical ionization (NCI) in SIM mode. The GC oven temperature program for NPAHs and OPAHs was 60 °C for 1 min, ramped at 15 °C /min to 150 °C, to 300 °C at a rate of 5 °C, then held for 15 min. The targeted analytes included acenaphthene (ACE), acenaphthylene (ACY), fluorene (FLU), phenanthrene (PHE), anthracene (ANT), fluoranthene (FLT), pyrene (PYR), benzo(a)anthracene (BaA), chrysene (CHY), benzo(b)fluoranthene (BbF), benzo(k)fluoranthene (BkF), benzo(a)pyrene (BaP), benzo(e)pyrene (BeP), indeno(1,2,3-cd)pyrene (IcdP), dibenzo(a,h)anthracene (DahA), benzo(g,h,i)perylene (BghiP), coronene (COR), 5-nitroacenaphthene (5N-ACE), 2-nitrofluorene (2N-FLU), 9-nitroanthracene (9N-ANT), 9-nitrophenanthrene (9N-PHE), 3-nitrophenanthrene (3N-PHE), 2-nitroanthracene (2N-ANT), 2+3-nitrofluoranthene (2+3N-FLT), 1-nitropyrene (1N-PYR), 2-nitropyrene (2N-PYR), 7-nitrobenzanthracene (7N-BaA), 6-nitrochrysene (6N-CHR), 6-nitrobenz(a)pyrene (6N-BaP), 9-fluorenone (9FO), anthraquinone (ATQ), phenanthrene-9-aldehyde (PHE-9-ALD), benzanthrone (BZO), benzaanthracene-7,12-dione (BaAQ).

Fig. 1 .

 1 Fig. 1. The three sampling locations (Wang et al., 2009). The squares indicate background sampling sites.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Diurnal variation (Mor: morning, Eve: evening, Nig: night) and average (Ave) concentration of PAHs, NPAHs, and OPAHs at the urban (JN), marine (TJ) and mountain (MT) locations.

Fig. 4 .

 4 Fig. 4. TEQ of particulate PAHs and NPAHs during the four different sampling periods at the three locations.

Table 1

 1 Diagnostic ratios of particulate PAHs at the three locations during the four sampling periods.

		FLT/(FLT+PYR)	IcdP/(IcdP+BghiP)
	JN
	Morning	0.68	0.41
	Day	0.70	0.43
	Evening	0.70	0.41
	Night	0.63	0.40
	TJ
	Morning	0.66	0.39
	Day	0.67	0.42
	Evening	0.73	0.39
	Night	0.66	0.37
	MT
	Morning	0.65	0.47
	Day	0.67	0.46
	Evening	0.69	0.42
	Night	0.63	0.45
	Reference source
	emissions
		>0.5 coal/ biomass combustion	>0.5 coal/ biomass combustion
		<0.5 and >0.4 petroleum	<0.5 and >0.2 petroleum
		combustion	combustion
		<0.2 petroleum source	<0.2 petroleum source

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 21577079 and 21307074). This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 690958.

was found at Finokalia, Island of Crete without local emissions [START_REF] Tsapakis | Diurnal Cycle of PAHs, Nitro-PAHs, and oxy-PAHs in a High Oxidation Capacity Marine Background Atmosphere[END_REF].

The six OPAHs components all presented higher levels in the daytime than those in the nighttime in marine and mountain background sites. The most abundant OPAH was 9FO, followed by ATQ in the three sites, accounting for 80.9%-96.1% of total OPAHs.

Source diagnostics

Diagnostic ratios are frequently used to identify the sources of PAHs because the distributions of the homologues are strongly related with the formation mechanisms of organic species with similar characteristics [START_REF] Kavouras | Source Apportionment of Urban Particulate Aliphatic and Polynuclear Aromatic Hydrocarbons (PAHs) Using Multivariate Methods[END_REF]. Diagnostic tool should be used with caution because some ratios are variable in the atmosphere due to the different degradation ratios of some PAH species [START_REF] Ding | Atmospheric polycyclic aromatic hydrocarbons observed over the North Pacific Ocean and the Arctic area: Spatial distribution and source identification[END_REF].

FLT, PYR, IcdP and BghiP have comparable degradation ratios [START_REF] Behymer | Photolysis of polycyclic aromatic hydrocarbons adsorbed on fly ash[END_REF], so the ratios of FLT/(FLT+PYR) and IcdP/(IcdP+BghiP) can reveal original compositional information during transportation and ensure the accuracy of source evaluation at receptor sites.

A FLT/(FLT+PYR) ratio higher than 0.5 indicates coal/biomass burning and between 0.4 and 0.5 indicates petroleum combustion [START_REF] Pio | Identification, abundance and origin of atmospheric organic particulate matter in a Portuguese rural area[END_REF][START_REF] Yunker | PAHs in the Fraser River basin: a critical appraisal PAH ratios as indicators of PAH source and composition[END_REF], as shown in Table 1.

A ratio of IcdP/(IcdP+BghiP) higher than 0.5 indicates coal/ biomass combustion, and a ratio lower than 0.2 is characteristic of petroleum source. A IcdP/(IcdP+BghiP) ratio between 0.2 and 0.5 (or 0.18-0.40) indicates petroleum combustion [START_REF] Pio | Identification, abundance and origin of atmospheric organic particulate matter in a Portuguese rural area[END_REF][START_REF] Yunker | PAHs in the Fraser River basin: a critical appraisal PAH ratios as indicators of PAH source and composition[END_REF]. The IcdP/(IcdP+BghiP) ratios ranged from 0.40 to 0.43, with an average value of 0.41 at the urban site (Table 1), implying that petroleum combustion was a strong contributor. Comparable values were also observed in other Chinese cities, such as Shanghai [START_REF] Feng | Characteristics of organic matter in PM2.5 in Shanghai[END_REF], Beijing [START_REF] Okuda | Polycyclic aromatic hydrocarbons (PAHs) in the aerosol in Beijing, China, measured by aminopropylsilane chemically-bonded stationary-phase column chromatography and HPLC/fluorescence detection[END_REF], Qingdao [START_REF] Guo | Seasonal variation of solvent extractable organic compounds in the aerosols in Qingdao, China[END_REF], and Nanjing [START_REF] Wang | Aliphatic and polycyclic aromatic hydrocarbons of atmospheric aerosols in five locations of Nanjing urban area, China[END_REF]. A negligible


Gilles Chardon

François Ollivier

José Picheral

Localization of sparse and coherent sources by Orthogonal Least Squares

This paper proposes an efficient method for the joint localization of sources and estimation of their mutual correlations. In practice, such an estimation is useful to study correlated sources existing for instance in presence of reverberations or for spatially distributed sources, but is confronted to the challenge of computational complexity due to a large number of required estimates. The proposed method is named CMF-OLS (for Covariance Matrix Fitting by Orthogonal Least Squares). It is based on a greedy approach exploiting the OLS algorithm in order to reduce the computational complexity of the estimation. Compared to existing methods for sources correlation matrix estimation, its lower computational complexity allows to deal with large dimensions and to explore large regions of interest. As shown by numerical results, it is more accurate and does not require the tuning of any regularization parameter. Experiments involving reverberations show the ability of the method to locate and identify physical and mirror sources as well.

I. INTRODUCTION

Source imaging methods have been developed for decades in order to locate acoustic sources and to estimate their power. Many works have proposed to overcome the well-known limitations of the delay and sum (DAS) beamforming technique, based on parametric approaches(?), or non-parametric approaches based on Bayesian estimation (??), or based on sparsity and compressed sensing (???).

This paper addresses the inverse problem of estimating the spatial covariance matrix of acoustic sources. This estimate not only quantifies the power of each point on the source grid but also estimates the correlation between each of these points.

In practice, sources correlation estimation can be useful in various scenarios: in a reverberant space, mirror sources will be correlated with the corresponding physical source. Estimating the coherence between sources will allow to pair physical sources with their reflections. Another typical case of correlated sources are extended sources whose distributions radiate correlated signals.

Localizing coherent sources poses an important challenge to subspace based localization methods such as MUSIC or ESPRIT. In this case the covariance matrix of the sources, and thus of the data, is rank-deficient, limiting the performances of these methods. For particular array configurations, this issue can be mitigated by the use of spatial smoothing, at the price of reduced array aperture (?). Methods based on sparse approximations a) gilles.chardon@centralesupelec.fr or Bayesian estimation can deal with correlated sources, using the complete measurements (??).

In the cases where correlations are not seen as a nuisance, but as parameters to be estimated, an additional challenge is the computational complexity of the estimation. Compared to a standard localization problem, where the space is usually discretized on a grid of L points, the estimation of the correlations between sources involves the estimation of a covariance matrix of size L × L. The computational cost increases dramatically with the number of points requiring suitable algorithms. Numerical methods with a complexity larger than linear in the size of the grid will be limited to small grid discretizations.

Beyond the coarse estimation provided by the delay and sum beamformer extended to covariance estimation (called DAS-C in the remainder of the article), few methods have been proposed in the literature to solve the covariance source estimation problem (a short review is given in section II). Based on convex optimization methods, their complexity is in the order of O(L 6 ) (?), or O(L 3 L 3 h ) where L h is an upper bound on the number of independent sources (?). Such computational complexities will limit the application of these methods to coarse discretizations of the physical space.

In this paper, we propose a method named CMF-OLS (for Covariance Matrix Fitting by Orthogonal Least Squares) to solve the covariance matching problem with a greedy approach. It is based on the Orthogonal Least Squares (OLS) algorithm (?), similar to the well-known Orthogonal Matching Pursuit algorithm (?), but better suited to the problem of covariance matrix estimation. Indeed, it can take full advantage of the matrix structure of the estimation problem. Moreover, OLS is expected to exhibit better behavior than OMP in cases where the dictionary is strongly coherent (in the sense that columns of the dictionary are near linearly dependent) (?).

The main advantage of this approach compared to existing methods is that its time complexity is linear with respect to the size of the discretization L, allowing fine grid discretizations and short running times. Moreover, in contrary to methods based on regularization, the algorithm takes only one parameter, the number of sources, that can be estimated by inspecting the convergence of the algorithm. A post-processing can then be applied to the estimated covariance matrix to extract the spatial shapes of each coherent source.

The article is structured as follows: Section ?? introduces the problem and notations. Correlated source localization methods and greedy sparse approximations are briefly reviewed in section ??. Section ?? and ?? introduce the CMF-OLS algorithm for covariance matrix estimation, and the post-processing respectively.

Simulation results presented in Section ?? performed in a 1D scenario show that the proposed method is more accurate and faster than the methods of the literature such as DAS-C or MACS. In addition, Section ?? introduces experiments that have been conducted in an anechoic room in various settings : uncorrelated sources, correlated sources, and reflections. Results confirm that positions and correlations of the sources can be accurately estimated in large-scale (in fact, realistic) scenarios where other methods are too demanding in time or memory size. Section ?? concludes the paper.

II. PROBLEM FORMULATION

Assume that N microphones provides the N ×1 measured signals x(t i ) and let be I the number of available snapshots.

The possible positions of the source are described by the parameter Θ ∈ R. The region R can be, depending on the cases, a line, a surface, or a volume, and is discretized on a grid of L points defined by their position {Θ } =1,...,L .

Assuming that the discretization of R is fine enough, sources can be considered located at a point of the grid. For narrow band sources, the measured signals can be modeled by:

x(t i ) = L =1 a(Θ )s (t i ) + n(t i ), (1)
where a l = a(Θ ) is the N ×1 steering vector for a source at the position Θ , s (t i ) is the source amplitude at the instant t i and n(t i ) is an additive centered noise assumed to be spatially white of variance σ 2 . The coefficients of the steering vector a(Θ ) are the values of the Green function of the propagation medium between the position parametrized by Θ l and a microphone at position r n . In an homogeneous medium and assuming free propagation, the Green function is G(r 1 , r 2 ) = exp(-j r 1 -r 2 )/ r 1r 2 .

Let the N × L matrix A = [a(Θ 1 ), . . . , a(Θ L )] be formed by the L steering vectors associated to the L points of the source grid, the signal model can be rewritten as

x(t i ) = As(t i ) + (t i ), (2)
where the L×1 vector s(t i ) = [s 1 (t i ), . . . , s L (t i )] contains the amplitudes of the sources.

Under the hypothesis of independence between the source signals and the noise, the covariance matrix can be expressed as:

Γ = E{x(t i )x(t i ) H } = ACA H + σ 2 I, (3)
where C = E{s(t i )s(t i ) H } is the L × L source covariance matrix (or spatial covariance matrix). Estimation of C is the key point of the work presented in this paper since its diagonal describes the power of the sources, and its offdiagonal coefficients the covariance between each source. In practice, the covariance matrix Γ is estimated by the sample covariance matrix using the set of I measurements:

G = 1 I I i=1 x(t i )x(t i ) H ≈ Γ (4)
The objective of our method will be to estimate the positions, powers, and mutual covariances of the sources from the matrix G.

III. STATE OF THE ART

A. Correlated sources estimation

A first estimation of the source covariance matrix is given by the delay-and-sum beamformer for covariance estimation (DAS-C):

C DAS-C = 1 L 2 A H GA. (5)
The diagonal of C DAS-C is the output of the standard DAS beamformer, and has the same limitations, i.e. wide main lobes at low frequencies and presence of sidelobes.

In the case of punctual sources, the sparsity of the covariance matrix can be promoted by using an componentwise 1 regularization term, as in the Sparse Spectrum Fitting method (??). The covariance matrix is estimated as the solution of the following optimization problem:

C SpSF = argmin C G -ACA H 2 F + λ C 1 s.t. C ≥ 0. (6)
Alternatively, the CMF-C method (?) jointly estimates the covariance matrix and the noise level assuming that the rank of the covariance matrix is low. The estimate is found as the solution of an optimization algorithm fitting the covariance matrix to the data while bounding its trace, equal to the 1 norm of its eigenvalues, as a convex surrogate for limiting its rank:

C CM F -C = argmin C,σ G -ACA H -σ 2 I 2 F , s.t. C ≥ 0, tr(C) ≤ λ, σ 2 ≥ 0. (7)
Sparsity and low-rankedness can be combined using two regularization terms (?), yielding the following penalized optimization problem:

C SP LR = argmin C G -ACA H 2 F +λ 1 C 1 +λ 2 tr(C), s.t. C ≥ 0. (8)
These three optimisation problems are convex, and can be solved using off-the-shelf toolboxes such as CVX (??), or more specialized algorithms (e.g. Simultaneous Directions of Multipliers Method). However, the computational complexity of solving these algorithms prevents their application for large-scale problems, where the discretization grid has e.g. more than ≈ 1000 elements. Estimation of the covariance matrix by Sparse Spectrum Fitting and CMF-C with standard convex optimization (O(L 6 )) methods, is therefore limited to low dimensional problems, i.e. coarse discretization of the physical space.

Yardibi et al. proposed MACS (Mapping of Acoustic Correlated Sources) (?) with reduced complexity by assuming that the rank of the covariance matrix C to be estimated is at most L h , an upper bound for the number of independent sources. The covariance matrix is factorized as C = C CH , where C has dimension L×L h . By adding an additional sparsity constraint on the coefficients of C, the following non-convex problem is formulated:

argmin C,Q ḠQ H -AC 2 F s.t. C 1 ≤ β, Q H Q = I (9)
where Ḡ is the matrix square root of a low-rank approximation of G. The authors propose an algorithm alternating between 1 constrained least-squares minimization and updates of Q, which is not guaranteed to converge towards a global minimum. Improved MACS (IMACS) (?) was recently proposed, by updating the bound β between the iterations.

The complexity of the estimation is reduced to O(L 3 L 3 h ), which makes estimation problems of moderate dimensions tractable. However, the complexity remains too high for large scale or real time problems, as running time of the order of the minute are announced for problems of moderate dimensions (L < 1000).

B. Greedy source localization

An alternative to regularization based sparse estimation methods are greedy algorithms. They are known to be computationally less expensive than optimization based method, at the price of reduced performances. In particular, Orthogonal Matching Pursuit (OMP) (?) has been used for several acoustical inverse problems, such as Nearfield Acoustical Holography (?), source localization (?), or DAMAS-like deconvolution of beamformer output (?).

In general, OMP aims at estimating a sparse solution of the undetermined linear system y = Dx, where y are the observations, D a known dictionary with normalized columns d i (called atoms), and x the sparse coefficients to be estimated. OMP works as follows:

1. Initialization: k = 1, residual r 0 = y, set of identi- fied indices S 0 = ∅ 2.
Computation of the correlations of the residual with the dictionary, ρ

k,l = |d H l r k-1 | 2 3. An atom (i.e. a nonzero coefficient in x) is identified by the maximal correlation l = argmax 1≤l≤L ρ k,l 4. Its index is added to the set S k+1 = S k ∪ {l }
5. The residual is updated by projecting y on the orthogonal of the space spanned by identified atoms:

r k = y -Π S k (y)
6. k = k + 1 and go to step 2 until a stopping criterion is met (number of iterations, norm of the residual, etc.).

Under certain conditions on the dictionary D and the number of non-zero coefficients in x, OMP is guaranteed to recover x exactly. Variants of OMP can deal with structured sparsity, e.g. block sparsity (?), where the support of x has a specific structure. In particular, block sparsity can be applied to joint localization and characterization of anisotropic sources (?) or extended sources (??).

IV. ORTHOGONAL LEAST SQUARES FOR CORRELATED SOURCES LOCALIZATION

In this section, a greedy method is proposed for correlated sources localization, using a slightly different algorithm, Orthogonal Least Squares. The use of this algorithm is justified by its better behavior in presence of correlated dictionaries (?), which is the case in source localization, when the possible source positions are discretized with a step smaller than the main lobe width. Moreover, the selection criterion of OLS can be efficiently computed using the matrix structure of the problem.

For a set of indices S, we name A S the matrix with columns a l , l ∈ S extracted from A.

The goal of sparse correlated sources estimation is to decompose the data matrix G as

G ≈ A S CA H S ( 10
)
where S is the set of indices of the J sources, and the positive definite matrix C is the J × J covariance matrix of the sources. In particular, the power of the individual sources can be found on its diagonal. The data matrix can be rewritten

G ≈ i∈ S j∈ S a i a H j Cij , (11)
showing that G is a linear combination of J 2 rank-1 matrices a i a H j . With the complete dictionary A of steering vectors, G can be decomposed as:

G ≈ ACA H , ( 12
)
where C is positive semi-definite and sparse, as it has J 2 nonzero coefficients, corresponding to the J sources and their mutual covariances. These nonzero coefficients are given by the coefficients of C.

Standard greedy recovery algorithm, such as OMP, can be used to estimate C using the following reformulation of the problem:

• The matrix G is vectorized as the N 2 × 1 vector g

• A dictionary of rank-one matrices D 1 is built, of dimension N 2 ×L 2 , with vectorized rank-1 matrices a l a H m as its columns.

• The covariance matrix C is vectorized as c, with dimension L 2 × 1.

This reparametrization yields the linear problem g = D 1 c. The direct application of OMP to this problem is however computationally expensive (D 1 has dimension N 2 × L 2 , and J 2 iterations are necessary), and the particular structure of the dictionary (a collection of rank-1 matrices) and of the decomposition coefficients (they form a positive definite matrix) are not used.

A. Leveraging the structure

The estimation of the covariance matrix C can be improved using structured sparsity, i.e. the particular structure of its support. Here, the structure of the support of the covariance matrix C stems from its non-negativity.

Indeed, in addition to the equality C lm = Cml , the absolute value of the off-diagonal terms is controlled by the diagonal terms:

|C lm | = |C ml | ≤ √ C ll C mm .
This implies that off-diagonal terms appear as pairs, and only if the associated diagonal terms are non-zero. It is then sufficient to know the support of the diagonal terms to control the support of the complete matrix.

An efficient sparse recovery algorithm will thus identify a diagonal term at each iteration k, along with the 2(k -1) off-diagonal terms describing the covariance of this source with the previously identified sources. This selection rule implies that only J iterations are needed. The principle of the selection rule is illustrated on figure ??. At step 1, a first source is identified. At step 2, a second source and its covariance with the first source are identified, etc. until all sources are located. The OMP algorithm can be modified to take into account structured sparsity. In particular, block structures can be identified by replacing the scalar product in step 3, by orthogonal projection on the space spanned by the atoms of a block (?). In the covariance matrix case, a block is a diagonal term along with its 2(k -1) associated off-diagonal terms.

Step 3 of OMP is replaced by:

• For all l, compute the norms of the projection of the residual matrix R k-1 on the space E k,l spanned by a m a H l , a l a H m and a l a H l for m ∈ S k-1 :

ρ k,l = Π E k,l R k-1 2 2 .
The matrix structure can be efficiently leveraged by using the Orthogonal Least-Squares algorithm. OLS is similar to OMP, with the identification step replaced by the maximization of the projection of the signal to be decomposed in the space spanned by the candidate atoms and the previously identified atoms.

Step 3 of the OMP algorithm is further replaced by the following step:

• compute the norms of the projection of the residual on the space F k,l spanned by

a n a H m , for n, m ∈ S k,l = (S k-1 ∪ {l}) : ρ k,l = Π F k,l R k-1 2 F .
In this case, simple algebraic manipulations show that the orthogonal projection of a matrix M in the space F S spanned by the rank-1 terms a l a H m for l, m ∈ S is

Π F S (M) = A ⊥ S A ⊥H S MA ⊥ S A ⊥H S ( 13
)
where A ⊥ S is an orthogonal basis for the space spanned by the a l , l ∈ S. The selection criterion at iteration k is:

ρ k,l = Π F k,l (G) 2 F (14) = A ⊥ S k,l A ⊥H S k,l GA ⊥ S k,l A ⊥H S k,l 2 F (15) = A ⊥H S k,l GA ⊥ S k,l 2 F ( 16
)
The CMF-OLS algorithm for covariance matrix estimation then writes:

1. Initialization: k = 1, residual R 0 = G, set of in- dices S 0 = ∅ 2.
Projections of the residual on the blocks are computed,

ρ k,l = Π F k,l (R k-1 ) 2 F
3. An additional source is identified by the maximal norm of the projection l = argmax l ρ k,l 4. Its index is added to the set S k+1 = S k ∪ {l } 5. The residual is updated by orthogonaly projecting G on the space spanned by the identified atoms:

R k = G -Π F k+1 (G)
6. k = k + 1 and go to step 2 until a stopping criterion is met.

After K iterations, the OLS estimation of the K × K covariance matrix C is given by the solution of the leastsquares problem

ĈO LS = argmin C G -A S K CA H S K 2 F . ( 17
)
with explicit solution ĈOLS = A † S K GA †H S K . where • † denotes the Moore-Penrose pseudo-inverse. The estimate ĈOLS of the complete covariance matrix C is then given by setting the diagonal and off-diagonal coefficients with indices in S K with the coefficients of ĈOLS .

The main computational burden is the computation of the selection criterion. This criterion can be efficiently computed the following way. The orthogonal matrix A ⊥ S k,l is obtained by concatenating A ⊥ S k with the normalized orthogonal projection ãl of a l on the orthogonal of A ⊥ S k . The criterion then writes

A ⊥H S k,l GA ⊥ S k,l 2 F = A ⊥H S k-1 ãH l G A ⊥ S k-1 ãl 2 F (18) = A ⊥H S k-1 GA ⊥ S k-1 2 F + (19) 2 ãH l GA ⊥ S k-1 2 2 + |ã H l Gã l | 2 . ( 20
)
The first term being constant with respect to l, only the last two terms have to be computed.

B. Computational complexity

The computational complexity of the algorithm depends on the number of sensors N , the discretization size L and the number of iterations K, that are such that K ≤ N ≤ L. The computational complexity of an iteration of OLS is governed by

• the construction of the orthogonal matrices A ⊥ S k,l , by projection and normalization of the a l : O(LKN )

• and the computation of the norm of the projection using the two last terms of (??): O(LN 2 )

As K ≤ N , the total cost is O(LN 2 K). We note that the complexity is linear with respect to the size of the grid L. The memory usage of CMF-OLS is dominated by the size of the dictionary LN .

As a comparison, MACS has a time complexity in L 3 , and the time complexity of DAS-C is O(L 2 N ), quadratic in the size of the grid. Memory footprint of MACS and DAS-C is at least the size of the covariance matrix L 2 .

V. SEPARATION OF THE SOURCES

Once the covariance matrix is estimated, the different sets of correlated sources can be identified. First, the number of groups of correlated sources is estimated by computing the eigenvalues of the covariance matrix. The number of groups G is the number of singular values higher than the noise floor.

The information on their spatial shape is included in the singular vectors of the estimated covariance matrix. The singular vector associated to a group describe the relative level of the sources at their respective locations. Combined with the corresponding singular values, respective powers of the sources can be estimated in each group.

However, because of the presence of noise, the singular vectors are combinations of several spatial shapes for sources associated with similar eigenvalues. A simple algorithm is proposed to disentangle the sources, based on the assumption that the supports of the sources are disjoint. With v k the first K singular vectors of ĈOLS , assumed to be normalized, and v kl their coefficients, the source shapes s k are estimated by the following algorithm:

1. k = 1 2. Compute l = argmax l | K n=1 v nl | 2 , 3. Let s k = K n=1 vnl v n / K n=1 |v nl | 2 ,
4. Replace the K vector v n by their projections on the orthogonal of s k .

5. k = k + 1 and go to step 2 until k = G.

The algorithm is supported by the following interpretation: the vectors v k form an orthogonal basis of the space spanned by the shape vectors s k , itself an orthogonal basis as their support are disjoint. Each step of the algorithm rotates the basis v k such that one of the vector is equal to one of the shape vectors. The algorithm is then iterated in the space orthogonal to this vector.

The estimated covariance matrix is then projected on the rank 1 matrices s k s H k , with coefficients α k . The final estimation of the covariance matrix is:

Ĉ = G i=1 α i s i s H i . ( 21
)
From this decomposition, one can

• compute the power emitted at each location of space:

Pl = G k=1 α k |s kl | 2 ,
• or analyze a unique source by using its rank-one description α k s k s H k . The computational complexity of this step is dominated by the SVD of the matrix ĈOLS , in O(K 3 ), itself dominated by the complexity of the OLS algorithm.

VI. SIMULATIONS

The method is demonstrated on a simple case by simulating a linear antenna, and locating correlated sources on a line parallel to the array at a distance of 5m. The antenna is composed of N = 19 sensors spaced by a half wavelength. Two groups of coherent sources are considered, with respectively 2 and 3 narrow band sources emitting at 3500 Hz. Locations and powers of the sources are given in table ??. The SNR is set to 0 dB and I = 500 time samples are collected. The 1D region of interest of the sources is discretized with a 5 mm step, such that L = 400 grid points are considered.

The estimation of the source covariance matrix provided by the DAS-C beamformer is pictured on figure ??. Its diagonal, the output of the standard DAS beamformer, is plotted on figure ??. We note in particular that the two less powerful sources cannot be identified by DAS beamforming, as they are below the level of the sidelobes of more powerful sources. Correlations between sources are represented by the off-diagonal coefficients.

The coefficients of the covariance matrix estimated by CMF-OLS are pictured on figure ??. One can note that the two groups of correlated sources can be easily identified from this estimation while it was not possible with the DAS-C estimation. The estimated positions and powers of the sources estimated by CMF-OLS are given in table ??, and plotted on figure ??. Positions and powers of the five sources are estimated correctly, even for the sources that cannot be identified by beamforming.

The source powers estimated by IMACS are plotted on fig ??. As the value proposed for the regularization parameter in (?) did not yield accurate results, it was set manually. The rank of the covariance matrix is assumed to be L h = 2, and 50 iterations are used. The weaker sources are not estimated accurately by IMACS. Moreover, for some sources, the power is spread over contiguous grid points, making the estimation of the power difficult. This is a well known phenomenon in sparse deconvolution (?), that cannot be avoided by refining the discretization.

The energy of the residual before each step of CMF-OLS is plotted on figure ??. The number of sources is estimated by the location of the discontinuity in the decay of the energy, here at K = 5 iterations. The singular values of the estimated covariance matrix with 5 iterations are plotted on the same figure, showing that the sources can be separated in two correlated groups.

Computation times for CMF-OLS is 0.003s, and 22.7s for IMACS. For this set of data, the proposed methods is about 10 000 times faster that IMACS algorithm which is known as one of the fastest approaches for source covariance matrix estimation. The algorithm is implemented in MATLAB R2018b, and is run on a laptop equipped with an Intel Core i7-7820HQ CPU @ 2.90GHz × 8 CPU and 16 GB memory.

VII. EXPERIMENTAL VALIDATION

The method is now tested experimentally in an anechoic chamber. The following experiments, make use of the same sources built out of baffled broadband omnidirectional loudspeakers (Visaton-BF32 -[150Hz-20kHz]).

B. Experiment 1: Linear array

The linear array is used in this experiment. Four sources are located at a 5.18 m distance. They are correlated by pairs. The source space consists of a parallel 2m long straight line with a 5 mm step (L = 400 points).

The output of the DAS beamforming is pictured on figure ?? at frequency F = 11kHz. The power of the weaker source is below level of a more powerful source, and cannot be located. On the same figure, crosses and circles indicates the sources found by CMF-OLS. They are correctly grouped, and their location is close to the actual locations of the source (dashed lines). The number of iterations, K = 5, and the number of groups, J = 2 are obtained form the decay of the residual energy and the singular values of the covariance matrix. The output of the DAS beamforming is pictured on figure ?? at frequency F = 2.2kHz. Source 4 cannot be identified as it is below the level of the mainlobe of source 2.

The sources identified by CMF-OLS are superimposed on the same image. The number of iterations (K = 4) and number of source groups 4) are chosen cording to the residual energy decay and the singular values of the estimated covariance matrix, see figure ??.

The computation time is here 1.4s. As the complexity of the MACS method is proportional to L 3 , computation times for MACS would be in the order of several years. The size of the output of DAS-C is L 2 , more than 25 GB as single floats, larger than the memory of the computer used for the numerical applications.

D. Experiment 3: 2D array, Pairs of correlated sources

In the next experiment, the same setup is used, with two pairs of correlated sources (1-2, 3-4). As in the previous experiment, source 4 cannot be identified by DAS beamforming. For CMF-OLS, the residual energy decay indicates four sources as above. Here, two groups are identified using the singular values of the estimated covariance matrix, superimposed on the output of the beamformer on figure ??.

The estimated covariances with individual sources are pictured on figure ??. The covariances are given by the column of the estimated covariance matrix C associated to a given source. In the case of source 1, both DAS-C and OMF-CLS yield correct estimation of the covariances, as source 1 is correlated with source 2 only. The covariances estimated by DAS-C for source 4 are however inexact, as source 4 is estimated to be correlated with all four sources. This is explained by the fact that source 4 is in the main lobe of source 3, itself correlated with source 1. CMF-OLS does not find significant correlation with source 3 only.

E. Experiment 4: 2D array, Sources with reflections

Finally, the identification of reflections is tested. A reflector is set up in the anechoic room, and uncorrelated sources (3 and 4) are used. The sources and their reflections are expected to be strongly correlated, and the number of correlated blocks is the number of actual sources. The scan area is augmented to include points in the reflected, virtual space, with dimension 7m × 1.5m, and L = 1.05e5 points. The computation time is here 1.74s. The four sources located by OLS are correctly identified as two pairs of correlated sources, one real source and its reflection.

VIII. CONCLUSION

In this paper the CMF-OLS method is proposed for the estimation of the source covariance matrix which provides simultaneously location, power, and mutual covariances of acoustic sources. The interest of this approach compared to standard methods is its ability to distinguish correlated sources. Simulations and experimental results are presented that illustrate this capacity.

The proposed method is a greedy approach based on the OLS algorithm. Its advantage lies in a very low numerical complexity which is linear with respect to the number of grid points in the scanned source domain. Consequently it is drastically faster than similar methods based on the optimization of a regularized criterion. Numerical examples show that the computing time is divided by a factor 1000 at least. To our knowledge, it is the first method for source covariance estimation that can deal with large numbers of grid points, making it usable in a wide range of applications. An other advantage of the CMF-OLS method upon the regularization approach, is that it does not require the tuning of any parameter to get the optimal solution.

Finally experimental results in free field and semi free field were presented which prove that the accuracy of CMF-OLS outperforms those of regularized approaches such as the MACS or IMACS methods, in terms both of localization and power estimation.

  FIG.1. Principle of the greedy source identification algorithm: at each step, a source (diagonal term) is identified along the covariance between itself and the previously identified sources.

FIG

  FIG. 2. Simulations (5 sources) -source covariance matrix. In both representation, the powers of the sources are found on the diagonal, off-diagonal terms indicate correlation between sources. Left: Output of DAS-C, the actual sources are superimposed, crosses and circles denotes the two source groups. Right: Covariance matrix estimated by CMF-OLS, the radius of the disks are proportional to the absolute value of the coefficients.

  FIG. 4. Simulations (5 sources).Left: Energy of the residual of the CMF-OLS. Right: Singular values of the covariance matrix.

  A. Set Up Two different acoustic antennas are implemented. They use the same acoustic sensors : MEMS digital microphones (invensense -INMP441) with a 26 dBFS sensitivity (1kHz, 94dBSPL) and a flat response in the band [150 Hz -15 kHz]. The first antenna counts 32 elements irregularly spaced on a straight line, 1.36 m long, with an average step of 45 mm. The second antenna counts 128 elements distributed along 16 linear rays. The 8 microphones on a ray are spaced according to a geometric law and the origins of the 16 rays follow a pseudo random distribution. The second microphone array and the sources are pictured on fig. ??. They are located in two parallel planes, at a distance d = 4.3m. The microphone signals are sampled at F s = 50 kHz and analyzed by Short-Term Fourier Transform, with a 2048 samples Hann window (41ms duration and 75% overlap).

FIG. 5 .

 5 FIG. 5. Experimental results, linear array. Top: Two pairs of correlated F = 2.2 kHz. The sources identified by CMF-OLS are superimposed over the output of the standard beamformer. Bottom: Estimation by IMACS.

  FIG. 9. Experimental results with uncorrelated (Exp. 2) and correlated sources (Exp. 3). Left: Energy of the residual before each step of the CMF-OLS algorithm. Right: Singular values of the estimated covariance matrix for K = 4.

  FIG. 11. Experimental results. Covariances estimated by DAS-C and CMF-OLS with a source. Top: source 4 , bottom: source 1.

  FIG. 12. Experimental results with two sources and their reflections at F = 2.93 kHz. The sources identified by CMF-OLS are superimposed over the output of the standard beamformer.

J. Acoust. Soc. Am. / 21 June 2019

J. Acoust. Soc. Am. / 21 June 2019