## Recherche

###### Article de journal

## Band-limited impulse response estimation performance

**Signal Processing, vol. 208, Art. no 108998, July, 2023.**

When a signal is strongly distorted by a reflecting surface, the surface can be seen as a filter whose impulse response is convoluted with the incident signal. Depending on the application, it can be useful to estimate this impulse response in order to either compensate or interpret it. When it comes to estimation, a performance lower bound should be computed in order to better understand the performance limits of the observation model at hand. Hence, a first contribution of this work is to provide an easy-to-use closed-form Cramér–Rao bound for the proposed signal model. The validation process of this lower bound raises the problem of the size, generally unknown, of the impulse response to be estimated. A second contribution of this study is then to provide adapted theoretical and practical tools to determine the size of a given impulse response along with its estimation.

Traitement du signal et des images / Localisation et navigation

###### Article de conférence

## RF Telecommunication Systems Characterization and Optimization

**In Proc. Indo-French Workshop on Microwave and Photonic Technologies (WS ITM), Madras, India, February 20-22, 2023.**

Communications numériques / Systèmes spatiaux de communication

###### Thèse de Doctorat

## Signal Processing for GNSS Reflectometry

**Defended on February 14, 2023.**

Global Navigation Satellite Systems (GNSS) Reflectometry, or GNSS-R, is the study of GNSS signals reflected from the Earth’s surface. These so-called signals of opportunity, usually seen as a nuisance in standard navigation applications, contain meaningful information on the nature and relative position of the reflecting surface. Depending on the receiver platform (e.g., ground-based, airplane, satellite) and the reflecting surface itself (e.g., rough sea, lake), the reflected signal, more or less distorted, is difficult to model, and the corresponding methods to estimate the signal parameters of interest may vary. This thesis starts from the navigation multipath problem in harsh environments, which can be seen as a dual source estimation problem where the main source is the signal of interest, and the secondary one is a single reflection of the main source. Depending on the scenario and the resources at hand, it is possible i) to estimate the parameters of interest (i.e., time-delay, Doppler frequency, amplitude and phase) of both sources, or ii) to estimate only one source’s parameters, although these estimates may be biased because of the interfering source. Either way, it is necessary to know the achievable performance for these estimation problems. For this purpose, tools from the estimation theory, such as the Cramér-Rao bound (CRB), can be used. In this thesis a CRB expression was derived for the properly specified case (dual source), and the misspecified one (single source). These bounds were compared to the performance obtained with different estimators, in order to theoretically characterize the problem at hand. This study allowed to establish a clear mathematical framework that also fits the groundbased GNSS-R problem, for which the reflected signal is little distorted by the reflecting surface. In this case, the direct and reflected signals are close in time, which inevitably leads to interference, or crosstalk, and then to a clear performance degradation. Standard GNSS-R techniques, which do not perform well in this ground-based scenario, were compared to the CRB and two proposed approaches: i) a Taylor approximation of the dual source likelihood criterion when both sources are very close in time, and ii) a dual source estimation strategy to reduce or cancel the crosstalk. This part on ground-based GNSS-R was supported by a real data set, obtained from a data collection campaign organized by CNES (Toulouse, France). The problem changes slowly when the satellite elevation increases : the reflection, assumed coherent so far, turns non-coherent because of the reflecting surface roughness. The automatic detection of this transition (i.e., from coherent to non-coherent) is of great interest for future satellite missions. Reflection coherence is mainly observed by looking at the relative phase between the reflected and direct signals. Consequently, a statistical study of phase difference time series allowed to build tests that depend on the time series Gaussianity or regularity. The proposed tests were applied to a data set provided by the IEEC (Barcelona, Spain). Finally, for scenarios where the reflecting surface distorts the signal significantly, it is necessary to adapt the signal model. The approach proposed in this thesis is to consider the received signal as a convolution between the transmitted signal and the reflecting surface impulse response. This signal model goes with the derivation of the corresponding CRB and the implementation of the maximum likelihood estimator. The question of the impulse response size determination, that is, the determination of the number of pulses required to describe the impulse response, was also tackled based on hypothesis tests. Simulation results show the potential of this approach.

Traitement du signal et des images / Localisation et navigation

###### Présentation de soutenance de thèse

## Signal Processing for GNSS Reflectometry

**Defended on February 14, 2023.**

Global Navigation Satellite Systems (GNSS) Reflectometry, or GNSS-R, is the study of GNSS signals reflected from the Earth’s surface. These so-called signals of opportunity, usually seen as a nuisance in standard navigation applications, contain meaningful information on the nature and relative position of the reflecting surface. Depending on the receiver platform (e.g., ground-based, airplane, satellite) and the reflecting surface itself (e.g., rough sea, lake), the reflected signal, more or less distorted, is difficult to model, and the corresponding methods to estimate the signal parameters of interest may vary. This thesis starts from the navigation multipath problem in harsh environments, which can be seen as a dual source estimation problem where the main source is the signal of interest, and the secondary one is a single reflection of the main source. Depending on the scenario and the resources at hand, it is possible i) to estimate the parameters of interest (i.e., time-delay, Doppler frequency, amplitude and phase) of both sources, or ii) to estimate only one source’s parameters, although these estimates may be biased because of the interfering source. Either way, it is necessary to know the achievable performance for these estimation problems. For this purpose, tools from the estimation theory, such as the Cramér-Rao bound (CRB), can be used. In this thesis a CRB expression was derived for the properly specified case (dual source), and the misspecified one (single source). These bounds were compared to the performance obtained with different estimators, in order to theoretically characterize the problem at hand. This study allowed to establish a clear mathematical framework that also fits the groundbased GNSS-R problem, for which the reflected signal is little distorted by the reflecting surface. In this case, the direct and reflected signals are close in time, which inevitably leads to interference, or crosstalk, and then to a clear performance degradation. Standard GNSS-R techniques, which do not perform well in this ground-based scenario, were compared to the CRB and two proposed approaches: i) a Taylor approximation of the dual source likelihood criterion when both sources are very close in time, and ii) a dual source estimation strategy to reduce or cancel the crosstalk. This part on ground-based GNSS-R was supported by a real data set, obtained from a data collection campaign organized by CNES (Toulouse, France). The problem changes slowly when the satellite elevation increases: the reflection, assumed coherent so far, turns non-coherent because of the reflecting surface roughness. The automatic detection of this transition (i.e., from coherent to non-coherent) is of great interest for future satellite missions. Reflection coherence is mainly observed by looking at the relative phase between the reflected and direct signals. Consequently, a statistical study of phase difference time series allowed to build tests that depend on the time series Gaussianity or regularity. The proposed tests were applied to a data set provided by the IEEC (Barcelona, Spain). Finally, for scenarios where the reflecting surface distorts the signal significantly, it is necessary to adapt the signal model. The approach proposed in this thesis is to consider the received signal as a convolution between the transmitted signal and the reflecting surface impulse response. This signal model goes with the derivation of the corresponding CRB and the implementation of the maximum likelihood estimator. The question of the impulse response size determination, that is, the determination of the number of pulses required to describe the impulse response, was also tackled based on hypothesis tests. Simulation results show the potential of this approach.

Traitement du signal et des images / Localisation et navigation

###### Thèse de Doctorat

## Precise Cooperative Positioning of Low-Cost Mobiles in an Urban Environment

**Defended on February 10, 2023.**

In recent years, our society has been preparing for a paradigm shift toward the hyperconnectivity of urban areas. This highly anticipated rise of connected smart city centers is led by the development of low-cost connected smartphone devices owned by each one of us. In this context, the demand for low-cost, high-precision localization solutions is driven by the development of novel autonomous systems. After Google announced the release of Android GNSS raw data measurements on mobile devices, the enthusiasm around those low-cost positioning devices quickly grew in the scientific community. The increasing need of Location Based Services (LBS) provoked the rapid evolution of smartphones embedded low-cost Global Navigation Satellite System (GNSS) chipsets within the last few years. Most Android devices are now equipped with multi-constellation and multi-frequency positioning units. Preliminary studies explored the implementation of advanced positioning algorithms aiming at answering the demand for precise navigation and positioning on mobile devices. However, various drawbacks prevent the realization of above-mentioned techniques on hand-held mobiles. Smartphones positioning capabilities are limited by the tight-integration of hardware components within the device. Integrated low-cost components, such as the linearly polarized antenna, are unoptimized for acquiring multi-frequency GNSS signals and their operation in constrained environment quickly becomes a challenge for mitigating disruptive multipath events. Moreover, due to a fierce technological competition between chipset manufacturers, embedded GNSS receivers have been conceived to act as ”blackbox” processes. The receiver parameterization is kept confidential and only GNSS raw data measurements are outputted to the user. In order to overcome those difficulties, this research work ambitions to develop a collaborative network positioning system between smartphones. A collaborative system is defined as a set of inter-connected users exchanging GNSS data in order to enhance network’s users positioning performance. The implementation of a cooperative smartphone network takes advantage of the tremendous number of connected Android devices present in today’s city centers for refining and improving users position accuracy and integrity in urban environment. This research thesis presents a thorough analysis of Android GNSS raw data measurements aiming at lifting the ambiguity generated by receivers’ ”black-box” processes on a wide variety of Android smartphone brand and models. A wide data collection campaign, on 7 different smartphone models in real-life urban conditions, has been conducted for assessing the positioning performance of those contemporary low-cost devices. After grasping the receivers’ mechanisms, the implementation of Android GNSS raw data measurements in collaborative positioning algorithm has been investigated. An innovative smartphone-based double code difference method has been employed to compute the inter-phone distance between network’s users, named Inter-Phone Ranging (IPR). This technique was tested for nominal and urban scenario cases and has demonstrated its reliability for collaborative positioning implementation. Finally, a smartphone-based cooperative engine, called SmartCoop, was developed and evaluated. This software-based engine is integrated within the cooperative network infrastructure for delivering accurate positioning solutions to network’s users. This collaborative estimation technique exploits the previously computed IPR ranges in a non-linear constrained optimization problem. An experimental protocol has been put in place in order to determine the estimation method efficiency through a series of simulation runs for both nominal and urban scenarios. The presented results analysis supports our hypothesis that smartphone-based collaborative engine enhances Android positioning performance in urban canyon.

Communications numériques / Localisation et navigation

###### Présentation de soutenance de thèse

## Precise Cooperative Positioning of Low-Cost Mobiles in an Urban Environment

**Defended on February 10, 2023.**

In recent years, our society has been preparing for a paradigm shift toward the hyperconnectivity of urban areas. This highly anticipated rise of connected smart city centers is led by the development of low-cost connected smartphone devices owned by each one of us. In this context, the demand for low-cost, high-precision localization solutions is driven by the development of novel autonomous systems. After Google announced the release of Android GNSS raw data measurements on mobile devices, the enthusiasm around those low-cost positioning devices quickly grew in the scientific community. The increasing need of Location Based Services (LBS) provoked the rapid evolution of smartphones embedded low-cost Global Navigation Satellite System (GNSS) chipsets within the last few years. Most Android devices are now equipped with multi-constellation and multi-frequency positioning units. Preliminary studies explored the implementation of advanced positioning algorithms aiming at answering the demand for precise navigation and positioning on mobile devices. However, various drawbacks prevent the realization of above-mentioned techniques on hand-held mobiles. Smartphones positioning capabilities are limited by the tight-integration of hardware components within the device. Integrated low-cost components, such as the linearly polarized antenna, are unoptimized for acquiring multi-frequency GNSS signals and their operation in constrained environment quickly becomes a challenge for mitigating disruptive multipath events. Moreover, due to a fierce technological competition between chipset manufacturers, embedded GNSS receivers have been conceived to act as ”blackbox” processes. The receiver parameterization is kept confidential and only GNSS raw data measurements are outputted to the user. In order to overcome those difficulties, this research work ambitions to develop a collaborative network positioning system between smartphones. A collaborative system is defined as a set of inter-connected users exchanging GNSS data in order to enhance network’s users positioning performance. The implementation of a cooperative smartphone network takes advantage of the tremendous number of connected Android devices present in today’s city centers for refining and improving users position accuracy and integrity in urban environment. This research thesis presents a thorough analysis of Android GNSS raw data measurements aiming at lifting the ambiguity generated by receivers’ ”black-box” processes on a wide variety of Android smartphone brand and models. A wide data collection campaign, on 7 different smartphone models in real-life urban conditions, has been conducted for assessing the positioning performance of those contemporary low-cost devices. After grasping the receivers’ mechanisms, the implementation of Android GNSS raw data measurements in collaborative positioning algorithm has been investigated. An innovative smartphone-based double code difference method has been employed to compute the inter-phone distance between network’s users, named Inter-Phone Ranging (IPR). This technique was tested for nominal and urban scenario cases and has demonstrated its reliability for collaborative positioning implementation. Finally, a smartphone-based cooperative engine, called SmartCoop, was developed and evaluated. This software-based engine is integrated within the cooperative network infrastructure for delivering accurate positioning solutions to network’s users. This collaborative estimation technique exploits the previously computed IPR ranges in a non-linear constrained optimization problem. An experimental protocol has been put in place in order to determine the estimation method efficiency through a series of simulation runs for both nominal and urban scenarios. The presented results analysis supports our hypothesis that smartphone-based collaborative engine enhances Android positioning performance in urban canyon.

Communications numériques / Localisation et navigation

###### Article de journal

## Accounting for Acceleration – Signal Parameters Estimation Performance Limits in High Dynamics Applications

**IEEE Transactions on Aerospace and Electronic Systems, Vol 59, Issue 1, pp 610-622, February 2023.**

The derivation of estimation lower bounds is paramount to designing and assessing the performance of new estimators. A lot of effort has been devoted to the range-velocity estimation problem, a fundamental stage on several applications, but very few works deal with acceleration, being a key aspect in high dynamics applications. Considering a generic band-limited signal formulation, we derive a new general compact form Cramér-Rao bound (CRB) expression for joint time-delay, Doppler stretch, and acceleration estimation. This generalizes and expands upon known delay/Doppler estimation CRB results for both wideband and narrowband signals. This new formulation, especially easy to use, is created based on baseband signal samples, making it valid for a variety of remote sensors. The new CRB expressions are illustrated and validated with representative GPS L1 C/A and Linear Frequency Modulated (LFM) chirp band-limited signals. The mean square error (MSE) of a misspecified estimator (conventional delay/Doppler) is compared with the derived bound. The comparison indicates that for some acceleration ranges the misspecified estimator outperforms a well specified estimator that accounts for acceleration.

Traitement du signal et des images / Localisation et navigation et Systèmes spatiaux de communication

###### Séminaire

## Caractérisation et Optimisation des Amplificateurs Non Linéaires

**Presentation at ONERA Toulouse, February 1, 2023.**

Communications numériques / Systèmes spatiaux de communication

###### Article de conférence

## A Robust Time Scale Based on Maximum Likelihood Estimation

**In Proc. Institute of Navigation Precise Time and Time Interval Systems and Applications (PTTI), Long Beach, California-USA, January 23-26, 2023.**

This paper introduces a new statistical model for clock phases assuming a multivariate Gaussian distribution for the clock phase deviations from a common time scale. This model allows us to derive a maximum likelihood estimator for the clock phases, which is consistent with the current methods of computing a common time scale for a collection of clocks. Detailing a statistical model of the clock phases, which assumes a Gaussian distribution allows us to find the MLE for each clock’s phase deviation from a common time scale. For verification, the MLE for the clock phases is shown to be consistent with the result of the existing basic time scale equation. The statistical distribution of the frequency states resulting from this statistical model is Gaussian over a window of past time instants. This property can be used to design a new time scale based on the maximum likelihood estimator of frequency and frequency variances that are alternatives to the exponential filters designed for AT1. With the appropriate number of past frequency samples, this MLE has identical performance to the optimal AT1 algorithm in a nominal context. The statistical distribution of the frequency when the clock suffers a phase jump anomaly is then identified as a Student’s t-distribution. The Student’s t-distribution models the statistics of datasets contaminated by outliers, leading to the derivation of a different MLE that is robust to those outliers. The time scale using the robust MLE provides estimates of each clock’s frequency and frequency variance that are unaffected by phase jump anomalies and improves the long-term frequency stability when each clock in the ensemble experiences phase jump anomalies within some window of time.

Traitement du signal et des images / Localisation et navigation

###### Article de journal

## Delay Optimization of Conventional Non-Coherent Differential CPM Detection

**IEEE Communications Letters, vol. 27, issue 1, pp. 234-238, January, 2023.**

The conventional non-coherent differential detection of continuous phase modulations (CPM) is quite robust to channel impairments such as phase and Doppler shifts. Its implementation is on top of that simple. It consists in multiplying the received baseband signal by its conjugate version delayed by one symbol period. However it suffers from a signal-to-noise ratio gap compared to the optimum coherent detection. In this paper, we improve the error rate performance of the conventional differential detection by using a delay higher than one symbol period. We derive the trellis description as well as the branch and cumulative metrics that take into account a delay of K symbol periods. We then determine an optimized delay K opt based on the minimum Euclidean distance between two differential signals for some popular CPM formats. The optimized values are confirmed by error rate simulations.

Communications numériques / Systèmes de communication aéronautiques et Systèmes spatiaux de communication

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