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.

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.

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.

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.

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.

This work derives compact closed-form expressions of the misspecified Cramér–Rao bound and pseudo-true parameters of time-delay and Doppler for a high dynamics signal model. Those expressions are validated by analyzing the mean square error (MSE) of the misspecified maximum likelihood estimator. A noteworthy outcome of these MSE results is that, for some magnitudes of acceleration and signal-to-noise ratios, neglecting the acceleration is beneficial in the MSE sense. The variance performance improvement is obtained at the cost of a systematic error in the true parameter estimation. This can be seen as a specific case of the trade-off between bias and variance. Neglecting the acceleration can improve the Doppler estimation when the error induced on the misspecified model is less than the variance increase due to including an extra parameter to estimate. Then, for some non-zero acceleration magnitudes and short integration times, the Doppler estimation using a misspecified model outperforms a correctly specified model in the MSE sense.

This is a supplementary material associated with the article "Band-limited impulse response estimation performance" that can be found, in the online version, at doi: https://doi.org/10.1016/j.sigpro.2023.108998.

In ranging-based applications, ignoring the presence of multipath often leads to a bias upon the estimated range, which actually originates from misspecified estimation problem because the assumed data signal model, here without multipath, is not equal to the true one. Such misspecification also results in an error covariance matrix around the biased estimates, so-called pseudotrue parameters, that differs from the Cramér–Rao bound applied to the true model. This error covariance matrix can be lower bounded by a misspecified Cramér–Rao bound (MCRB). In this work, a closed-form expression of the MCRB under multipath conditions is proposed, which only depends on the baseband signal samples and both delay, Doppler and complex amplitude pseudotrue parameters. These MCRB expressions are fundamental (i) to understand and characterize the impact of multipath conditions when not taken into account, (ii) for system/signal design, and (iii) to derive new robust estimators. The proposed MCRBs are validated for a representative navigation signal, comparing the resulting bounds with the mean square error obtained by the misspecified maximum likelihood estimator with respect to the pseudotrue parameters.

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.