Carles Fernández-Prades

ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers

This paper addresses the estimation of the code-phase (pseudorange) and the carrier-phase of the direct signal received from a direct-sequence spread-spectrum satellite transmitter. The signal is received by an antenna array in a scenario with interference and multipath propagation. These two effects are generally the limiting error sources in most high-precision positioning applications. A new estimator of the code- and carrier-phases is derived by using a simplified signal model and the maximum likelihood (ML) principle. The simplified model consists essentially of gathering all signals, except for the direct one, in a component with unknown spatial correlation. The estimator exploits the knowledge of the direction-of-arrival of the direct signal and is much simpler than other estimators derived under more detailed signal models. Moreover, we present an iterative algorithm, that is adequate for a practical implementation and explores an interesting link between the ML estimator and a hybrid beamformer. The mean squared error and bias of the new estimator are computed for a number of scenarios and compared with those of other methods. The presented estimator and the hybrid beamforming outperform the existing techniques of comparable complexity and attains, in many situations, the Crame/spl acute/r-Rao lower bound of the problem at hand.

A Bayesian Approach to Multipath Mitigation in GNSS Receivers

Multipath is known to be one of the most dominant sources of accuracy degradation in satellite-based navigation systems. Multipath may cause biased position estimates that could jeopardize high-precision applications. This paper considers the problem of tracking the time-variant synchronization parameters of both the line-of-sight signal (LOSS) and its multipath replicas. In particular, the proposed algorithm tracks time-delays, amplitudes, phases and proposes a procedure to extract Doppler shifts from complex amplitudes. However, the interest is focused on LOSS time-delay estimates, since those provide the means to compute users position. The undertaken Bayesian approach is implemented by a particle filter. The selection of the importance density function, from which particles are generated, is performed using a Gaussian approximation of the posterior function. This selection provides a particle generating function close to the optimal, which yields to an efficient usage of particles. The complex-linear part of the model, i.e., complex amplitudes, is tackled by a Rao-Blackwellization procedure that implements a complex Kalman filter for each generated particle, thus reducing the computational load. Computer simulation results are compared to other Bayesian filtering alternatives (namely, the extended Kalman filter, the unscented Kalman filter and the sequential importance resampling algorithms) and the posterior Cramer-Rao bound.

Satellite Radiolocalization From GPS to GNSS and Beyond: Novel Technologies and Applications for Civil Mass Market

It is known that satellite radiolocalization was born in the military environment and was originally conceived for defense purposes. Nevertheless, the commercial explosion (dated to 20 years ago) of global positioning system (GPS) in the civil market (automotive, tourism, etc.) significantly changed the original perspectives of this technology. Another big change is expected when other global navigation satellite systems (GNSSs) such as the European Galileo or the Chinese COMPASS become operational and commercial. In fact, modern GNSSs are conceived principally for the civil market (at the opposite of GPS, whose civil employment is given as a sort of “kind gift,” with lower performance than that one granted to military users). The scope of this paper is to provide readers with a clear focus about the potentialities of current and forthcoming GNSSs and associated technologies in a renewed mass-market perspective. The paper also opens a window to the future of radiolocalization technology beyond GPS and GNSS, dealing with the role of digital signal processing and software-defined radio (SDR) in next-generation navigation systems and with the seamless integration of satellite-based navigation with other technologies in order to provide reliable position information also in hostile environments.

CramÉr–Rao Bound Analysis of Positioning Approaches in GNSS Receivers

Recently, direct position estimation (DPE) has arisen as a potential approach to deal with the positioning problem in global navigation satellite system receivers. The conventional navigation solution is obtained in two steps: synchronization parameters are estimated and then a trilateration procedure is in charge of computing users position, based on those parameters. In contrast, DPE estimates receivers position directly from digitized signal. DPE was seen to provide GNSS receivers with appealing capabilities, such as multipath mitigation. However, a theoretical bound for those estimates is still missing and the answer to ldquohow better can DPE perform compared to the conventional approach?rdquo has not been addressed in the literature. Aiming at clarifying those issues, this paper presents the derivation of the CramEacuter-Rao bound (CRB) of position for both conventional and DPE approaches. We present the derivation for a multiantenna receiver as a general case. In addition, a number of realistic scenarios are tested in order to compare the theoretical performance bounds of both alternatives and the actual root mean squared error performance of the corresponding maximum likelihood estimator.

Antenna Array Based GNSS Signal Acquisition for Interference Mitigation

This work addresses the signal acquisition problem using an array of antennas in the general framework of Global Navigation Satellite Systems (GNSS) receivers. We propose a statistical approach, using the Neyman-Pearson (NP) detection theory and the generalized likelihood ratio test (GLRT), to obtain a new detector which is able to mitigate temporally uncorrelated interferences even if the array is unstructured and moderately uncalibrated. The key statistical feature is the assumption of an arbitrary and unknown covariance noise matrix, which attempts to capture the statistical behavior of the interferences and of other nondesirable signals, while exploiting the spatial dimension provided by antenna arrays. Closed-form expressions for detection and false alarm probabilities are provided. The performance and interference rejection capability are modeled and compared with their theoretical bound. Furthermore the proposed detector is analyzed under realistic conditions, which accounts for the presence of errors in the covariance matrix estimation, the residual Doppler and delay errors, and the signal quantization effects. The theoretical results are supported by Monte Carlo simulations.

Multiple Quadrature Kalman Filtering

Bayesian filtering is a statistical approach that naturally appears in many signal processing problems. Ranging from Kalman filter to particle filters, there is a plethora of alternatives depending on model assumptions. With the exception of very few tractable cases, one has to resort to suboptimal methods due to the inability to analytically compute the Bayesian recursion in general dynamical systems. This is why it has attracted the attention of many researchers in order to develop efficient algorithms to implement it. We focus our interest into a recently developed algorithm known as the Quadrature Kalman filter (QKF). Under the Gaussian assumption, the QKF can tackle arbitrary nonlinearities by resorting to the Gauss-Hermite quadrature rules. However, its complexity increases exponentially with the state-space dimension. In this paper we study a complexity reduction technique for the QKF based on the partitioning of the state-space, referred to as the Multiple QKF. We prove that partitioning schemes can effectively be used to reduce the curse of dimensionality in the QKF. Simulation results are also provided to show that a nearly-optimal performance can be attained, while drastically reducing the computational complexity with respect to state-of-the-art algorithms that are able to deal with such nonlinear filtering problems.

Bayesian Nonlinear Filtering Using Quadrature and Cubature Rules Applied to Sensor Data Fusion for Positioning

This paper shows the applicability of recently-developed Gaussian nonlinear filters to sensor data fusion for positioning purposes. After providing a brief review of Bayesian nonlinear filtering, we specially address square-root, derivative-free algorithms based on the Gaussian assumption and approximation rules for numerical integration, namely the Gauss--Hermite quadrature rule and the cubature rule. Then, we propose a motion model based on the observations taken by an Inertial Measurement Unit, that takes into account its possibly biased behavior, and we show how heterogeneous sensors (using time-delay or received-signal-strength based ranging) can be combined in a recursive, online Bayesian estimation scheme. These algorithms show a dramatic performance improvement and better numerical stability when compared to typical nonlinear estimators such as the Extended Kalman Filter or the Unscented Kalman Filter, and require several orders of magnitude less computational load when compared to Sequential Monte Carlo methods, achieving a comparable degree of accuracy.

Bayesian nonlinear filters for Direct Position Estimation

The use of a Direct Position Estimation approach has recently deserved some attention in the satellite-based navigation topic. In this paper, the core idea is to merge a motion model based on the observations of an Inertial Measurement Unit, accounting for possible biased measures, with a signal model parameterized by the position of the receiver. Indeed, this position is to be estimated. Bayesian nonlinear filtering theory is reviewed in the paper. Particularly, we focus our attention on the study of particle filtering and square-root derivative-free algorithms based on the Gaussian assumption and approximation rules for numerical integration, namely the Gauss-Hermite quadrature rule or the third-degree spherical-radial cubature rule. These algorithms exhibit a dramatic improvement and better numerical stability than classical Kalman filter-like methods, for example the extended Kalman filter or the unscented Kalman filter. The paper presents an analysis of the computational complexity of each algorithm and a performance comparison using computer simulations under a realistic scenario.

Robust GNSS Receivers by Array Signal Processing: Theory and Implementation

One of the main vulnerabilities of GNSS receivers is their exposure to intentional or unintentional jamming signals, which could even cause service unavailability. Several alternatives to counteract these effects were proposed in the literature, being the most promising those based on multiple antenna architectures. This is specially the case for high-grade receivers used in applications requiring reliability and robustness. This article provides an overview of the possible receiver architectures encompassing antenna arrays and the associated signal processing techniques. Emphasis is also put on the most typical implementation issues found when dealing with such technology. A thorough survey is complemented with a set of experiments, including real data processing by a working prototype, which exemplifies the above ideas.

Bayesian filtering for indoor localization and tracking in wireless sensor networks

In this article, we investigate experimentally the suitability of several Bayesian filtering techniques for the problem of tracking a moving device by a set of wireless sensor nodes in indoor environments. In particular, we consider a setup where a robot was equipped with an ultra-wideband (UWB) node emitting ranging signals; this information was captured by a network of static UWB sensor nodes that were in charge of range computation. With the latter, we ran, analyzed, and compared filtering techniques to track the robot. Namely, we considered methods falling into two families: Gaussian filters and particle filters. Results shown in the article are with real data and correspond to an experimental setup where the wireless sensor network was deployed. Additionally, statistical analysis of the real data is provided, reinforcing the idea that in this kind of ranging measurements, the Gaussian noise assumption does not hold. The article also highlights the robustness of a particular filter, namely the cost-reference particle filter, to model inaccuracies which are typical in any practical filtering algorithm.