Jordi Vilà-Valls

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.

An interactive multiple model approach for robust GNSS carrier phase tracking under scintillation conditions

This contribution deals with robust carrier phase tracking in Global Navigation Satellite Systems, where the ultimate goal is to obtain accurate and robust phase estimates under non-nominal conditions, such as high dynamics, strong fading and ionospheric scintillation. Within this framework, an Interacting Multiple Model approach, using a bank of parallel Kalman-based filters with different dynamic state models, is proposed to cope with signals corrupted by severe ionospheric scintillation. In the proposed formulation, the time-varying and correlated scintillation phase is introduced into the dynamic system using an AR(1) model. Simulation results are provided to show the enhanced robustness and improved accuracy of the proposed approach, with respect to state-of-the-art carrier phase tracking techniques.

Advanced KF-based methods for GNSS carrier tracking and ionospheric scintillation mitigation

Ionospheric scintillation is the name given to the disturbance caused by electron density irregularities along the propagation path of electromagnetic waves through the ionosphere. These non-nominal propagation conditions mainly cause carrier phase variations and amplitude fades. It is important to point out that both degradations are correlated, and thus deep amplitude fades and rapid phase variations (the so-called canonical fades) occur in a simultaneous and random manner. Regarding the carrier synchronization problem under harsh propagation conditions, such as high dynamics, multipath effects or ionospheric scintillation, canonical fades make the latter the most challenging scenario, which can be considered as a benchmark on the performance of robust carrier tracking techniques. This phenomenon particularly affects satellite-based positioning systems in the equatorial regions and at high latitudes. In this work, both amplitude and phase variations due to scintillation are first modeled using an autoregressive (AR) model, and then included into the system state-space formulation. Therefore, a Kalman filter (KF) based solution can be aware of both dynamics and scintillation phase evolutions. This arises as the natural solution to mitigate those undesired propagation effects. Moreover, in order to counteract the main drawbacks of standard KF-based tracking solutions, an extended KF (EKF) architecture is considered, tracking both the phase dynamics, scintillation phase and amplitude. This implies directly operating with the baseband received signals complex samples, avoiding the use discriminators and thus its saturation and the loss of Gaussianity. Simulation results are provided to support the theoretical discussion and to show the performance improvements of such new approach.

Adaptive GNSS Carrier Tracking Under Ionospheric Scintillation: Estimation vs. Mitigation

This letter deals with carrier synchronization in Global Navigation Satellite Systems. The main goals are to design robust methods and to obtain accurate phase estimates under ionospheric scintillation conditions, being of paramount importance in safety critical applications and advanced receivers. Within this framework, the estimation versus mitigation paradigm is discussed together with a new adaptive Kalman filter-based carrier phase synchronization architecture that copes with signals corrupted by ionospheric scintillation. A key point is to model the time-varying correlated scintillation phase as an AR(p) process, which can be embedded into the filter formulation, avoiding possible loss of lock due to scintillation. Simulation results are provided to show the enhanced robustness and improved accuracy with respect to state-of-the-art techniques.

Nonlinear Filtering for Ultra-Tight GNSS/INS Integration

This paper considers the problem of ultra-tight GNSS/INS integration. We propose a new approach, deriving the direct relation between Inertial Measurement Unit (IMU) measurements and synchronization parameters, used in the trilateration algorithm to compute the position of the receiver. We take into account the IMUs eventual biased behavior by introducing it into the state representation. We use a recently-developed, square-root derivative-free Gaussian nonlinear filter to solve the estimation problem.

Simultaneous tracking and RSS model calibration by robust filtering

Received Signal Strength (RSS) localization is widely used due to its simplicity and availability in most mobile devices. The RSS channel model is defined by the propagation losses and the shadow fading. These parameters might vary over time because of changes in the environment. In this paper, the problem of tracking a mobile node by RSS measurements is addressed, while simultaneously estimating a two-slope RSS model. The methodology considers a Kalman filter with Interacting Multiple Model architecture, coupled to an on-line estimation of the observations variance. The performance of the method is shown through numerical simulations in realistic scenarios.

NLOS mitigation in TOA-based indoor localization by nonlinear filtering under skew t-distributed measurement noise

Wireless localization by time-of-arrival (TOA) measurements is typically corrupted by non-line-of-sight (NLOS) conditions, causing biased range measurements that can degrade the overall positioning performance of the system. In this article, we propose a localization algorithm that is able to mitigate the impact of NLOS observations by employing a heavy-tailed noise statistical model. Modeling the observation noise by a skew t-distribution allows us to, on the one hand, employ a computationally light sigma-point Kalman filtering method while, on the other hand, be able to effectively characterize the positive skewed non-Gaussian nature of TOA observations under LOS/NLOS conditions. Numerical results show the enhanced performance of such approach.

Computational complexity reduction techniques for quadrature Kalman filters

Nonlinear filtering is a major problem in statistical signal processing applications and numerous techniques have been proposed in the literature. Since the seminal work that led to the Kalman filter to the more advanced particle filters, the goal has been twofold: to design algorithms that can provide accurate filtering solutions in general systems and, importantly, to reduce their complexity. If Gaussianity can be assumed, the family of sigma-point KFs is a powerful tool that provide competitive results. It is known that the quadrature KF provides the best performance among the family, although its complexity grows exponentially on the state dimension. This article details the asymptotic complexity of the legacy method and discusses strategies to alleviate this cost, thus making quadrature-based filtering a real alternative in high-dimensional Gaussian problems.

Uncertainty Exchange Through Multiple Quadrature Kalman Filtering

One of the major challenges in Bayesian filtering is the curse of dimensionality. The quadrature Kalman filter (QKF) is the method of choice in many real-life Gaussian problems, but its computational complexity increases exponentially with the dimension of the state. As a promising solution to overcome the filter limitations in such scenarios, we further explore the multiple state-partitioning approach, which considers the partition of the original space into several subspaces, with the goal to apply a low-dimensional filter at each partition. In this contribution, the key idea is to take advantage of the estimation uncertainty provided by the QKF to improve the interaction among filters and avoid the point estimate approximation performed in the original Multiple QKF (MQKF). The new filter formulation, named Improved MQKF, considers Gauss-Hermite quadrature rules to propagate the subspaces of interest, together with cubature rules for marginalization purposes. The nested quadrature-cubature approximation provides robustness and improves the filter performance. Simulation results for a multiple target tracking scenario are provided to support the discussion.