A Box Regularized Particle Filter for state estimation with severely ambiguous and non-linear measurements

International audienceThe first stage in any control system is to be able to accurately estimate the system's state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems. Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error. Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, that of Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), Monte Carlo Markov Chain (MCMC), and the original Box Particle Filter (BPF). The algorithm outperforms existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty. The BRPF reduces the computational load by 73% and 90% for SIR-PF and MCMC, respectively, with similar RMSE values. This work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods.The first stage in any control system is to be able to accurately estimate the system’s state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems.Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error.Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, the Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), the Markov Chain Monte Carlo approach (MCMC), and the original Box Particle Filter (BPF). The algorithm is demonstrated to outperform existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty.The BRPF yields a computational load reduction of 73% with respect to the SIR-PF and of 90% with respect to MCMC for similar RMSE orders of magnitude. The present work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods

Nonlinear Estimation of Sensor Faults With Unknown Dynamics for a Fixed Wing Unmanned Aerial Vehicle

International audienceIn this paper, the estimation of additive inertial navigation sensor faults with unknown dynamics is considered with application to the longitudinal navigation and control of a fixed wing unmanned aerial vehicle. The faulty measurement is on the pitch angle. A jump Markov regularized particle filter is proposed for fault and state estimation of the nonlinear aircraft dynamics, with a Markovian jump strategy to manage the probabilistic transitions between the fault free and faulty modes. The jump strategy uses a small number of sentinel particles to continue testing the alternate hypothesis under both fault free and faulty modes. The proposed filter is shown to outperform the regularized particle filter for this application in terms of fault estimation accuracy and convergence time for scenarios involving both abrupt and incipient faults, without prior knowledge of the fault models. The state estimation is also more accurate and robust to faults using the proposed approach. The root-mean-square error for the altitude is reduced by 77 % using the jump Markov regularized particle filter under a pitch sensor fault amplitude of up to 10 degrees. Performance enhancement compared to the regularized particle filter was found to be more pronounced when fault amplitudes increase

Simultaneous Actuator and Sensor Faults Estimation for Aircraft Using a Jump-Markov Regularized Particle Filter

International audienceThe advances in aircraft autonomy have led to an increased demand for robust sensor and actuator fault detection and estimation methods in challenging situations including the onset of ambiguous faults. In this paper, we consider potential simultaneous fault on sensors and actuators of an Unmanned Aerial Vehicle. The faults are estimated using a Jump-Markov Regularized Particle Filter. The jump Markov decision process is used within a regularized particle filter structure to drive a small subset of particles to test the likelihood of the alternate hypothesis to the current fault mode. A prior distribution of the fault is updated using innovations based on predicted control and measurements. Fault scenarios were focused on cases when the impacts of the actuator and sensor faults are similar. Monte Carlo simulations illustrate the ability of the approach to discriminate between the two types of faults and to accurately and rapidly estimate them. The states are also accurately estimated

Adaptive Approximate Bayesian Computational Particle Filters for Underwater Terrain Aided Navigation

International audienceTo perform long-term and long-range missions, underwater vehicles need reliable navigation algorithms. This paper considers multi-beam Terrain Aided Navigation which can provide a drift-free navigation tool. This leads to an estimation problem with implicit observation equation and unknown likelihood. Indeed, the measurement sensor is considered to be a numerical black box model that introduces some unknown stochastic noise. We introduce a measurement updating procedure based on an adaptive kernel derived from Approximate Bayesian Computational filters. The proposed method is based on two well-known particle filters: Regularized Particle Filter and Rao-Blackwellized Particle Filter. Numerical results are presented and the robustness is demonstrated with respect to the original filters, yielding to twice as less non-convergence cases. The proposed method increases the robustness of particle-like filters while remaining computationally efficient

Navigation à l'aide d'un gravimètre atomique

International audienceCold atom interferometer is a promising technology to obtain a highly sensitive and accurate absolute gravimeter. With the help of an anomalies gravity map, local measurements of gravity allow a terrain-based navigation. This paper follows the one we published in Fusion 2017. Based on an atomic gravimeter we present a method to map the gravity anomaly. We propose a modification of the Laplace-based particle filter so as to make it more robust. Some simulation results demonstrate a better robustness of the proposed filter.L'interférométrie à atomes froids est une technologie prometteuse pour obtenir un gravimètre absolu de grande sensibilité et précision. A partir d'une carte d'anomalies gravimétriques, la mesure locale de la gravité permet une navigation par corrélation de terrain. Ce papier fait suite à celui publié au congrès Fusion 2017. Nous présentons une méthode d'élaboration de cartes d’anomalies gravimétriques à partir du gravimètre atomique. Nous proposons une modification du filtre Particulaire de Laplace qui offre une meilleure robustesse. Des résultats de simulation montrent une meilleure robustesse de ce filtre

Adaptive Approximate Bayesian Computational Particle Filters for Underwater Terrain Aided Navigation

International audienceTo perform long-term and long-range missions, underwater vehicles need reliable navigation algorithms. This paper considers multi-beam Terrain Aided Navigation which can provide a drift-free navigation tool. This leads to an estimation problem with implicit observation equation and unknown likelihood. Indeed, the measurement sensor is considered to be a numerical black box model that introduces some unknown stochastic noise. We introduce a measurement updating procedure based on an adaptive kernel derived from Approximate Bayesian Computational filters. The proposed method is based on two well-known particle filters: Regularized Particle Filter and Rao-Blackwellized Particle Filter. Numerical results are presented and the robustness is demonstrated with respect to the original filters, yielding to twice as less non-convergence cases. The proposed method increases the robustness of particle-like filters while remaining computationally efficient

Nouvelles méthodes en filtrage particulaire-Application au recalage de navigation inertielle par mesures altimétriques

In this report, the aim is to develop and study a new particle filter called «The Kalman-Particle Kernel Filter (KPKF)». The KPKF represents the conditional density of the state as a mixture of n-dimensional gaussian densities each centered on a particle and having a small covariance matrix. The algorithm corrects the system state both by a Kalman-type correction and a particle-type correction, by changing the particle weights. In addition an original resampling method is performed to keep the appropriate properties of gaussian mixture. The KPKF combines advantages of the Regularized Particle Filter (RPF) in term of robustness and of the Extended Kalman Filter (EKF) in term of accuracy. This new method of filtering is applied to inertial navigation update of an aircraft equipped with a radar altimeter. The results show a good behaviour of the KPKF for a large initial uncertainty of the aircraft?s position.L'objectif de ce mémoire est de développer et d'étudier un nouveau type de filtre particulaire appelé le filtre de Kalman-particulaire à noyaux (KPKF). Le KPKF modélise la densité conditionnelle de l'état comme un mélange de gaussiennes centrées sur les particules et ayant des matrices de covariance de norme petite. L'algorithme du KPKF utilise une correction de l'état de type Kalman et une correction de type particulaire modifiant les poids des particules. Un nouveau type de ré-échantillonnage permet de préserver la structure de cette mixture. Le KPKF combine les avantages du filtre particulaire régularisé en terme de robustesse et du filtre de Kalman étendu en terme de précision. Cette nouvelle méthode de filtrage a été appliquée au recalage de navigation inertielle d'un aéronef disposant d'un radio altimètre. Les résultats obtenus montrent que le KPKF fonctionne pour de grandes zones d'incertitude initiale de position