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

Estimation de parametres pour des modeles a erreur bornee

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Estimation ensembliste pour la recherche et le suivi multi-cibles par une flotte de drones

International audienceThis paper presents a set-membership approach for the coordinated control of a fleet of UAVs aiming to search and track an a priori unknown number of targets spread over some delimited geographical area. The originality of the approach lies in the description of the perturbations and measurement uncertainties via bounded sets. A set-membership approach is used to address the localization and tracking problem. At each time step, sets guaranteed to contain the actual state of already localized targets are provided. A set containing the states of targets still to be discovered is also evaluated. These sets are then used to evaluate the control input to apply to the UAVs so as to minimize the estimation uncertainty at the next time step. Simulations considering several UAVs show that the proposed set-membership estimator and the associated control input optimization are able to provide good localization and tracking performance for multiple targets.Cet article présente une approche d'estimation ensembliste permettant de déterminer les lois de commande d'une flotte coordonnée d'UAV's pour rechercher et suivre un nombre a priori inconnu de ciblesréparties sur une zone géographique délimitée. L'originalité de la démarche réside dans la description des perturbations etincertitudes de mesure via des ensembles bornés. Un estimateur ensembliste est utilisé pour résoudre le problème de localisation et de suivi. À chaque pas de temps, les ensembles contenant l'état actuel des cibles déjà localisées est fourni. Un ensemble contenant les états des cibles restant à découvrir est également évalué. Ces ensembles sont ensuite utilisés pour évaluer les lois de commande distribuées à appliquer aux UAV afin de minimiser l'incertitude d'estimation au prochain pas de temps. Des simulations considérant plusieurs UAV illustrent la qualité des performances obtenues pour la localisation et le suivi multi cibles à l'aide de l'estimateur proposé et de la loi de commande associée

New state estimators and communication protocol for distributed event-triggered consensus of linear multi-agent systems with bounded perturbations

International audienceThis paper extends recent results by Garcia et al. on event-triggered communication to reach consensus in multi-agent systems. First, it studies the effect of two types of additive and bounded state perturbations on the consensus and on the communications. Second, it describes an improved agent state estimator as well as an estimator of the state estimation uncertainty to trigger communications. Convergence to consensus is studied. Simulations show the effectiveness of the proposed estimators in presence of state perturbations

Attitude tracking of rigid bodies on the special orthogonal group with bounded partial state feedback

A solution to the attitude tracking problem of rigid bodies with kinematic representation directly on the special orthogonal group SO(3) of rotation matrices is proposed. A dynamic partial state feedback controller is designed to address the case where no angular velocity measurements are available. In addition, the gains in the control design can be tuned in advance to ensure that the torque inputs satisfy arbitrary saturation bounds. Stability conditions are provided based on Lyapunov function analysis and Barbalat's lemma. Simulation results are presented to illustrate the performance of the proposed control scheme