Deterministic Gaussian Particles in Non-Linear MaximumLikelihood EstimationApplication to optimal Filtering of Radar and GPS Signals ; Particules Gaussiennes d´eterministes en Maximum de vraisemblance Non-lineaire :Application au Filtrage Optimal des Signaux Radar et GPS

Abstract

National audience ; Particle filter is now a well-knwon numeric solution for the non-linear estimation problem. Based on a reinterpretation of Stratonovich non- linear filtering equation as the generator of branching process, it provides a general finite-dimensionnal solution to the non-linear filtering problem. Previous improvement of the method point out, in one hand, the ben- efit of gaussian particles for the state space dynamic representation, and in the other one, the economy of the deterministic sampling, specially in the maximum likelihood case. We therefore present here a maximum likelihood deterministic particle filter generalized to the continous state space case, using extended Gauss particles. This particle filter was completed with optimization steps, such as non-overlapping selection to guarantee optimal use of computational resources. Besides deterministic particle filter description first part of this report present a "non-exhaustive" survey of non-linear filtering methods and par- ticulary "Random" particles ones. High performances of the proposed filtering method is illustrated through two applications of interest: " Radar detection and tracking of manoeuvring target: where perfor- mances are studied, untill real data provided by military experimen- tations, and compared to "random" particles ones. " GPS receiver: where tracking problem is firstly adressed under high dynamic noises. Then acquisition one is solved with similar dynam- ics constraints by a modified signal processing structure. ; Le filtre particulaire "aléatoire", bien connu aujourd'hui, est basé sur une interprétation par processus de branchement du générateur de filtrage non-linéaire. Sa généralité permet d'aborder tout problème d'estimation dynamique sans restriction concernant la nature des équations d'état ou des densités de probabilité. Cette technique procède par simulation numérique aléatoire des flots du système dynamique au moyen de particules de Dirac, corrigées par les observations et adaptées à l'évolution des ...