Riemann-Langevin Particle Filtering in Track-Before-Detect

Track-before-detect (TBD) is a powerful approach that consists in providing the tracker with sensor measurements directly without pre-detection. Due to the measurement model non-linearities, online state estimation in TBD is most commonly solved via particle filtering. Existing particle filters for TBD do not incorporate measurement information in their proposal distribution. The Langevin Monte Carlo (LMC) is a sampling method whose proposal is able to exploit all available knowledge of the posterior (that is, both prior and measurement information). This letter synthesizes recent advances in LMC-based filtering to describe the Riemann-Langevin particle filter and introduces its novel application to TBD. The benefits of our approach are illustrated in a challenging low-noise scenario.Comment: Minor grammatical update

Labeled Random Finite Sets in Multi-target Track-Before-Detect

In this paper we address the problem of tracking multiple targets based on raw measurements by means of Particle filtering. Bayesian multitarget tracking, in the Random Finite Set framework, propagates the multitarget posterior density recursively in time. Sequential Monte Carlo (SMC) approximations of the optimal filter are computationally expensive and lead to high-variance estimates as the number of targets increases. We propose a novel, efficient and reliable Labeled RFS based tracking algorithms suitable for, among others, the TBD surveillance application. This algorithm uses the Interacting Population based MCMC-PF (IP-MCMC-PF), first introduced in [6], as the core engine of a Multiple Cardinality Hypotheses Tracker (MCHT), where each cardinality is treated independently. The proposed multi-target filter is built upon the concept of labeled Random Finite Set (RFS) [40], [41], and formally incorporates the propagation and estimation of track labels within the RFS filtering framework. Simulation analyses demonstrate that the proposed Multiple Cardinality Hypotheses Particle Filter (MCHPF) yields higher consistency, accuracy and reliability in multitarget tracking. I

Multitarget tracking with IP reversible jump MCMC-PF

In this paper we address the problem of tracking multiple targets based on raw measurements by means of Particle filtering. Bayesian multitarget tracking, in the Random Finite Set framework, propagates the multitarget posterior density recursively in time. Sequential Monte Carlo (SMC) approximations of the optimal filter are computationally expensive and lead to high-variance estimates as the number of targets increases. We present an extension of the Interacting Population-based MCMC-PF (IP-MCMC-PF) [1]. This extension exploits reversible jumps. Incorporation of Reversible Jump MCMC (RJMCMC) [2] methods into a tracking framework gives the possibility to deal with multiple appearing and disappearing targets, and makes the statistical inference more tractable. In our case, the technique is adopted to efficiently solve the high-dimensional state estimation problem, where the estimation of the existence and positions of many targets from a sequence of noisy measurements is required. Simulation analyses demonstrate that the proposed IP-RJMCMC-PF yields higher consistency, accuracy and reliability in multitarget tracking

Langevin Monte Carlo filtering for target tracking

This paper introduces the Langevin Monte Carlo Filter (LMCF), a particle filter with a Markov chain Monte Carlo algorithm which draws proposals by simulating Hamiltonian dynamics. This approach is well suited to non-linear filtering problems in high dimensional state spaces where the bootstrap filter requires an impracticably large number of particles. The simulation of Hamiltonian dynamics is motivated by leveraging more model knowledge in the proposal design. In particular, the gradient of the posterior energy function is used to draw new samples with high probability of acceptance. Furthermore, the introduction of auxiliary variables (the so-called momenta) ensures that new samples do not collapse at a single mode of the posterior density. In comparison with random-walk Metropolis, the LMC algorithm has been proven more efficient as the state dimension increases. Therefore, we are able to verify through experiments that our LMCF is able to attain multi-target tracking using small number of particles when other MCMC-based particle filters relying on random-walk Metropolis require a considerably larger particle number. As a conclusion, we claim that performing little additional work for each particle (in our case, computing likelihood energy gradients) turns out to be very effective as it allows to greatly reduce the number of particles while improving tracking performance

Advanced IP-MCMC-PF design ingredients

This paper proposes techniques to improve the properties of Sequential Markov Chain Monte Carlo (SMCMC) methods in the context of multi-target tracking. In particular, we extend the Interacting Population-based MCMC Particle Filter (IP-MCMC-PF) with three different methods: delayed rejection, genetic algorithms, and simulated annealing. Each of these methods furnishes the IP-MCMC-PF algorithm with different theoretical guarantees which are empirically analysed in this paper. Firstly, the use of delayed rejection in the Metropolis-Hastings (MH) samplers is proposed in order to reduce the asymptotic variance of the estimate. Secondly, the crossover operator, inspired by genetic algorithms, is presented as a mechanism to increase the interaction of the MH samplers. Thus, attaining fast convergence of the time-consuming MCMC step. Thirdly, simulated annealing is introduced with the goal of increasing the robustness of the algorithm against divergence due to e.g. poor initialisations. Finally, the results from our experiments show that the proposed methods strengthen the multi-target tracker in the aforementioned aspects

Optimisation d'un filtre particulaire en contexte track-before-detect

National audienceIn this paper, we are concerned with the detection and tracking of a target in TBD context. We propose here an efficient particle filter based on a relevant proposal density justified by radar detection considerations. This filter performs well compared to the classical laws used in the literature, especially in terms of speed of convergence for detection. We also identify a minimum number of particles required to ensure interesting detection performance.Dans cet article, nous nous intéressons à la détection et au pistage d'une cible en contexte Track-Before-Detect (TBD). Nous proposons ici un filtre particulaire efficace, fondé sur le choix d'une loi instrumentale pertinente motivée par des considérations de détection radar et permettant un gain significatif par rapport aux lois classiquement utilisées dans la littérature, notamment en terme de rapidité de convergence du filtre pour la détection. Nous déterminons également un nombre minimal de particules requis pour garantir des performances de détection intéressantes