François Septier

Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced.

The Gaussian mixture MCMC particle algorithm for dynamic cluster tracking

We present a new filtering algorithm for tracking multiple clusters of coordinated targets. Based on a Markov Chain Monte Carlo (MCMC) mechanism, the new algorithm propagates a discrete approximation of the underlying filtering density. A dynamic Gaussian mixture model is utilized for representing the time-varying clustering structure. This involves point process formulations of typical behavioral moves such as birth and death of clusters as well as merging and splitting. Following our previous work, we adopt here two strategies for increasing the sampling efficiency of the basic MCMC scheme: an evolutionary stage which allows improved exploration of the sample space, and an EM-based method for making optimized proposals based on the frame likelihood. The algorithms performance is assessed and demonstrated in both synthetic and real tracking scenarios.

On MCMC-Based particle methods for Bayesian filtering: Application to multitarget tracking

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. In this context, one of the most successful and popular approximation techniques is sequential Monte Carlo (SMC) methods, also known as particle filters. Nevertheless, these methods tend to be inefficient when applied to high dimensional problems. In this paper, we present an overview of Markov chain Monte Carlo (MCMC) methods for sequential simulation from posterior distributions, which represent efficient alternatives to SMC methods. Then, we describe an implementation of this MCMC-Based particle algorithm to perform the sequential inference for multitarget tracking. Numerical simulations illustrate the ability of this algorithm to detect and track multiple targets in a highly cluttered environment.

Monte Carlo Methods for Channel, Phase Noise, and Frequency Offset Estimation With Unknown Noise Variances in OFDM Systems

In this paper, we address the problem of orthogonal frequency-division multiplexing (OFDM) channel estimation in the presence of phase noise (PHN) and carrier frequency offset (CFO). In OFDM systems, PHN and CFO cause two effects: the common phase error (CPE) and the intercarrier interference (ICI) which severely degrade the accuracy of the channel estimate. In literature, several algorithms have been proposed to solve this problem. Nevertheless, in all these existing schemes, both the PHN and the additive white Gaussian noise (AWGN) powers are assumed to be known. Because no a priori knowledge of PHN and AWGN powers is available at the receiver, we propose different strategies for the estimation of channel impulse response (CIR), CFO, PHN, and also the PHN and the AWGN powers. Based on Monte Carlo methods, the proposed approaches estimate these many unknowns in the time domain from a training OFDM symbol using either offline or online estimators. In the online case, we propose sequential Monte Carlo algorithms and especially an original maximization step of the joint a posteriori probability density function for the unknown parameters. Simulation results are provided to illustrate the efficiency of the proposed algorithms in terms of mean square error (MSE) on channel, phase distortions, and also noise power estimation.

Non-Pilot-Aided Sequential Monte Carlo Method to Joint Signal, Phase Noise, and Frequency Offset Estimation in Multicarrier Systems

We address the problem of phase noise (PHN) and carrier frequency offset (CFO) mitigation in multicarrier receivers. In multicarrier systems, phase distortions cause two effects: the common phase error (CPE) and the intercarrier interference (ICI) which severely degrade the accuracy of the symbol detection stage. Here, we propose a non-pilot-aided scheme to jointly estimate PHN, CFO, and multicarrier signal in time domain. Unlike existing methods, non-pilot-based estimation is performed without any decision-directed scheme. Our approach to the problem is based on Bayesian estimation using sequential Monte Carlo filtering commonly referred to as particle filtering. The particle filter is efficiently implemented by combining the principles of the Rao-Blackwellization technique and an approximate optimal importance function for phase distortion sampling. Moreover, in order to fully benefit from time-domain processing, we propose a multicarrier signal model which includes the redundancy information induced by the cyclic prefix, thus leading to a significant performance improvement. Simulation results are provided in terms of bit error rate (BER) and mean square error (MSE) to illustrate the efficiency and the robustness of the proposed algorithm.

Estimation of Spatially Correlated Random Fields in Heterogeneous Wireless Sensor Networks

We develop new algorithms for spatial field reconstruction, exceedance level estimation and classification in heterogeneous (mixed analog & digital sensors) Wireless Sensor Networks (WSNs). We consider spatial physical phenomena which are observed by a heterogeneous WSN, meaning that it consists partially of sparsely deployed high-quality sensors and partially of low-quality sensors. The high-quality sensors transmit their (continuous) noisy observations to the Fusion Centre (FC), while the low-quality sensors first perform a simple thresholding operation and then transmit their binary values over imperfect wireless channels to the FC. The resulting observations are mixed continuous and discrete (1-bit decisions) observations, and are combined in the FC to solve the inference problems. We first formulate the problem of spatial field reconstruction, exceedance level estimation and classification in such heterogeneous networks. We show that the resulting posterior predictive distribution, which is key in fusing such disparate observations, involves intractable integrals. To overcome this problem, we develop an algorithm that is based on a multivariate series expansion approach resulting in a Saddle-point type approximation. We then present comprehensive study of the performance gain that can be obtained by augmenting the high-quality sensors with low-quality sensors using real data of insurance storm surge database known as the Extreme Wind Storms Catalogue.

Tracking of coordinated groups using marginalised MCMC-based Particle algorithm

In this paper, we address the problem of detection and tracking of group and individual targets. In particular, we focus on a group model with a virtual leader which models the bulk or group parameter. To perform the sequential inference, we propose a Markov Chain Monte Carlo (MCMC)-based Particle algorithm with a marginalisation scheme using pairwise Kalman filters. Numerical simulations illustrate the ability of the algorithm to detect and track targets within groups, as well as infer both the correct group structure and the number of targets over time.

Robust visual tracking via MCMC-based particle filtering

We present in this paper a new visual tracking framework based on the MCMC-based particle algorithm. Firstly, in order to obtain a more informative likelihood, we propose to combine the color-based observation model with a detection confidence density obtained from the Histograms of Oriented Gradients (HOG) descriptor. The MCMC-based particle algorithm is then employed to estimate the posterior distribution of the target state to solve the tracking problem. The global system has been tested on different real datasets. Experimental results demonstrate the robustness of the proposed system in several difficult scenarios.

Blind Detection of Severely Blurred 1D Barcode

In this paper, we present a joint blind channel estimation and symbol detection for decoding a blurred and noisy 1D barcode captured image. From an information transmission point of view, we show that the channel impulse response, the noise power and the symbols can be efficiently estimated by taking into account the signal structure such as the cyclostationary property of the hidden Markov process to estimate. Based on the Expectation- Maximisation method, we show that the new algorithm offers significative performance gain compared to classical ones pushing back the frontiers of the barcode technology.

Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms.