Bernard Joseph

Jeffrey's divergence for state-space model comparison

Optimal filters such as Kalman filters are used in a wide range of applications from speech enhancement to biomedical applications. They are based on an a priori state-space model describing a dynamic system. If this model is not well-suited, the accuracy of the state vector may be poor. Therefore, several estimators based on different models can be combined. However, state-space models that are dissimilar enough must be chosen. To our knowledge, there are no guidelines to select them, we hence address this issue in this paper. Given an initial model set, our aim is to determine subsets of similar models by using Jeffrey?s divergence between the distributions of the state-vector time paths based on the different models. Our approach operates with the following steps: the so-called dissimilarity matrix composed of Jeffrey?s divergences between model pairs is created. Then, this matrix is transformed to get the same properties as a correlation matrix and an eigenvalue decomposition is performed. Subsequently, we propose an interpretation of the predominant eigenvalues which is then used to deduce the number of model subsets and their cardinals. A classification algorithm can then be considered to determine which models belong to which subsets. HighlightsWe propose to compare two state models by using the Jeffreys divergence (JD).We generalize the above approach to determine subsets in an initial model set.The eigenvalues decomposition is then interpreted to deduce the number of model subsets.Then, a classification algorithm can be used to determine which model belongs to which subset.The method is more particularly applied to a toy example and to tracking.

Classifying several state models using Jeffrey's divergence: Application to target tracking

One of the most important challenges when applying multiple-model approaches is model-set design. However, to our knowledge, there are not general rules to choose models. For this purpose, we recently proposed an approach based on the Jeffreys divergence to characterize dissimilarities between two state models. In this paper, our contribution is to use the Jeffreys divergence to classify at least two models into subsets. Our approach consists in creating a dissimilarity matrix composed of Jeffreys divergences between model pairs. Then, we transform this matrix to get a correlation-like matrix and an eigenvalue decomposition is computed. We propose an interpretation of the predominant eigenvalues and use it to deduce the number of model subsets and their cardinals. Finally, a classification algorithm can be considered to determine which models belong to which subsets. Among the applications, we focus on target tracking.

Classifying autoregressive models using dissimilarity measures: A comparative study

Autoregressive (AR) models are used in various applications, from speech processing to radar signal analysis. In this paper, our purpose is to extract different model subsets from a set of two or more AR models. The approach operates with the following steps: firstly the matrix composed of dissimilarity measures between AR-model pairs are created. This can be based on the symmetric Itakura divergence, the symmetric Itakura-Saito divergence, the log-spectral distance or Jeffreys divergence (JD), which corresponds to the symmetric version of the Kullback-Leibler divergence. These matrices are then transformed to get the same properties as correlation matrices. Eigenvalue decompositions are performed to get the number of AR-model subsets and the estimations of their cardinals. Finally, K-means are used for classification. A comparative study points out the relevance of the JD-based method. Illustrations with sea radar clutter are also provided.

Design of a multi-resolution phase-coded waveform in the presence of a colored Gaussian clutter

In current airborne radars, detection and identification are done with two distinct waveforms. However, while the radar switches from one function to another, the target scene can change. In this paper, we propose a hybrid waveform combining intra and interpulse phase codes. This waveform is first processed in a low-resolution “channel”. Then, if a target is detected, the received signal is reprocessed in a high-resolution “channel”. Given the above scenario and assuming that the received data are disturbed by a colored Gaussian clutter, we address the optimization of the phase codes by searching the Pareto front of a multi-objective optimization problem. Finally, we aim at analyzing the sensitivity of the Pareto front to the clutter properties. For this purpose, we study whether a first-order autoregressive (AR) modelling for the clutter in the high-resolution case is relevant or not.

Multi-target tracking using a PHD-based joint tracking and classification algorithm

When using Bayesian estimation techniques for target tracking, the algorithm accuracy is induced by the choice of the system evolution model. Information on the type of target and its maneuver capability can then be helpful to choose relevant motion models. Joint tracking and classification (JTC) methods based on target features have thus been introduced. Among them, we recently proposed to take into account the target extent measurements for single-target tracking. In this paper, we extend this work to multi-target tracking (MTT) by using probability hypothesis density (PHD) filters. More precisely, assuming that each target class is characterized by its own kinematic-model set, a multiple-model (MM) PHD filter is used for each class. State estimates from each class are then combined by using class probabilities. Finally, the proposed approach, namely a multiclass MM-GMPHD, is applied to maritime-target tracking and simulation results show the relevance of the proposed approach regarding the tracking of various types of targets.

Bayesian non-parametric methods for dynamic state-noise covariance matrix estimation

When using Bayesian estimation techniques, the algorithm is strongly sensitive to the system evolution model and more particularly to the setting of the state-noise covariance matrix. Recently, Bayesian non-parametric models and in particular Dirichlet processes (DPs) have been proposed as a scalable solution to this issue. They assume that the system can switch between an infinite number of state-space representations corresponding to different values of the state-noise covariance matrix. In this framework, jointly estimating the state vector and the covariance matrix is a non-linear non-Gaussian problem. The inference is thus classically carried out using particle filtering techniques. In this case, the choice of the proposal distribution for the particles is of paramount importance regarding the estimation accuracy. A first contribution of this paper is to derive an approximation of the optimal proposal distribution of the particle filter when a DP prior is placed on the distribution of the state-noise covariance matrix. Then, an alternative DP-based formulation of the inference problem is proposed to reduce its dimensionality. It takes advantage that the possible functional forms of the state-noise covariance matrices are known up to a reduced number of time-switching hyperparameters in many applications. An approximation of the optimal proposal distribution is also derived. Finally, the relevance of both proposed approaches is analyzed in the framework of target tracking and a comparative study with existing methods is carried out. HighlightsWe address the joint estimations of the state vector and the state-noise covariance matrix.We use Bayesian non-parametric methods implemented by particle filtering.Two approaches are presented.In both cases, the optimal proposal distribution is derived.Both proposed algorithms are applied to target tracking.

Dirichlet-process-mixture-based Bayesian nonparametric method for Markov switching process estimation

Dirichlet process (DP) mixtures were recently introduced to deal with switching linear dynamical models (SLDM). They assume the system can switch between an a priori infinite number of state-space representations (SSR) whose parameters are on-line inferred. The estimation problem can thus be of high dimension when the SSR matrices are unknown. Nevertheless, in many applications, the SSRs can be categorized in different classes. In each class, the SSRs are characterized by a known functional form but differ by a reduced set of unknown hyperparameters. To use this information, we thus propose a new hierarchical model for the SLDM wherein a discrete variable indicates the SSR class. Conditionally to this class, the distributions of the hyperparameters are modeled by DPs. The estimation problem is solved by using a Rao-Blackwellized particle filter. Simulation results show that our model outperforms existing methods in the field of target tracking.

Bernoulli filter based algorithm for joint target tracking and classification in a cluttered environment

In this paper, single-target tracking using radar measurements is addressed. Recently, algorithms based on Bernoulli random finite sets have proved efficient in a cluttered environment. However, in Bayesian approaches, the choice of the motion model impacts the trajectory estimation accuracy. To select an appropriate set of motion models, a joint tracking and classification (JTC) algorithm can be used. The principle is to consider different target classes depending on their maneuvrability, each of them being associated to a set of motion models. In this context, additional information such as a target length extent measurement can improve both classification and trajectory estimation. Therefore, we propose a multiple-model Bernoulli filter to perform JTC. To jointly estimate the trajectory and the target length which is constant, a Rao-Blackwellized approach is considered. Another contribution is that a bank of probabilistic data association filters is run instead of Kalman filters to account for false detections.

Analysis of a GLRT for the detection of an extended target

For a high-resolution radar, an extended target is characterized by a few main scatterers spread over several range gates not necessarily consecutive. The joint detections and localizations of these scatterers are of particular interest in order to estimate the range profile and identify the target. In this paper, we study a detector based on the Generalized Likelihood Ratio Test considering the unknown locations of the scatterers. Given the number of scatterers and using order statistics results, we derive approximations of the probability of false alarm and the probability of detection and localization which can be a relevant measure of performance in this context. Finally, a comparative study is carried out with other existing detectors.