Branko Ristic

A Metric for Performance Evaluation of Multi-Target Tracking Algorithms

Performance evaluation of multi-target tracking algorithms is of great practical importance in the design, parameter optimization and comparison of tracking systems. The goal of performance evaluation is to measure the distance between two sets of tracks: the ground truth tracks and the set of estimated tracks. This paper proposes a mathematically rigorous metric for this purpose. The basis of the proposed distance measure is the recently formulated consistent metric for performance evaluation of multi-target filters, referred to as the OSPA metric. Multi-target filters sequentially estimate the number of targets and their position in the state space. The OSPA metric is therefore defined on the space of finite sets of vectors. The distinction between filtering and tracking is that tracking algorithms output tracks and a track represents a labeled temporal sequence of state estimates, associated with the same target. The metric proposed in this paper is therefore defined on the space of finite sets of tracks and incorporates the labeling error. Numerical examples demonstrate that the proposed metric behaves in a manner consistent with our expectations.

Adaptive Target Birth Intensity for PHD and CPHD Filters

The standard formulation of the probability hypothesis density (PHD) and cardinalised PHD (CPHD) filters assumes that the target birth intensity is known a priori. In situations where the targets can appear anywhere in the surveillance volume this is clearly inefficient, since the target birth intensity needs to cover the entire state space. This paper presents a new extension of the PHD and CPHD filters, which distinguishes between the persistent and the newborn targets. This extension enables us to adaptively design the target birth intensity at each scan using the received measurements. Sequential Monte-Carlo (SMC) implementations of the resulting PHD and CPHD filters are presented and their performance studied numerically. The proposed measurement-driven birth intensity improves the estimation accuracy of both the number of targets and their spatial distribution.

A Tutorial on Bernoulli Filters: Theory, Implementation and Applications

Bernoulli filters are a class of exact Bayesian filters for non-linear/non-Gaussian recursive estimation of dynamic systems, recently emerged from the random set theoretical framework. The common feature of Bernoulli filters is that they are designed for stochastic dynamic systems which randomly switch on and off. The applications are primarily in target tracking, where the switching process models target appearance or disappearance from the surveillance volume. The concept, however, is applicable to a range of dynamic phenomena, such as epidemics, pollution, social trends, etc. Bernoulli filters in general have no analytic solution and are implemented as particle filters or Gaussian sum filters. This tutorial paper reviews the theory of Bernoulli filters as well as their implementation for different measurement models. The theory is backed up by applications in sensor networks, bearings-only tracking, passive radar/sonar surveillance, visual tracking, monitoring/prediction of an epidemic and tracking using natural language statements. More advanced topics of smoothing, multi-target detection/tracking, parameter estimation and sensor control are briefly reviewed with pointers for further reading.

Kernel design for time-frequency signal analysis using the Radon transform

The authors present a kernel design technique based on using the Radon transform of the modulus of the ambiguity function of the signal for determination of angles and distances of radially distributed contents of the autoterms in the ambiguity domain. The proposed kernel effectively reduces the cross-terms and noise for linear FM signals. The result is a tool for high-resolution time-frequency representation of nonstationary, primarily linear FM signals. >

Comments on "The Cramer-Rao lower bounds for signals with constant amplitude and polynomial phase

For original paper see IEEE Trans. Signal Processing, vol.39, p.749-52 (March 1991). Different expressions for the Cramer-Rao lower bounds (CRLBs) of constant amplitude polynomial phase signals embedded in white Gaussian noise appear in the literature. The present paper revisits the derivation of the bounds reported by Peleg and Porat (1991) and indicates that the resulting expressions depend on the interval over which the signal is defined. The proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds.

Bernoulli Forward-Backward Smoothing for Joint Target Detection and Tracking

In this correspondence, we derive a forward-backward smoother for joint target detection and estimation and propose a sequential Monte Carlo implementation. We model the target by a Bernoulli random finite set since the target can be in one of two “present” or “absent” modes. Finite set statistics is used to derive the smoothing recursion. Our results indicate that smoothing has two distinct advantages over just using filtering: First, we are able to more accurately identify the appearance and disappearance of a target in the scene, and second, we can provide improved state estimates when the target exists.

Bernoulli Particle/Box-Particle Filters for Detection and Tracking in the Presence of Triple Measurement Uncertainty

This work presents sequential Bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahlers framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements. Two numerical implementations of the optimal filter are developed. The first is the Bernoulli particle filter (PF), which turns out to require a large number of particles in order to achieve a satisfactory performance. For the sake of reduction in the number of particles, the paper also develops an implementation based on box particles, referred to as the Bernoulli Box-PF. A box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space. Manipulation of boxes utilizes the methods of interval analysis. The two implementations are compared numerically and found to perform remarkably well: the target is reliably detected and the posterior probability density function of the target state is estimated accurately. The Bernoulli Box-PF, however, when designed carefully, is computationally more efficient.

Relationship between the polynomial and the higher order Wigner-Ville distribution

The paper establishes the relationship between the two methods of higher order time-frequency analysis: the polynomial Wigner-Ville distribution (WVD) and the higher order WVD. Using the projection-slice theorem, it is shown that the polynomial WVD represents a unique projection of the higher-order WVD from the time-multifrequency space to the time-frequency subspace. The implication of this relationship is investigated from the aspect of the analysis of multicomponent signals.

Radiological Source Detection and Localisation Using Bayesian Techniques

The problem considered in this paper is detection and estimation of multiple radiation sources using a time series of radiation counts from a collection of sensors. A Bayesian framework is adopted. Source detection is approached as a model selection problem in which competing models are compared using partial Bayes factors. Given the number of sources, the posterior mean is the minimum mean square error estimator of the source parameters. Exact calculation of the partial Bayes factors and the posterior mean is not possible due to the presence of intractable integrals. Importance sampling using progressive correction is proposed as a computationally efficient method for approximating these integrals. Previously proposed algorithms have been restricted to one or two sources. A simulation analysis shows that the proposed methods can detect and accurately estimate the parameters of four sources with reasonable computational expense.

Bernoulli Particle Filter with Observer Control for Bearings-Only Tracking in Clutter

The context is autonomous bearings-only tracking of a single appearing/disappearing target in the presence of detection uncertainty (false and missed detections) with observer control. The optimal tracking method for this problem in the sequential Bayesian estimation framework is the Bernoulli filter. Observer control is based on previously acquired measurements and is formulated as a partially observable Markov decision process (POMDP) where future actions are ranked according to their associated reward. The paper develops a sequential Monte Carlo implementation of the Bernoulli filter and the reward based on an information theoretic criterion.