We investigate the problem of bearings-only tracking of manoeuvring targets using particle filters (PFs). Three different (PFs) are proposed for this problem which is formulated as a multiple model tracking problem in a jump Markov system (JMS) framework. The proposed filters are (i) multiple model PF (MMPF), (ii) auxiliary MMPF (AUX-MMPF), and (iii) jump Markov system PF (JMS-PF). The performance of these filters is compared with that of standard interacting multiple model (IMM)-based trackers such as IMM-EKF and IMM-UKF for three separate cases: (i) single-sensor case, (ii) multisensor case, and (iii) tracking with hard constraints. A conservative CRLB applicable for this problem is also derived and compared with the RMS error performance of the filters. The results confirm the superiority of the PFs for this difficult nonlinear tracking problem.

This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.

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.

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.

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.

The context is sensor control for multi-object Bayes filtering in the framework of partially observed Markov decision processes (POMDPs). The current information state is represented by the multi-object probability density function (pdf), while the reward function associated with each sensor control (action) is the information gain measured by the alpha or Rényi divergence. Assuming that both the predicted and updated state can be represented by independent identically distributed (IID) cluster random finite sets (RFSs) or, as a special case, the Poisson RFSs, this work derives the analytic expressions of the corresponding Rényi divergence based information gains. The implementation of Rényi divergence via the sequential Monte Carlo method is presented. The performance of the proposed reward function is demonstrated by a numerical example, where a moving range-only sensor is controlled to estimate the number and the states of several moving objects using the PHD filter.