A Multi-Scan Labeled Random Finite Set Model for Multi-object State Estimation

State space models in which the system state is a finite set--called the multi-object state--have generated considerable interest in recent years. Smoothing for state space models provides better estimation performance than filtering by using the full posterior rather than the filtering density. In multi-object state estimation, the Bayes multi-object filtering recursion admits an analytic solution known as the Generalized Labeled Multi-Bernoulli (GLMB) filter. In this work, we extend the analytic GLMB recursion to propagate the multi-object posterior. We also propose an implementation of this so-called multi-scan GLMB posterior recursion using a similar approach to the GLMB filter implementation

A Consistent Metric for Performance Evaluation of Multi-Object Filters

The concept of a miss-distance, or error, between a reference quantity and its estimated/controlled value, plays a fundamental role in any filtering/control problem. Yet there is no satisfactory notion of a miss-distance in the well-established field of multi-object filtering. In this paper, we outline the inconsistencies of existing metrics in the context of multi-object miss-distances for performance evaluation. We then propose a new mathematically and intuitively consistent metric that addresses the drawbacks of current multi-object performance evaluation metrics

Bayesian Filtering With Random Finite Set Observations

This paper presents a novel and mathematically rigorous Bayes’ recursion for tracking a target that generates multiple measurements with state dependent sensor field of view and clutter. Our Bayesian formulation is mathematically well-founded due to our use of a consistent likelihood function derived from random finite set theory. It is established that under certain assumptions, the proposed Bayes’ recursion reduces to the cardinalized probability hypothesis density (CPHD) recursion for a single target. A particle implementation of the proposed recursion is given. Under linear Gaussian and constant sensor field of view assumptions, an exact closed-form solution to the proposed recursion is derived, and efficient implementations are given. Extensions of the closed-form recursion to accommodate mild nonlinearities are also given using linearization and unscented transforms

A Generalized Labeled Multi-Bernoulli filter for maneuvering targets

A multiple maneuvering target system can be viewed as a Jump Markov System (JMS) in the sense that the target movement can be modeled using different motion models where the transition between the motion models by a particular target follows a Markov chain probability rule. This paper describes a Generalized Labelled Multi-Bernoulli (GLMB) filter for tracking maneuvering targets whose movement can be modeled via such a JMS. The proposed filter is validated with two linear and nonlinear maneuvering target tracking examples

The Cardinality Balanced Multi-Target Multi-Bernoulli Filter and Its Implementations

It is shown analytically that the multi-target multi- Bernoulli (MeMBer) recursion, proposed by Mahler, has a significant bias in the number of targets. To reduce the cardinality bias, a novel multi-Bernoulli approximation to the multi-target Bayes recursion is derived. Under the same assumptions as the MeMBer recursion, the proposed recursion is unbiased. In addition, a sequential Monte Carlo (SMC) implementation (for generic models) and a Gaussian mixture (GM) implementation (for linear Gaussian models) are proposed. The latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform