Labeled Random Finite Set

—Most tracking algorithms in the literature assume that the targets always generate measurements independently of each other, i.e. the sensor is assumed to have infinite resolution. Such algorithms have been dominant because addressing the presence of merged measurements increases the computational complexity of the tracking problem, and limitations on computing resources often make this infeasible. When merging occurs, these algorithms suffer degraded performance, often due to tracks being terminated too early. In this paper, we use the theory of random finite sets (RFS) to develop a principled Bayesian solution to tracking an unknown and variable number of targets in the presence of merged measurements. We propose two tractable implementations of the resulting filter, with differing computational requirements. The performance of these algorithms is demonstrated by Monte Carlo simulations of a multi-target bearings-only scenario, where measurements become merged due to the effect of finite sensor resolution.

—This paper proposes a generalization of the multi-Bernoulli filter called the labeled multi-Bernoulli filter that outputs target tracks. Moreover, the labeled multi-Bernoulli filter does not exhibit a cardinality bias due to a more accurate update approximation compared to the multi-Bernoulli filter by exploiting the conjugate prior form for labeled Random Finite Sets. The proposed filter can be interpreted as an efficient approximation of the δ-Generalized Labeled Multi-Bernoulli filter. It inherits the advantages of the multi-Bernoulli filter in respect of particle implementation and state estimation. It also inherits advantages of the δ-Generalized Labeled Multi-Bernoulli filter in that it outputs (labeled) target tracks and achieves better performance.

—An analytic solution to the multi-target Bayes re-cursion known as the δ-Generalized Labeled Multi-Bernoulli (δ-GLMB) filter has been recently proposed in [1]. As a sequel to [1], this paper details efficient implementations of the δ-GLMB multi-target tracking filter. Each iteration of this filter involves an update operation and a prediction operation, both of which result in weighted sums of multi-target exponentials with intractably large number of terms. To truncate these sums, the ranked assignment and K-th shortest path algorithms are used in the update and prediction, respectively, to determine the most significant terms without exhaustively computing all of the terms. In addition, using tools derived from the same framework, such as probability hypothesis density filtering, we present inexpensive (relative to the δ-GLMB filter) look-ahead strategies to reduce the number of computations. Characterization of the L1-error in the multi-target density arising from the truncation is presented.

The δ-generalized labeled multi-Bernoulli (δ-GLMB) tracker is the first multiple hypothesis tracking (MHT)-like tracker that is provably Bayes-optimal. However, in its basic form, the δ-GLMB provides no mechanism for adaptively initializing targets at their first appearance from unlabeled measurements. By introducing a new multitarget likelihood function that accounts for new target appearance, a data-driven δ-GLMB tracker is derived that automatically initializes new targets in the tracker measurement update. Monte Carlo results of simulated multitarget tracking problems demonstrate improved multitarget tracking accuracy over comparable adaptive birth methods.

—In multi-object inference, the multi-object probability density captures the uncertainty in the number and the states of the objects as well as the statistical dependence between the objects. Exact computation of the multi-object density is generally intractable and tractable implementations usually require statistical independence assumptions between objects. In this paper we propose a tractable multi-object density approximation that can capture statistical dependence between objects. In particular, we derive a tractable Generalized Labeled Multi-Bernoulli (GLMB) density that matches the cardinality distribution and the first moment of the labeled multi-object distribution of interest. It is also shown that the proposed approximation minimizes the Kullback-Leibler divergence over a special tractable class of GLMB densities. Based on the proposed GLMB approximation we further demonstrate a tractable multi-object tracking algorithm for generic measurement models. Simulation results for a multi-object Track-Before-Detect example using radar measurements in low signal-to-noise ratio (SNR) scenarios verify the applicability of the proposed approach.

—We propose a Bayesian multi-target batch processing algorithm capable of tracking an unknown number of targets that move close and/or cross each other in a dense clutter environment. The optimal Bayes multi-target tracking problem is formulated in the random finite set framework and a Particle Marginal Metropolis-Hastings (PMMH) technique which is a combination of Metropolis-Hastings (MH) algorithm and sequential Monte Carlo methods is applied to compute the multi-target posterior distribution. The PMMH technique is used to design a high dimensional proposal distributions for the MH algorithm and allows the proposed batch process multi-target tracker to handle a large number of tracks in a computationally feasible manner. Our simulations show that the proposed tracker reliably estimates the number of tracks and their trajectories in scenarios with a large number of closely spaced tracks in a dense clutter environment albeit, more expensive than on-line methods.

—The objective of multi-object estimation is to simultaneously estimate the number of objects and their states from a set of observations in the presence of data association uncertainty, detection uncertainty, false observations and noise. This estimation problem can be formulated in a Bayesian framework by modeling the (hidden) set of states and set of observations as random finite sets (RFSs) that covers thinning, Markov shifts and superposition. A prior for the hidden RFS together with the likelihood of the realization of the observed RFS gives the posterior distribution via the application of Bayes rule. We propose a new class of RFS distributions that is conjugate with respect to the multi-object observation likelihood and closed under the Chapman-Kolmogorov equation. This result is tested via a Bayesian multi-target tracking example.