Abstract We propose a new framework that extends the standard Probability Hypothesis Density (PHD) filter for multiple targets having N ⩾ 2 different types based on Random Finite Set theory, taking into account not only background clutter, but also confusions among detections of different target types, which are in general different in character from background clutter. Under Gaussianity and linearity assumptions, our framework extends the existing Gaussian mixture (GM) implementation of the standard PHD filter to create a N-type GM-PHD filter. The methodology is applied to real video sequences by integrating object detectors’ information into this filter for two scenarios. For both cases, Munkres’s variant of the Hungarian assignment algorithm is used to associate tracked target identities between frames. This approach is evaluated and compared to both raw detection and independent GM-PHD filters using the Optimal Sub-pattern Assignment metric and discrimination rate. This shows the improved performance of our strategy on real video sequences.
To address the problems of increasing complexity, a unified framework that directly extends single to multiple target tracking by representing multi-target states and observations as RFS was developed by Mahler @cite_42 . This estimates the states and cardinality of an unknown and time varying number of targets in the scene, and allows for target birth, death, handles clutter (false alarms) and missing detections. Mahler propagated the first-order moment of the multi-target posterior, called the Probability Hypothesis Density (PHD), rather than the full multi-target posterior.
@cite_42
2127929072 2143073828 2014787937 2150440166
Bayesian single-target tracking techniques can be extended to a multiple-target environment by viewing the multiple-target state as a random finite set, but evaluating the multiple-target posterior distribution is currently computationally intractable for real-time applications. A practical alternative to the optimal Bayes multitarget filter is the probability hypothesis density (PHD) filter, which propagates the first-order moment of the multitarget posterior instead of the posterior distribution itself. It has been shown that the PHD is the best-fit approximation of the multitarget posterior in an information-theoretic sense. The method avoids the need for explicit data association, as the target states are viewed as a single global target state, and the identities of the targets are not part of the tracking framework. Sequential Monte Carlo approximations of the PHD using particle filter techniques have been implemented, showing the potential of this technique for real-time tracking applications. This paper presents mathematical proofs of convergence for the particle filtering algorithm and gives bounds for the mean-square error This paper describes a probabilistic multiple-hypothesis framework for tracking highly articulated objects. In this framework, the probability density of the tracker state is represented as a set of modes with piecewise Gaussians characterizing the neighborhood around these modes. The temporal evolution of the probability density is achieved through sampling from the prior distribution, followed by local optimization of the sample positions to obtain updated modes. This method of generating hypotheses from state-space search does not require the use of discrete features unlike classical multiple-hypothesis tracking. The parametric form of the model is suited for high dimensional state-spaces which cannot be efficiently modeled using non-parametric approaches. Results are shown for tracking Fred Astaire in a movie dance sequence. The theoretically optimal approach to multisensor-multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. Even in single-target problems, this optimal filter is so computationally challenging that it must usually be approximated. Consequently, multitarget Bayes filtering will never be of practical interest without the development of drastic but principled approximation strategies. In single-target problems, the computationally fastest approximate filtering approach is the constant-gain Kalman filter. This filter propagates a first-order statistical moment - the posterior expectation - in the place of the posterior distribution. The purpose of this paper is to propose an analogous strategy for multitarget systems: propagation of a first-order statistical moment of the multitarget posterior. This moment, the probability hypothesis density (PHD), is the function whose integral in any region of state space is the expected number of targets in that region. We derive recursive Bayes filter equations for the PHD that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets. We also show that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense. The problem of associating data with targets in a cluttered multi-target environment is discussed and applied to passive sonar tracking. The probabilistic data association (PDA) method, which is based on computing the posterior probability of each candidate measurement found in a validation gate, assumes that only one real target is present and all other measurements are Poisson-distributed clutter. In this paper, a new theoretical result is presented: the joint probabilistic data association (JPDA) algorithm, in which joint posterior association probabilities are computed for multiple targets (or multiple discrete interfering sources) in Poisson clutter. The algorithm is applied to a passive sonar tracking problem with multiple sensors and targets, in which a target is not fully observable from a single sensor. Targets are modeled with four geographic states, two or more acoustic states, and realistic (i.e., low) probabilities of detection at each sample time. A simulation result is presented for two heavily interfering targets illustrating the dramatic tracking improvements obtained by estimating the targets' states using joint association probabilities.