This paper addresses the problem of fixed motion and measurement models for multi-target filtering using an adaptive learning framework. This is performed by defining target tuples with random finite set terminology and utilisation of recurrent neural networks with a long short-term memory architecture. A novel data association algorithm compatible with the predicted tracklet tuples is proposed, enabling the update of occluded targets, in addition to assigning birth, survival and death of targets. The algorithm is evaluated over a commonly used filtering simulation scenario, with highly promising results (https: github.com mehryaragha MTF).
Mahler proposed random finite sets (RFS) formulation for multi-target filtering @cite_5 . RFS provides an encapsulated formulation for multi-target filtering, incorporating clutter density, probabilities of detection, survival and birth of targets @cite_0 @cite_5 @cite_8 . To this end, targets and measurements assume to form sets with variable random cardinalities. Using Finite Set Statistics @cite_5 , the posterior distribution in ) can be extended from vectors to RFS as follows, where @math and @math are measurement (containing both clutter and true positives) and target RFS, respectively, and @math an appropriate reference measure @cite_3 . One approach to represent targets is to use Probability Hypothesis Density (PHD) maps @cite_0 @cite_3 . These maps have two basic features: 1) Their peaks correspond to the location of targets; 2) Their integration gives the expected number of targets at each time step. Vo and Ma proposed Gaussian Mixture PHD (GM-PHD), which propagates the first-order statistical moments to estimate the posterior in ) as a mixture of Gaussians @cite_3 .
@cite_0 @cite_5 @cite_3 @cite_8
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Random finite sets (RFSs) are natural representations of multitarget states and observations that allow multisensor multitarget filtering to fit in the unifying random set framework for data fusion. Although the foundation has been established in the form of finite set statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multitarget filtering is not yet practical due to the inherent computational hurdle. Even the probability hypothesis density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multitarget posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multitarget filter. In addition, an SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving nonlinear nonGaussian dynamics. Convergence results for these filters are also established. 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. An analytic solution to the multi-target Bayes recursion known as the @math -Generalized Labeled Multi-Bernoulli ( @math -GLMB) filter has been recently proposed by Vo and Vo in [“Labeled Random Finite Sets and Multi-Object Conjugate Priors,” IEEE Trans. Signal Process., vol. 61, no. 13, pp. 3460–3475, 2014]. As a sequel to that paper, the present paper details efficient implementations of the @math -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 @math -GLMB filter) look-ahead strategies to reduce the number of computations. Characterization of the @math -error in the multi-target density arising from the truncation is presented. Random finite sets are natural represen- tations of multi-target states and observations that al- low multi-sensor multi-target tmcking to fit in the uni- fying random set framework for Data fision. Although a rigorous foundation has been developed in the form of Finite Set Statistics, optimal Bayesian multi-target filtering is not yet practical. Sequential Monte Carlo (SMC) approzimations of the optimal filter are compu- tationally ezpensive. A practical altemative to the opti- mal filter is the Probability Hypothesis Density (PHD) filter, which propagates the PHD or first moment in- stead of the full multi-target posterior. The propagation of the PHD involves multiple integrals which do not ad- mit closed form. We propose to approzimate the PHD by a set of weighted random samples which are propa- gated over time using a generalised SMC method. The resulting algorithm is very attractive as it is general enough to handle non-linear non-Gaussian dynamics and the computational complezity is independent of the (time-varying) number of targets.