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).
In a Bayesian formulation of a multi-target filtering, the goal is to estimate the (hidden) target state @math at the @math time step, from a set of observations in the previous time steps @math , i.e. , where @math and @math are the likelihood and transition densities, respectively. From ), it is clear that this is an recursive problem. The state estimation at the @math iteration is usually obtained by Maximum A Posteriori (MAP) criterion. Kalman filter is arguably the most popular online filtering approach. It assumes linear motion models with Gaussian distributions for both of the prediction and update steps. Using the Taylor series expansion and deterministic approximation of non-Gaussian distributions, non-linearity and non-Gaussian behaviour are addressed by Extended and Unscented Kalman Filters (EKF, UKF) , respectively. Using the importance sampling principle, particle filters are also used to estimate the likelihood and posterior densities. Particle filters are one of the most widely used multi-target filtering algorithms capable of addressing non-linearity and non-Gaussian motions @cite_9 @cite_0 .
@cite_0 @cite_9
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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. 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.