Multiple-model Bayesian filtering with random finite set observation

The finite set statistics provides a mathematically rig- orous single target Bayesian filter （STBF） for tracking a target that generates multiple measurements in a cluttered environment. However, the target maneuvers may lead to the degraded track- ing performance and even track loss when using the STBF. The multiple-model technique has been generally considered as the mainstream approach to maneuvering the target tracking. Moti- vated by the above observations, we propose the multiple-model extension of the original STBF, called MM-STBF, to accommodate the possible target maneuvering behavior. Since the derived MM- STBF involve multiple integrals with no closed form in general, a sequential Monte Carlo implementation （for generic models） and a Gaussian mixture implementation （for linear Gaussian models） are presented. Simulation results show that the proposed MM-STBF outperforms the STBF in terms of root mean squared errors of dynamic state estimates.

Review:Recent advances in multisensor multitarge11racking using random finite set

In this study,we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set(RFS)approach.The fusion that plays a fundamental role in multisensor filtering is classified into data-level multitarget measurement fusion and estimate-level multitarget density fusion,which share and fuse local measurements and posterior densities between sensors,respectively.Important properties of each fusion rule including the optimality and sub-optimality are presented.In particulax,two robust multitarget density-averaging approaches,arithmetic-and geometric-average fusion,are addressed in detail for various RFSs.Relevant research topics and remaining challenges are highlighted.

A random finite set based joint probabilistic data association filter with non-homogeneous Markov chain

We demonstrate a heuristic approach for optimizing the posterior density of the data association tracking algorithm via the random finite set(RFS)theory.Specifically,we propose an adjusted version of the joint probabilistic data association(JPDA)filter,known as the nearest-neighbor set JPDA(NNSJPDA).The target labels in all possible data association events are switched using a novel nearest-neighbor method based on the Kullback-Leibler divergence,with the goal of improving the accuracy of the marginalization.Next,the distribution of the target-label vector is considered.The transition matrix of the target-label vector can be obtained after the switching of the posterior density.This transition matrix varies with time,causing the propagation of the distribution of the target-label vector to follow a non-homogeneous Markov chain.We show that the chain is inherently doubly stochastic and deduce corresponding theorems.Through examples and simulations,the effectiveness of NNSJPDA is verified.The results can be easily generalized to other data association approaches under the same RFS framework.

Research and Application of Multi-Target Tracking Based on GM-PHD Filter

In recent years, multi-target tracking technology based on Gaussian Mixture- Probability Hypothesis Density (GM-PHD) filtering has become a hot field of information fusion research. This article outlines the generation and development of multi-target tracking methods based on GM-PHD filtering, and the principle and implementation method of GM-PHD filtering are explained, and the application status based on GM-PHD filtering is summarized, and the key issues of the development of GM-PHD filtering technology are analyzed.

Multi-Bernoulli Filter for Tracking Multiple Targets Using Sensor Array

This paper presents a multi-Bernoulli filter for tracking the direction of arrival(DOAs)of time-varying number of targets using sensor array.Our method operates directly on the measurements of sensor array and does not require any detection.Firstly,more information is reserved and compared with the after-detection measurements using a finite set of detected points.It can significantly improve the tracking performance,especially in low signal-to-noise ratio.Secondly,it inherits the advantages of the multi-Bernoulli approximation which models each of the targets individually.This allows more accurate multi-target state estimation,especially when targets cross.The proposed filter does not need clustering step and simulation results showcase the improved performance of the proposed filter.

Performance evaluation for multi-target tracking with temporal dimension specifics

With the great development of Multi-Target Tracking(MTT)technologies,many MTT algorithms have been proposed with their own advantages and disadvantages.Due to the fact that requirements to MTT algorithms vary from the application scenarios,performance evaluation is significant to select an appropriate MTT algorithm for the specific application scenario.In this paper,we propose a performance evaluation method on the sets of trajectories with temporal dimension specifics to compare the estimated trajectories with the true trajectories.The proposed method evaluates the estimate results of an MTT algorithm in terms of tracking accuracy,continuity and clarity.Furthermore,its computation is based on a multi-dimensional assignment problem,which is formulated as a computable form using linear programming.To enhance the influence of recent estimated states of the trajectories in the evaluation,an attention function is used to reweight the trajectory errors at different time steps.Finally,simulation results show that the proposed performance evaluation method is able to evaluate many aspects of the MTT algorithms.These evaluations are worthy for selecting suitable MTT algorithms in different application scenarios.

A robust Poisson multi-Bernoulli filter for multi-target tracking based on arithmetic average fusion

The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally difficult to handle the above problems simultaneously,such as the Track-Oriented marginal Multi-Bernoulli/Poisson(TOMB/P)and Measurement-Oriented marginal Multi-Bernoulli/Poisson(MOMB/P)filters.Based on the Arithmetic Average(AA)fusion rule,this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli(PMB)filter,which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence.In order to fuse the different PMB distributions,the Bernoulli components in different Multi-Bernoulli(MB)distributions are associated with each other by Kullback-Leibler Divergence(KLD)minimization.Moreover,an adaptive AA fusion rule is designed on the basis of the exponential fusion weights,which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT.Finally,by comparing with the TOMB/P and MOMB/P filters,the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.

Variational Bayesian labeled multi-Bernoulli filter with unknown sensor noise statistics

It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian （VB） approximation is proposed. The variational approximation technique is introduced to the labeled multi-Bernoulli （LMB） filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density （VB-PHD） filter and the VB cardinality balanced multi-target multi-Bernoulli （VB-CBMeMBer） filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.

A Poisson multi-Bernoulli mixture filter with spawning based on Kullback–Leibler divergence minimization

In the classical form,the Poisson Multi-Bernoulli Mixture(PMBM)filter uses a PMBM density to describe target birth,surviving,and death,which does not model the appearance of spawned targets.Although such a model can handle target birth,surviving,and death well,its performance may degrade when target spawning arises.The reason for this is that the original PMBM filter treats the spawned targets as birth targets,ignoring the surviving targets’information.In this paper,we propose a Kullback–Leibler Divergence(KLD)minimization based derivation for the PMBM prediction step,including target spawning,in which the spawned targets are modeled using a Poisson Point Process(PPP).Furthermore,to improve the computational efficiency,three approximations are used to implement the proposed algorithm,such as the Variational MultiBernoulli(VMB)filter,the Measurement-Oriented marginal MeMBer/Poisson(MOMB/P)filter,and the Track-Oriented marginal MeMBer/Poisson(TOMB/P)filter.Finally,simulation results demonstrate the validity of the proposed filter by using the spawning model in these three approximations.

Convolution Kernels Implementation of Cardinalized Probability Hypothesis Density Filter

The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.

PTMOT: A Probabilistic Multiple Object Tracker Enhanced by Tracklet Confidence for Autonomous Driving

Real driving scenarios,due to occlusions and disturbances,provide disordered and noisy measurements,which makes the task of multi-object tracking quite challenging.Conventional approach is to find deterministic data association;however,it has unstable performance in high clutter density.This paper proposes a novel probabilistic tracklet-enhanced multiple object tracker(PTMOT),which integrates Poisson multi-Bernoulli mixture(PMBM)filter with confidence of tracklets.The proposed method is able to realize efficient and robust probabilistic association for 3D multi-object tracking(MOT)and improve the PMBM filter’s continuity by smoothing single target hypothesis with global hypothesis.It consists of two key parts.First,the PMBM tracker based on sets of tracklets is implemented to realize probabilistic fusion of disordered measure-ments.Second,the confidence of tracklets is smoothed through a smoothing-while-filtering approach.Extensive MOT tests on nuScenes tracking dataset demonstrate that the proposed method achieves superior performance in different modalities.

A novel variable-lag probability hypothesis density smoother for multi-target tracking

It is understood that the forward-backward probability hypothesis density （PHD） smoothing algorithms proposed recently can significantly improve state estimation of targets. However, our analyses in this paper show that they cannot give a good cardinality （i.e., the number of targets） estimate. This is because backward smoothing ignores the effect of temporary track drop- ping caused by forward filtering and/or anomalous smoothing resulted from deaths of targets. To cope with such a problem, a novel PHD smoothing algorithm, called the variable-lag PHD smoother, in which a detection process used to identify whether the filtered cardinality varies within the smooth lag is added before backward smoothing, is developed here. The analytical results show that the proposed smoother can almost eliminate the influences of temporary track dropping and anomalous smoothing, while both the cardinality and the state estimations can significantly be improved. Simulation results on two multi-target tracking scenarios verify the effectiveness of the proposed smoother.