Multi-target multi-Bernoulli Filter Research Articles

Measurement-Driven Multi-Target Multi-Bernoulli Filter

A measurement-driven multi-target multi-Bernoulli (MeMBer) filter which modifies the MeMBer filter by the measurements information is proposed in this paper. The proposed filter refines both the legacy estimates and the data-induced estimates of the MeMBer filter. For the targets under the legacy track set, the detection probabilities derived from the measurements are employed to refine the multi-target distribution. And for the targets under the data-induced track set, the multi-target distribution is further improved by the modified existence probabilities of the legacy tracks. Unlike the cardinality balanced MeMBer (CBMeMBer) filter, the proposed filter removes the cardinality bias in the MeMBer filter by utilizing the measurements information. Simulation results show that, compared with the traditional methods, the proposed filter can improve the stability and accuracy of the estimates and does not need the high detection probability hypothesis.

An ellipse extended target CBMeMBer filter using gamma and box-particle implementation

This work presents a gamma box-particle implementation of the ellipse extended target cardinality balanced multi-target multi-Bernoulli (ET-CBMeMBer) filter, named the ellipse extended target gamma box particle CBMeMBer (EET-GBP-CBMeMBer) filter, where the ellipse extended targets are characterized using a Poisson model suggested by Gilholm et al. The proposed filter is capable of dynamically tracking multiple ellipse extended targets and estimating the target kinematics and extents as well as the measurement rates of targets, in the presence of clutter measurements, false alarms and missed detections. To get the CBMeMBer recursion of the EET-GBP-CBMeMBer filter, a suitable measurement likelihood is derived for a given partitioning cell, and the main gamma box-particle implementation are given along with the necessary box manipulations and approximations. The capabilities and limitations of the proposed EET-GBP-CBMeMBer filter are demonstrated by simulation examples. The simulation results show that a gamma box-particle implementation of the ET-CBMeMBer filter can avoid the high number of particles and reduce computational burden, compared to a particle implementation of that for extended target tracking.

A Student’s T Mixture Cardinality-Balanced Multi-Target Multi-Bernoulli Filter With Heavy-Tailed Process and Measurement Noises

The cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter is a promising solution for multi-target tracking. However, the performance of the CBMeMBer filter will be degraded severely by outliers in the presence of heavy-tailed process noise and measurement noise. To address this challenging issue, a novel CBMeMBer filter called the Student’s t mixture CBMeMBer (STM-CBMeMBer) filter is proposed in this paper, by assuming that the joint probability density function (pdf) of the state and process noise and the joint pdf of the state and measurement noise follow joint Student’s t distributions. Following that, a closed-form solution of the CBMeMBer recursion is obtained by approximating the probability density parameter of the multi-Bernoulli as a STM. The proposed algorithm is a generalization of existing Gaussian mixture CBMeMBer (GM-CBMeMBer) filter, and it reduces to the GM-CBMeMBer filter in some special cases. Simulation results demonstrate that robust multi-target tracking can be achieved in the presence of outliers in process and measurement noises.

A Novel Joint Multitarget Estimator for Multi-Bernoulli Models

In this paper, the joint multitarget (JoM) estimator proposed for the joint target detection and tracking (JoTT) filter is reformulated for the Gaussian mixture (GM) implementations of the multitarget multi-Bernoulli (MeMBer) filters. For this purpose, a mode-finding algorithm is employed to search for the most significant mode of a GM density. Thus, the maximum a posterior (MAP) estimates of Bernoulli targets are determined. In addition, the multi-Bernoulli versions of the two conflicting objective functions for the Pareto-optimal value of the unknown JoM estimation constant are derived. Simulations compare the performance of the proposed JoM estimator with that of the marginal multitarget (MaM) estimator in a multitarget tracking scenario, where the probability of target detection is a function of target states. The simulation results demonstrate that the proposed JoM estimator outperforms the MaM estimator under moderately low-observable conditions. This is because the incomplete cost function of the MaM estimator is not adequate to obtain accurate cardinality estimates of targets without considering how well targets are localized. Nevertheless, the proposed JoM estimator may suffer from track termination latency more than the MaM estimator due to the definition of its cost function.

Cardinality Balanced Multi-Target Multi-Bernoulli Filter with Error Compensation.

The cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter developed recently has been proved an effective multi-target tracking (MTT) algorithm based on the random finite set (RFS) theory, and it can jointly estimate the number of targets and their states from a sequence of sensor measurement sets. However, because of the existence of systematic errors in sensor measurements, the CBMeMBer filter can easily produce different levels of performance degradation. In this paper, an extended CBMeMBer filter, in which the joint probability density function of target state and systematic error is recursively estimated, is proposed to address the MTT problem based on the sensor measurements with systematic errors. In addition, an analytic implementation of the extended CBMeMBer filter is also presented for linear Gaussian models. Simulation results confirm that the proposed algorithm can track multiple targets with better performance.

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.

Extensions of the CBMeMBer filter for joint detection, tracking, and classification of multiple maneuvering targets

This paper addresses the problem of joint detection, tracking and classification (JDTC) of multiple maneuvering targets in clutter. The multiple model cardinality balanced multi-target multi-Bernoulli (MM-CBMeMBer) filter is a promising algorithm for tracking an unknown and time-varying number of multiple maneuvering targets by utilizing a fixed set of models to match the possible motions of targets, while it exploits only the kinematic information. In this paper, the MM-CBMeMBer filter is extended to incorporate the class information and the class-dependent kinematic model sets. By following the rules of Bayesian theory and Random Finite Set (RFS), the extended multi-Bernoulli distribution is propagated recursively through prediction and update. The Sequential Monte Carlo (SMC) method is adopted to implement the proposed filter. At last, the performance of the proposed filter is examined via simulations.

Adaptive parameter particle CBMeMBer tracker for multiple maneuvering target tracking

Cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter has been demonstrated as a promising algorithm for multi-target tracking, and the multi-model (MM) method has been incorporated into the CBMeMBer filter to solve the problem of multiple maneuvering target tracking. However, it is difficult to construct a proper set of models due to the unknown maneuvering parameters of the targets. Moreover, the number of models may increase exponentially if more unknown parameters have to be taken into account to match the target motion modes, which may lead to prohibitive computational complexity. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation (APE) method in the framework of CBMeMBer filters, so that the model with unknown maneuvering parameter can be modified adaptively by using the selected parameter particles. Moreover, a particle labeling technique is introduced in the proposed algorithm in order to obtain the individual target track, which results in the adaptive parameter particle filter CBMeMBer (APPF-CBMeMBer) tracker. Simulation results show that the proposed algorithm can effectively track multiple maneuvering targets with abruptly changing parameters and exhibit better robustness than those of the well-known MM-based approaches.

Cardinality balanced multitarget multi‐Bernoulli filter for multipath multitarget tracking in over‐the‐horizon radar

Conventional multitarget tracking systems presume that each target produces at most one measurement per scan. Owing to the multiple ionosphere propagation paths in over-the-horizon radar, this assumption is not valid. To solve this problem, a novel multitarget tracking algorithm based on the finite set statistics (FISST), called multipath cardinality balanced multitarget multi-Bernoulli (MP-CBMeMBer) filter, is proposed in this study. First, the authors derive the MP-CBMeMBer filter based on the FISST, and then both the sequential Monte Carlo and Gaussian mixture (GM) method are used to implement the proposed filter. Moreover, the extended Kalman filter is implemented to deal with the problem of the non-linear measurement models for the GM-MP-CBMeMBer filter. Eventually, the simulation results are presented to demonstrate the effectiveness of the proposed filter.

Improved multi‐target multi‐Bernoulli filter with modelling of spurious targets

The cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter removes the positive bias from the data-updated cardinality estimate in the multi-target multi-Bernoulli (MeMBer) filter. In this study, the relationship between the MeMBer corrector and the multi-Bernoulli random finite set (RFS) distribution is analysed. By utilising this relationship, a filter that offers a new statistical framework for the MeMBer data update process is proposed. Thus, the multi-Bernoulli RFS distribution is extended to model spurious targets arising from targets under the legacy track set with high probabilities of existence. Unlike the CBMeMBer filter, the proposed filter removes the bias observed in the MeMBer filter by distinguishing spurious targets from actual targets, and while doing this, it does not make any limiting assumption on the probability of target detection. In addition, the modelling of spurious targets allows the refinement of the existence probabilities of targets in light of measurements. As a result, the stability of the cardinality estimate is improved while removing the bias. The theoretical analysis performed on the joint detection and state estimation problem of a single target reveals the strengths and limitations of the proposed filter. In addition, numerical simulations are performed in a scenario involving targets with crossing trajectories to demonstrate the filter performance.

Sequential Monte Carlo implementation of cardinality balanced multi‐target multi‐Bernoulli filter for extended target tracking

It has been shown that the cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter can extract multi-target states efficiently and reliably. However, when faced with extended targets, it will lead to overestimation. Therefore, a CBMeMBer filter for extended targets tracking is proposed in this study. Three main contributions are made in this study: first, analytical recursion equations of the proposed CBMeMBer filter are derived and relevant proofs are presented. Second, a novel sequential Monte Carlo (SMC) implementation is proposed, which approximates the sample point using several σ points rather than state transition function. Third, to reduce the particle weight degeneracy problem, a new resample method is introduced. Finally, comparisons between the CBMeMBer and probability hypothesis density (PHD) filters for extended targets tracking are studied through a non-linear example. Numerical study results show that the expanded CBMeMBer filter in the proposed SMC implementation can dramatically improve estimation accuracy in comparison with general SMC implementation. Meanwhile, the authors also find that the proposed CBMeMBer filter gives a more accurate estimation than original CBMeMBer filter while performs more time-efficiently than PHD filter for extended target tracking.

Multi-Bernoulli smoother for multi-target tracking

Multi-target tracking is an important research topic in the field of aerospace. In this paper, a multi-Bernoulli smoother, which consists of forward filtering followed by backward smoothing, is proposed for multi-target tracking. The forward filtering is accomplished by the cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter. For the backward smoothing, the smoothed multi-target probability density is approximated by a multi-Bernoulli density, whose backward recursion is derived by using finite set statistics. To solve the computational problem of multiple integrals in the smoother, a sequential Monte Carlo method is also proposed. Experimental results show that the proposed smoother improves the estimation accuracy of target number and target states over the CBMeMBer filter.

Error bounds for joint detection and estimation of multiple unresolved target-groups

According to random finite set (RFS) and information inequality, this paper derives an error bound for joint detection and estimation (JDE) of multiple unresolved target-groups in the presence of clutters and missed detections. The JDE here refers to determining the number of unresolved target-groups and estimating their states. In order to obtain the results of this paper, the states of the unresolved target-groups are modeled as a multi-Bernoulli RFS first. The point cluster model proposed by Mahler is used to describe the observation likelihood of each group. Then, the error metric between the true and estimated state sets of the groups is defined by the optimal sub-pattern assignment distance rather than the usual Euclidean distance. The maximum a posteriori detection and unbiased estimation criteria are used in deriving the bound. Finally, we discuss some special cases of the bound when the number of unresolved target-groups is known a priori or is at most one. Example 1 shows the variation of the bound with respect to the probability of detection and clutter density. Example 2 verifies the effectiveness of the bound by indicating the performance limitations of the cardinalized probability hypothesis density and cardinality balanced multi-target multi-Bernoulli filters for unresolved target-groups. Example 3 compares the bound of this paper with the (single-sensor) bound of [4] for the case of JDE of a single unresolved target-group. At present, this paper only addresses the static JDE problem of multiple unresolved target-groups. Our future work will study the recursive extension of the bound proposed in this paper to the filtering problems by considering the group state evolutions.

Evaluation of State-Dependent Pedestrian Tracking Based on Finite Sets

This paper addresses the use of multiobject filters based on finite set statistics with a special focus on sensor characteristics for the use in distributed indoor pedestrian tracking with multiple sensors. For this purpose, a sensing framework is presented consisting of Lidar sensors together with depth cameras. To make use of previously existing knowledge about the measuring process, an adaptive sensor model is presented with a focus on state-dependent modeling of the sensor characteristics. The model incorporates changes in the probability of detection due to the distance between the object and the sensor, occlusions, and the sensor location-dependent environment. The model is incorporated into three approximations of a Bayes optimal multiobject filter, namely, the probability hypothesis density filter, the cardinalized probability hypothesis filter, and the cardinality balanced multitarget multi-Bernoulli filter. Using labeled sequential Monte Carlo implementations, the filters are evaluated with and without the proposed adaptive sensor models for partly simulated and real data. The evaluation was done using ground truth data obtained by a marker-based motion capture system. It is shown that the adaptive model achieves superior tracking results in simulation and real experiments for all approximations with the cardinalized probability hypothesis filter producing the best results.

Multiple Model Multi-Bernoulli Filters for Manoeuvering Targets

The cardinality balanced multitarget multi-Bernoulli (CBMeMBer) filter is a recursive, multitarget tracking mechanism based on the random finite set (RFS) theory using the finite set statistics (FISST) framework. It provides an estimate of the number of targets in a given scenario space, along with the most likely locations of those targets. It also provides this estimate without the expensive operation of multidimensional assignment between measurements and target estimates. Unlike other RFS methods, the CBMeMBer filter outputs an estimate of the actual multitarget probability density function. Current implementations include a nonlinear sequential Monte Carlo (SMC) approximation, as well as an analytical Gaussian mixture (GM) solution. A new MeMBer recursion for tracking multiple targets traveling under multiple motion models is introduced. The multiple model CBMeMBer (MM-CBMeMBer) filter presented here uses jump Markov models (JMM) to extend the standard CBMeMBer recursion to allow for multiple target motion models. This extension is implemented using both the SMC- and GM-based CBMeMBer approximations. The recursive prediction and update equations are presented for both implementations. Each multiple model implementation is validated against its respective standard CBMeMBer implementation, as well as against each other. This validation is done using a simulated scenario containing multiple manoeuvering targets. A variety of metrics, including estimate accuracy, model detection capability, and algorithm computational efficiency are used for performance evaluation. The new method is shown to improve results in several metrics with only a minor increase in computational complexity.

Multitarget Track-Before-Detect via MeMBer Filtering and Track Consistency Test

This paper deals with the problem of time-varying multitarget track-before-detect (TBD) using image observation model. The multitarget state is formulated as random finite set (RFS) and its posterior distribution is approximated by multi-Bernoulli parameters, which are recursively evaluated using sequential Monte Carlo approach. The state estimates are first extracted from the updated Bernoulli components with moderate existence probabilities, allowing for all the true targets and false alarms. The extracted target states are then distilled using track consistency test strategy to remain only the true tracks. Simulation results show the improved performance of the proposed method over the traditional multitarget multi-Bernoulli (MeMBer) filter as well as its capability to provide the identity of individual target.

Robust Multi-Bernoulli Filtering

In Bayesian multi-target filtering knowledge of parameters such as clutter intensity and detection probability profile are of critical importance. Significant mismatches in clutter and detection model parameters results in biased estimates. In this paper we propose a multi-target filtering solution that can accommodate non-linear target models and an unknown non-homogeneous clutter and detection profile. Our solution is based on the multi-target multi-Bernoulli filter that adaptively learns non-homogeneous clutter intensity and detection probability while filtering.

An improved multi-target tracking algorithm based on CBMeMBer filter and variational Bayesian approximation

Random finite set (RFS) filters have been demonstrating a promising algorithm for tracking an unknown number of targets in real time. However, these methods can only be used in the multi-target tracking systems with known measurement noise variances; otherwise, their tracking performances will decline greatly. To solve this problem, an improved multi-target tracking algorithm is proposed based on the cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter and the variational Bayesian (VB) approximation technique to recursively estimate the joint posterior distributions of the multi-target states and the time-varying measurement noise variances. First, the variational calculus method is employed to derive the multi-target estimate recursions, and then the Gaussian and inverse Gamma mixture distributions are introduced to approximate the joint posterior density, and achieve a Gaussian closed-form solution. Simulation results show that the proposed algorithm can effectively estimate the unknown measurement noise variances and has a good performance of multi-target tracking with a strong robustness.

Multi‐model particle cardinality‐balanced multi‐target multi‐Bernoulli algorithm for multiple manoeuvring target tracking

Multiple manoeuvring target tracking is an extremely difficult problem in the target tracking field, especially under the non-linear systems. The probability hypothesis density (PHD) and cardinalised PHD (CPHD) algorithms based on the particle filter have proved to be promising algorithms for multi-target tracking. However, they have a heavy computational burden because of the particle clustering in the stage of state extraction. Especially, the additional calculation is added to the CPHD algorithm because of the estimation of the cardinality distribution. To solve the problem, the authors propose a novel multiple manoeuvring target tracking algorithm by extending the multi-model method to the cardinality-balanced multi-target multi-Bernoulli filter and then using the sequential Monte Carlo implementation. Moreover, in order to obtain the individual target tracks, the particle labelling technique is introduced in the proposed algorithm. Simulation results show that the proposed algorithm can effectively achieve the track continuity for the multiple manoeuvring target tracking and has a higher accuracy of state estimates than the multiple model particle PHD and CPHD algorithm with a better computational efficiency.

Multiple-Model Cardinality Balanced Multitarget Multi-Bernoulli Filter for Tracking Maneuvering Targets

By integrating the cardinality balanced multitarget multi-Bernoulli (CBMeMBer) filter with the interacting multiple models (IMM) algorithm, an MM-CBMeMBer filter is proposed in this paper for tracking multiple maneuvering targets in clutter. The sequential Monte Carlo (SMC) method is used to implement the filter for generic multi-target models and the Gaussian mixture (GM) method is used to implement the filter for linear-Gaussian multi-target models. Then, the extended Kalman (EK) and unscented Kalman filtering approximations for the GM-MM-CBMeMBer filter to accommodate mildly nonlinear models are described briefly. Simulation results are presented to show the effectiveness of the proposed filter.