Cardinality Balanced Multi-target multi-Bernoulli Filter Research Articles

An interval SLAM algorithm for leg–arm mobile robots based on a CBMeMBer filter with Gaussian indicator box-particles

During the implementation of SLAM methods based on probability hypothesis density with sequential Monte Carlo (SMC), it is necessary to generate a relatively large number of particles for mapping and to cluster particles for target state extraction, which brings about heavy computing requirements and difficulty in enhancing the estimation accuracy. Along these lines, in this work, an interval SLAM algorithm for a leg–arm mobile robot (LA-MR) is presented, which is based on cardinality-balanced multi-target multi-Bernoulli filter (CBMeMBer) with Gaussian indicator box-particles (GIBPs). First, an effective strategy for improving the selection criterion of subdivision box-particles is given via the indicator subdivision resampling to provide more reliable box-particles. In addition, mixtures of Gauss distributions with box supports were developed to fit the posterior probability, i.e. GIBP. Then, the GIBP filter was employed to implement the CBMeMBer filter and thus the particle numbers were significantly reduced to decrease the computational complexity compared with the SMC-CBMeMBer filter. In this way, the feature map learning is considered as a multi-target tracking problem, whereas a kind of SLAM algorithm for LA-MR was also designed and implemented through the GIBP-CBMeMBer filter, in which the GIBP filter is used to realize simultaneous localization and the GIBP-CBMeMBer filter is utilized to build a map. A series of experiments and a case study clearly illustrated the performance superiority of the proposed algorithms.

CBMeMBer filterwith adaptive target birth intensity

Appropriately modelling target-birth intensity is a significant but challenging issue in multi-target tracking systems. In existing cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filters, a priori knowledge about the locations where targets appear is required to model the target-birth intensity. Since the newborn targets can appear anywhere within the observation region, it is impractical to obtain such prior information. In this study, a novel CBMeMBer filter with adaptive target-birth intensity is presented, considering the newborn and surviving targets separately. The target-birth function of the target-birth intensity is modelled using current measurements rather than the known birth locations, and the target-birth magnitude is assigned by an allocation function rather than equally assigned. The new CBMeMBer filter can remove the restriction on the requirement of prior birth location information and can adapt well after continuous missing detection occurs. Simulations of the sequential Monte Carlo and Gaussian mixture implementations demonstrate the effectiveness of the proposed filter.

Optimization of Particle CBMeMBer Filters for Hardware Implementation

It is a promising solution for real-time multitarget tracking to implement particle cardinality balanced multitarget multi-Bernoulli (CBMeMBer) filters in hardware platforms. However, this solution is difficult to materialize since there is a contradiction between the time-varying number of Bernoulli intensity components in CBMeMBer filters and the limited number of particles in hardware platforms. Moreover, real-time hardware implementation requires a resampling procedure that is suitable for parallel processing, while the existing parallel resampling algorithms oversimplify this procedure, resulting in estimation performance degradation. In this paper, we propose an optimization algorithm of particle allocation to overcome the above-mentioned contradiction, and a parallel resampling algorithm to improve the estimation performance. Numerical experiments demonstrate the effectiveness of the proposed algorithms in multitarget 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.

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.

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.

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.

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.

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.

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.

Couple-sensor CBMeMBer filter

The cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter shows excellent performance compared with the probability hypothesis density (PHD) and cardinality PHD (CPHD) filters. However, the algorithm addressed only single-sensor scenarios. To resolve the problem of multisensor multi-target tracking with the CBMeMBer filter, an ad hoc approach is proposed. Simulation results verify the proposed solution.