Cardinality Balanced Multi-target multi-Bernoulli Research Articles

Sensor Management with Dynamic Clustering for Bearings-Only Multi-Target Tracking via Swarm Intelligence Optimization

Sensor management is a crucial research subject for multi-sensor multi-target tracking in wireless sensor networks (WSNs) with limited resources. Bearings-only tracking produces further challenges related to high nonlinearity and poor observability. Moreover, energy efficiency and energy balancing should be considered for sensor management in WSNs, which involves networking and transmission. This paper formulates the sensor management problem in the partially observable Markov decision process (POMDP) framework and uses the cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter for tracking. A threshold control method is presented to reduce the impact on tracking accuracy when using bearings-only measurements for sequential update. Moreover, a Cauchy–Schwarz divergence center is defined to construct a new objective function for efficiently finding the optimal sensor subset via swarm intelligence optimization. This is also conducive to dynamic clustering for the energy efficiency and energy balancing of the network. The simulation results illustrate that the proposed solution can achieve good tracking performance with less energy, and especially that it can effectively balance network energy consumption and prolong network lifetime.

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.

An Experimental Multi-Target Tracking of AM Radio-Based Passive Bistatic Radar System via Multi-Static Doppler Shifts.

This paper presents a description of recent research and the multi-target tracking in experimental passive bistatic radar (PBR) system taking advantage of numerous non-cooperative AM radio signals via multi-static doppler shifts. However, it raises challenges for use by multiple spatially distributed AM radio illuminators for multi-target tracking in PBR system due to complex data association hypotheses and no directly used tracking algorithm in the practical scenario. To solve these problems, after a series of key array signal processing techniques in the self-developed system, by constructing a nonlinear measurement model, the novel method is proposed to accommodate nonlinear model by using the unscented transformation (UT) in Gaussian mixture (GM) implementation of iterated-corrector cardinality-balanced multi-target multi-Bernoulli (CBMeMBer). Simulation and experimental results analysis verify the feasibility of this approach used in a practical PBR system for moving multi-target tracking.

Joint detection and tracking of non‐ellipsoidal extended targets based on cubature Kalman‐CBMeMBer sub‐random matrices filter

Joint detection and tracking of multiple extended targets (ETs) from image observations is a challenging radar technology; especially for extended stealth targets (ESTs). This work provides a new approach for the ESTs tracking under the non-linear Gaussian system based on track-before-detect (TBD) approach. The sequential Monte Carlo cardinality-balanced multi-target multi-Bernoulli (SMC-CBMeMBer) filter provides a good framework to cope with TBD approach. However, this filter suffers from the particles’ degradation problem seriously; especially for ETs tracking. Recently, the cubature Kalman (CK)-CBMeMBer filter which employs a third-degree spherical-radical cubature rule has been proposed to handle the non-linear models, the CK-CBMeMBer filter is more accurate and more principled in mathematical terms compared to SMC-CBMeMBer filter. To this point, the authors address a TBD of ESTs with extended CK-CBMeMBer filter based on random matrix model (RMM), which is an efficient way to track ellipsoidal ESTs. In RMM-ESTs scenarios, although the extension ellipsoid is efficient, it may not be accurate enough because of lacking useful information, such as size, shape, and orientation. Therefore, they introduce a filter composed of sub-ellipses; each one is represented by a RMM. The results confirm the effectiveness and robustness of the proposed filter.

Joint detection and tracking for stealth targets in noisy imagery based on variational Bayesian-sequential Monte Carlo-cardinality-balanced multitarget multi-Bernoulli filter

We explore the use of an improved particle filter to detect and track stealth targets (STs) in noisy imagery with unknown detection profile. Recently, a cardinality-balanced multitarget multi-Bernoulli (CBMeMBer) of variational Bayesian (VB) approximation has been proposed for tracking multitargets with unknown measurement variances. However, VB-CBMeMBer filter has been implemented with a known detection profile, which is unsuitable for ST tracking. The Bayesian track-before-detect (TBD) is an efficient way to detect low observable targets. A new VB-CBMeMBer-TBD filter is proposed to cope with jointly unknown detection profile and measurement variances for ST tracking. Furthermore, a sequential Monte Carlo implementation is applied to estimate augmented kinematic ST state. The results show that the proposed filter is more accurate than other filters in cardinality estimation and less optimal subpattern assignment errors.

Improved multi‐target tracking algorithm based on SMC‐CBMeMBer for the airborne Doppler radar

To effectively suppress clutter in airborne Doppler radar and improve multi-target tracking (MTT) performance, this study proposes an improved MTT algorithm based on Sequential Monte Carlo Cardinality Balanced Multi-target Multi-Bernoulli (SMC-CBMeMBer) filter. Firstly, the filter introduces Doppler information in the measurement process. Then, the more accurate likelihood function and state estimation are deduced again in the filtering update stage. Finally, the influence of particles number on the algorithm is analysed. Through the simulation experiment, when the number of particles is selected properly, the algorithm can more effectively suppress the clutter and improve the target tracking performance.

Labelled GM‐CBMEMBER filter with adaptive track initiation

The initial Gaussian mixture cardinality balanced multi-target multi-Bernoulli (GM-CBMeMBer) filter does not provide track information and assumes that the target birth intensity is known as a priori, but in reality the target may appear anywhere in the detection area. Therefore, the study proposes a labelled GM-CBMeMBer filter with adaptive track initiation. First, the filter introduces track label information and selects the measurements of newborn targets in the prediction process. In addition, it also makes full use of the Doppler information of the airborne Doppler radar. Then, the position estimate and velocity estimate of newborn targets are calculated by using position measurements converted and Doppler measurements, respectively. Further the label information in the prediction process is inherited during the update process, and the target states are updated sequentially with the Doppler measurements after having been updated by using position measurements. Monte–Carlo experiments show that the proposed filter can perform adaptive track initiation effectively, with good tracking performance, and provide target track information well.

Refined PHD Filter for Multi-Target Tracking under Low Detection Probability.

Radar target detection probability will decrease as the target echo signal-to-noise ratio (SNR) decreases, which has an adverse influence on the result of multi-target tracking. The performances of standard multi-target tracking algorithms degrade significantly under low detection probability in practice, especially when continuous miss detection occurs. Based on sequential Monte Carlo implementation of Probability Hypothesis Density (PHD) filter, this paper proposes a heuristic method called the Refined PHD (R-PHD) filter to improve multi-target tracking performance under low detection probability. In detail, this paper defines a survival probability which is dependent on target state, and labels individual extracted targets and corresponding particles. When miss detection occurs due to low detection probability, posterior particle weights will be revised according to the prediction step. Finally, we transform the target confirmation problem into a hypothesis test problem, and utilize sequential probability ratio test to distinguish real targets and false alarms in real time. Computer simulations with respect to different detection probabilities, average numbers of false alarms and continuous miss detection durations are provided to corroborate the superiority of the proposed method, compared with standard PHD filter, Cardinalized PHD (CPHD) filter and Cardinality Balanced Multi-target Multi-Bernoulli (CBMeMBer) filter.

Adaptive Target Birth Intensity Multi-Bernoulli Filter with Noise-Based Threshold.

Adaptively modeling the target birth intensity while maintaining the filtering efficiency is a challenging issue in multi-target tracking (MTT). Generally, the target birth probability is predefined as a constant and only the target birth density is considered in existing adaptive birth models, resulting in deteriorated target tracking accuracy, especially in the target appearing cases. In addition, the existing adaptive birth models also give rise to a decline in operation efficiency on account of the extra birth modeling calculations. To properly adapt the real variation of the number of newborn targets and improve the multi-target tracking performance, a novel fast sequential Monte Carlo (SMC) adaptive target birth intensity cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter is proposed in this paper. Through adaptively conducting the target birth probability in a pre-processing step, which incorporates the information of current measurements to correct the pre-setting of the target birth probability, the proposed filter can truly adapt target birth cases and achieve better tracking accuracy. Moreover, the implementation efficiency can be improved significantly by employing a measurement noise-based threshold in the likelihood calculations of the multi-target updating. Simulation results verify the effectiveness of the proposed filter.

A Labeled SMC-Cbmember Filter with Adaptive Track Initiation

The initial Sequential Monte Carlo cardinality balanced multi-target multi-Bernoulli (SMC-CBMeMBer) filter assumes that the target birth intensity is known as a priori, but in fact the new target may appear anywhere in the detected area. And SMC-CBMeMBer does not extract track label information and cannot distinguish the target. Therefore, this paper proposes a labeled SMC-CBMeMBer filter with adaptive track initiation (SMC-CBMeMBer-D-L-ATI). Firstly, the filter introduces the track label information in the prediction process, and selects the measurement that may correspond to the newborn target, obtaining the initial state of the newborn target according to the converted measurement. Then, the label information in the prediction process is inherited during the update process, and the target states are updated sequentially through the converted position measurement and Doppler measurement. The simulation proves that the proposed filter can effectively perform adaptive track initiation, with good tracking performance, and can provide the target track information.

Novel Rao–Blackwellized jump Markov CBMeMBer filter for multi-target tracking

The jump Markov cardinality balanced multi-target multi-Bernoulli (JM–CBMeMBer) filter can estimate both state and number of targets from uncertain measurements. To deal with high computational complexity and imprecise estimations of the existing JM–CBMeMBer filters, we put forward a novel Rao–Blackwellized JM–CBMeMBer filter and its sequential Monte Carlo implementation in this paper. Different from the previous works, we first divide target state space into the nonlinear and linear components based on the Rao–Blackwellized theory, where the linear component is estimated by the Kalman filter (KF) and the results are applied to extract the nonlinear component in lower dimension state space. Moreover, the track management scheme is considered to simplify tracking parameters and distinguish target track. After analysis on computational complexity, the optimised Rao–Blackwellized filtering scheme is presented to reduce the number of the KF recursions. As a result, the computational complexity is reduced and the estimation accuracy is improved owing to small estimation covariance during the whole filtering process. Finally, the numerical simulation results are provided to show the reliability and efficiency of the proposed filter.

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.

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.

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.