Multi-target multi-Bernoulli Filter 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.

Joint Direction of Arrival-Polarization Parameter Tracking Algorithm Based on Multi-Target Multi-Bernoulli Filter

This paper presents a tracking algorithm for joint estimation of direction of arrival (DOA) and polarization parameters, which exhibit dynamic behavior due to the movement of signal source carriers. The proposed algorithm addresses the challenge of real-time estimation in multi-target scenarios with an unknown number. This algorithm is built upon the Multi-target Multi-Bernoulli (MeMBer) filter algorithm, which makes use of a sensor array called Circular Orthogonal Double-Dipole (CODD). The algorithm begins by constructing a Minimum Description Length (MDL) principle, taking advantage of the characteristics of the polarization-sensitive array. This allows for adaptive estimation of the number of signal sources and facilitates the separation of the noise subspace. Subsequently, the joint parameter Multiple Signal Classification (MUSIC) spatial spectrum function is employed as the pseudo-likelihood function, overcoming the limitations imposed by unknown prior information constraints. To approximate the posterior distribution of MeMBer filters, Sequential Monte Carlo (SMC) method is utilized. The simulation results demonstrate that the proposed algorithm achieves excellent tracking accuracy in joint DOA-polarization parameter estimation, whether in scenarios with known or unknown numbers of signal sources. Moreover, the algorithm demonstrates robust tracking convergence even under low Signal-to-Noise Ratio (SNR) conditions.

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.

Multiple targets tracking by using improved labeled multi-target multi-Bernoulli filter with FDA-MIMO radar

In the traditional multi-target multi-Bernoulli (MeMBer) filter, only the radar signal after constant false alarm rate (CFAR) is considered. In addition, it is also necessary to assume that the detection probability of the target and the covariance matrix of the measurement noise are known. In fact, the detection probability of the target and the covariance matrix of the noise are difficult to determine. Therefore, this paper proposes an improved labeled multi-target multi-Bernoulli (IL-MeMBer) filter that can avoid considering the detection probability of the target and the covariance matrix of the measurement noise. Firstly, the multi-target superposition measurement model of FDA-MIMO is given in the presence of false targets. Secondly, the target likelihood function under the superposition measurement model is derived by analyzing the characteristics of the traditional point measurement likelihood function and the Music spatial spectrum. Thirdly, considering the unknown and time-varying number of targets, the original echo signals without detection probability before (CFAR) processing, and no target tracks output by the traditional MeMBer filter, we put forward an analytical solution of the IL-MeMBer filter. Finally, a fusion strategy based on Euclidean distance is proposed to solve the problem that the same target can be estimated to have multiple tracks in the IL-MeMBer filter. In addition, the sequential Monte Carlo (SMC) implementation of the IL-MeMBer filter is provided. Numerical experiences verify the effectiveness and superiority of the proposed methods.

IMM Robust Cardinality Balance Multi‐Bernoulli Filter for Multiple Maneuvering Target Tracking with Interval Measurement

This paper presents a novel Interacting multi-model (IMM) Robust Cardinality balance multi-target multi-Bernoulli (R-CBMeMBer) filter to solve the maneuvering target tracking problem in the case of interval measurement, unknown detection probability and unknown clutter density. In essence, IMM R-CBMeMBer filter is an extended application of R-CBMeMBer filter. In the IMM R-CBMeMBer filter, the target state is first extended to distinguish clutter from the real target. The detection probability and model probability of the target can be adaptively updated. Then, generalized likelihood function and IMM algorithm are introduced to interactively predict and update the state of the target in the IMM R-CBMeMBer filtering process. In addition, a particle application of the IMM R-CBMeMBer filter is given, and a numerical experiment is designed under nonlinear conditions. Meanwhile, Doppler information of the target is employed to estimate the velocity of each maneuvering target. Numerical experiments also verify that the IMM R-CBMeMBer filter can effectively estimate the target position, target velocity, target detection probability and clutter number in the condition of unknown detection probability, unknown clutter rate and interval measurement.

Robust Measurement-Driven Cardinality Balance Multi-Target Multi-Bernoulli Filter.

The multi-target tracking filter under the Bayesian framework has strict requirements on the prior information of the target, such as detection probability density, clutter density, and target initial position information. This paper proposes a novel robust measurement-driven cardinality balance multi-target multi-Bernoulli filter (RMD-CBMeMBer) for solving the multiple targets tracking problem when the detection probability density is unknown, the background clutter density is unknown, and the target’s prior position information is lacking. In RMD-CBMeMBer filtering, the target state is first extended, so that the extended target state includes detection probability, kernel state, and indicators of target and clutter. Secondly, the detection probability is modeled as a Beta distribution, and the clutter is modeled as a clutter generator that is independent of each other and obeys the Poisson distribution. Then, the detection probability, kernel state, and clutter density are jointly estimated through filtering. In addition, the correlation function (CF) is proposed for creating new Bernoulli component (BC) by using the measurement information at the previous moment. Numerical experiments have verified that the RMD-CBMeMBer filter can solve the multi-target tracking problem under the condition of unknown target detection probability, unknown background clutter density and inadequate prior position information of the target. It can effectively estimate the target detection probability and the clutter density.

Robust Multisensor MeMBer Filter for Multiple Extended-Target Tracking

This paper develops a robust extended-target multisensor multitarget multi-Bernoulli (ET-MS-MeMBer) filter for enhancing the unsatisfactory quality of measurement partitions arising in the classical ET-MS-MeMBer filter due to increased clutter intensities. Specifically, the proposed method considers the influence of the clutter measurement set by introducing the ratio of the target likelihood to the clutter likelihood. With the constraint of the clutter measurement set, it can obtain better multisensor measurement partitioning results under the original two-step greedy partitioning mechanism. Subsequently, the single-target multisensor likelihood function for the clutter case is derived. Simulation results reveal a favorable comparison to the ET-MS-MeMBer filter in terms of accuracy in estimating the target cardinality and target state under conditions with increased clutter intensities.

Group Target Tracking Based on MS-MeMBer Filters

This paper presents a new group target tracking method based on the standard multi-sensor multi-target multi-Bernoulli (MS-MeMBer) filter. In the prediction step, the group structure is used to constrain the movement of the constituent members within the respective groups. Specifically, the group of members is considered as an undirected random graph. Combined with the virtual leader-follower model, the motion equation of the members within groups is formulated. In the update step, the partitioning problem of multiple sensors is transformed into a multi-dimensional assignment (MDA) problem. Compared with the original two-step greedy partitioning mechanism, the MDA algorithm achieves better measurement partitions in group target tracking scenarios. To evaluate the performance of the proposed method, a simulation scenario including group splitting and merging is established. Results show that, compared with the standard MS-MeMBer filter, our method can effectively estimate the cardinality of members and groups at the cost of increasing computational load. The filtering accuracy of the proposed method outperforms that of the MS-MeMBer filter.

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.

A Novel MS-MeMBer Filter for Extended Targets Tracking

Conventional multi-sensor multi-target multi-Bernoulli (MS-MeMBer) filters are based on the assumption that each target produces at most one measurement per time step. However, this assumption is not always reasonable in practice as an extended target can generate multiple measurements per step due to the recent improvement in the sensor resolution. In this case, a potential estimation bias may occur in the current MS-MeMBer filters. Therefore, a novel extended target MS-MeMBer filter and its Gaussian inverse Wishart mixture implementation are given in this paper. Specifically, we modify the update process of the MS-MeMBer filter by assuming that the generation of extended target measurements follows an approximate Poisson-Body model. Simulation results validate that the proposed filter can effectively estimate the shape and position of the extended target.

A Novel Structure for a Multi-Bernoulli Filter without a Cardinality Bias

The original multi-target multi-Bernoulli (MeMBer) filter for multi-target tracking (MTT) is shown analytically to have a significant bias in its cardinality estimation. A novel cardinality balance multi-Bernoulli (CBMeMBer) filter reduces the cardinality bias by calculating the exact cardinality of the posterior probability generating functional (PGFl) without the second assumption of the original MeMBer filter. However, the CBMeMBer filter can only have a good performance under a high detection probability, and retains the first assumption of the MeMBer filter, which requires measurements that are well separated in the surveillance region. An improved MeMBer filter proposed by Baser et al. alleviates the cardinality bias by modifying the legacy tracks. Although the cardinality is balanced, the improved algorithm employs a low clutter density approximation. In this paper, we propose a novel structure for a multi-Bernoulli filter without a cardinality bias, termed as a novel multi-Bernoulli (N-MB) filter. We remove the approximations employed in the original MeMBer filter, and consequently, the N-MB filter performs well in a high clutter intensity and low signal-to-noise environment. Numerical simulations highlight the improved tracking performance of the proposed filter.

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.

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.

Multiple‐detection multi‐target tracking with labelled random finite sets and efficient implementations

Traditional multi-target tracking algorithms assume that each target can generate at most one detection per scan. However, a target may produce multiple detections (MDs) in many practical applications, e.g. over-the-horizon radar (OTHR), tracking for extended target and tracking with multiple sensors. In this study, the authors propose a new algorithm for tracking multiple targets with MD observation. The proposed technique is based on the labelled random finite set (RFS), which estimates the number of targets and the trajectories of their states. Furthermore, they propose two methods, pre-partition and joint partition, to implement the labelled RFS density recursion. The joint partition method derives a joint prediction, partition and update formulation of the MD filtering and extends the Gibbs sampler to provide global optimal results with low computational cost. The authors’ algorithm is demonstrated on an OTHR simulation compared with the previous approach, such as the MD probability hypothesis density filter and the multipath cardinality-balance multi-target multi-Bernoulli 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.