multi-Bernoulli Random Finite Set Research Articles

Evolutionary Computational Intelligence-Based Multi-Objective Sensor Management for Multi-Target Tracking

In multi-sensor systems (MSSs), sensor selection is a critical technique for obtaining high-quality sensing data. However, when the number of sensors to be selected is unknown in advance, sensor selection is essentially non-deterministic polynomial-hard (NP-hard), and finding the optimal solution is computationally unacceptable. To alleviate these issues, we propose a novel sensor selection approach based on evolutionary computational intelligence for tracking multiple targets in the MSSs. The sensor selection problem is formulated in a partially observed Markov decision process framework by modeling multi-target states as labeled multi-Bernoulli random finite sets. Two conflicting task-driven objectives are considered: minimization of the uncertainty in posterior cardinality estimates and minimization of the number of selected sensors. By modeling sensor selection as a multi-objective optimization problem, we develop a binary constrained evolutionary multi-objective algorithm based on non-dominating sorting and dynamically select a subset of sensors at each time step. Numerical studies are used to evaluate the performance of the proposed approach, where the MSS tracks multiple moving targets with nonlinear/linear dynamic models and nonlinear measurements. The results show that our method not only significantly reduces the number of selected sensors but also provides superior tracking accuracy compared to generic sensor selection methods.

Multi-Sensor Joint Adaptive Birth Sampler for Labeled Random Finite Set Tracking

This paper provides a scalable, multi-sensor measurement adaptive track initiation technique for labeled random finite set filters. A naive construction of the multi-sensor measurement adaptive birth set distribution leads to an exponential number of newborn components in the number of sensors. A truncation criterion is established for a labeled multi-Bernoulli random finite set birth density. The proposed truncation criterion is shown to have a bounded L1 error in the generalized labeled multi-Bernoulli posterior density. This criterion is used to construct a Gibbs sampler that produces a truncated measurement-generated labeled multi-Bernoulli birth distribution with quadratic complexity in the number of sensors. A closed-form solution of the conditional sampling distribution assuming linear Gaussian likelihoods is provided, alongside an approximate solution using Monte Carlo importance sampling. Multiple simulation results are provided to verify the efficacy of the truncation criterion, as well as the reduction in complexity.

Receiver selection for multi-target tracking in multi-static Doppler radar systems

This paper presents a novel receiver selection method for multi-target tracking in multi-static Doppler radar systems. The assumption is that in the surveillance volume of interest, a single transmitter with a known frequency is active and several spatially distributed radar receivers collect and report Doppler-only measurements. The Doppler measurements are not only affected by the additive noise but also contaminated by false and missed detections. In this paper, multi-target tracking is obtained by modeling the multi-target state as a labeled multi-Bernoulli random finite set and receiver selection is implemented during tracking. Receiver selection is solved under the partially observed Markov decision framework, and the variance of the cardinality estimate is used as the selection criterion. To increase the diversity of the selected sensors and overcome the low observability of the Doppler measurement, the receivers selected at previous time steps are taken into account by adding a window. Simulation studies demonstrate the tracking performance of the proposed method with different window lengths. The results show that the observability of the target state is a crucial factor in determining the performance of receiver selection. The proposed method with a suitable window length can effectively improve the tracking accuracy.

A Novel Gaussian Ant Colony Algorithm for Clustering Cell Tracking

Cell behavior analysis is a fundamental process in cell biology to obtain the correlation between many diseases and abnormal cell behavior. Moreover, accurate number estimation plays an important role for the construction of cell lineage trees. In this paper, a novel Gaussian ant colony algorithm, for clustering or spatial overlap cell state and number estimator, simultaneously, is proposed. We have introduced a novel definition of the Gaussian ant system borrowed from the concept of the multi-Bernoulli random finite set (RFS) in the way that it encourages ants searching for cell regions effectively. The existence probability of ant colonies is considered for the number and state estimation of cells. Through experiments on two real cell sequences, it is confirmed that our proposed algorithm could automatically track clustering cells in various scenarios and has enabled superior performance compared with other state-of-the-art approaches.

An Automated Cell Tracking Approach With Multi-Bernoulli Filtering and Ant Colony Labor Division.

In this article, we take as inspiration the labor division into scouts and workers in an ant colony and propose a novel approach for automated cell tracking in the framework of multi-Bernoulli random finite sets. To approximate the Bernoulli parameter sets, we first define an existence probability of an ant colony as well as its discrete density distribution. During foraging, the behavior of scouts is modeled as a chaotic movement to produce a set of potential candidates. Afterwards, a group of workers, i.e., a worker ant colony, is recruited for each candidate, which then embark on gathering heuristic information in a self-organized way. Finally, the pheromone field is formed by the corresponding worker ant colony, from which the Bernoulli parameter is derived and the state of the cell is estimated accordingly to be associated with the existing tracks. Performance comparisons with other previous approaches are conducted on both simulated and real cell image sequences and show the superiority of this algorithm.

Computationally Efficient Distributed Multi-Sensor Fusion With Multi-Bernoulli Filter

This paper proposes a computationally efficient algorithm for distributed fusion in a sensor network in which multi-Bernoulli (MB) filters are locally running in every sensor node for multi-target tracking. The generalized Covariance Intersection (GCI) fusion rule is employed to fuse multiple MB random finite set densities. The fused density comprises a set of fusion hypotheses that grow exponentially with the number of Bernoulli components. Thus, GCI fusion with MB filters can become computationally intractable in practical applications that involve tracking of even a moderate number of objects. In order to accelerate the multi-sensor fusion procedure, we derive a theoretically sound approximation to the fused density. The number of fusion hypotheses in the resulting density is significantly smaller than the original fused density. It also has a parallelizable structure that allows multiple clusters of Bernoulli components to be fused independently. By carefully clustering Bernoulli components into isolated clusters using the GCI divergence as the distance metric, we propose an alternative to build exactly the approximated density without exhaustively computing all the fusion hypotheses. The combination of the proposed approximation technique and the fast clustering algorithm can enable a novel and fast GCIMB fusion implementation. Our analysis shows that the proposed fusion method can dramatically reduce the computational and memory requirements with small bounded L1-error. The Gaussian mixture implementation of the proposed method is also presented. In various numerical experiments, including a challenging scenario with up to forty objects, the efficacy of the proposed fusion method is demonstrated.

Multi-Objective Optimization Based Multi-Bernoulli Sensor Selection for Multi-Target Tracking.

This paper presents a novel multi-objective optimization based sensor selection method for multi-target tracking in sensor networks. The multi-target states are modelled as multi-Bernoulli random finite sets and the multi-Bernoulli filter is used to propagate the multi-target posterior density. The proposed method is designed to select the sensor that provides the most reliable cardinality estimate, since more accurate cardinality estimate indicates more accurate target states. In the multi-Bernoulli filter, the updated multi-target density is a multi-Bernoulli random finite set formed by a union of legacy tracks and measurement-updated tracks. The legacy track and the measurement-updated track have different theoretical and physical meanings, and hence these two kinds of tracks are considered separately in the sensor management problem. Specifically, two objectives are considered: (1) maximizing the mean cardinality of the measurement-updated tracks, (2) minimizing the cardinality variance of the legacy tracks. Considering the conflicting objectives simultaneously is a multi-objective optimization problem. Tradeoff solutions between two conflicting objectives will be derived. Theoretical analysis and examples show that the proposed approach is effective and direct. The performance of the proposed method is demonstrated using two scenarios with different levels of observability of targets in the passive sensor network.

Sensor Selection for Decentralized Large-Scale Multi-Target Tracking Network.

A new optimization algorithm of sensor selection is proposed in this paper for decentralized large-scale multi-target tracking (MTT) network within a labeled random finite set (RFS) framework. The method is performed based on a marginalized δ-generalized labeled multi-Bernoulli RFS. The rule of weighted Kullback-Leibler average (KLA) is used to fuse local multi-target densities. A new metric, named as the label assignment (LA) metric, is proposed to measure the distance for two labeled sets. The lower bound of LA metric based mean square error between the labeled multi-target state set and its estimate is taken as the optimized objective function of sensor selection. The proposed bound is obtained by the information inequality to RFS measurement. Then, we present the sequential Monte Carlo and Gaussian mixture implementations for the bound. Another advantage of the bound is that it provides a basis for setting the weights of KLA. The coordinate descent method is proposed to compromise the computational cost of sensor selection and the accuracy of MTT. Simulations verify the effectiveness of our method under different signal-to- noise ratio scenarios.

Multi-sensor control for multi-object Bayes filters

Sensor management in multi-object stochastic systems is a theoretically and computationally challenging problem. This paper presents a new approach to the multi-target multi-sensor control problem within the partially observed Markov decision process (POMDP) framework. We model the multi-object state as a labeled multi-Bernoulli random finite set (RFS), and use the labeled multi-Bernoulli filter in conjunction with minimizing a task-driven control objective function: posterior expected error of cardinality and state (PEECS). A major contribution is a guided search for multi-dimensional optimization in the multi-sensor control command space, using coordinate descent method. In conjunction with the Generalized Covariance Intersection method for multi-sensor fusion, a fast multi-sensor control algorithm is achieved. Numerical studies are presented in several scenarios where numerous controllable (mobile) sensors track multiple moving targets with different levels of observability. The results show that our method works significantly faster than the approach taken by the state of the art methods, with similar tracking errors.

A Multisensor Multi-Bernoulli Filter

In this paper we derive a multi-sensor multi-Bernoulli (MS-MeMBer) filter for multi-target tracking. Measurements from multiple sensors are employed by the proposed filter to update a set of tracks modeled as a multi-Bernoulli random finite set. An exact implementation of the MS-MeMBer update procedure is computationally intractable. We propose an efficient approximate implementation by using a greedy measurement partitioning mechanism. The proposed filter allows for Gaussian mixture or particle filter implementations. Numerical simulations conducted for both linear-Gaussian and non-linear models highlight the improved accuracy of the MS-MeMBer filter and its reduced computational load with respect to the multi-sensor cardinalized probability hypothesis density filter and the iterated-corrector cardinality-balanced multi-Bernoulli filter especially for low probabilities of detection.

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.

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.

Sensor management for multi-target tracking via multi-Bernoulli filtering

In multi-object stochastic systems, the issue of sensor management is a theoretically and computationally challenging problem. In this paper, we present a novel random finite set (RFS) approach to the multi-target sensor management problem within the partially observed Markov decision process (POMDP) framework. The multi-target state is modelled as a multi-Bernoulli RFS, and the multi-Bernoulli filter is used in conjunction with two different control objectives: maximizing the expected Rényi divergence between the predicted and updated densities, and minimizing the expected posterior cardinality variance. Numerical studies are presented in two scenarios where a mobile sensor tracks five moving targets with different levels of observability.

A Quantitative Analysis on Two RFS-Based Filtering Methods for Multicell Tracking

Multiobject filters developed from the theory of random finite sets (RFS) have recently become well-known methods for solving multiobject tracking problem. In this paper, we present two RFS-based filtering methods, Gaussian mixture probability hypothesis density (GM-PHD) filter and multi-Bernoulli filter, to quantitatively analyze their performance on tracking multiple cells in a series of low-contrast image sequences. The GM-PHD filter, under linear Gaussian assumptions on the cell dynamics and birth process, applies the PHD recursion to propagate the posterior intensity in an analytic form, while the multi-Bernoulli filter estimates the multitarget posterior density through propagating the parameters of a multi-Bernoulli RFS that approximates the posterior density of multitarget RFS. Numerous performance comparisons between the two RFS-based methods are carried out on two real cell images sequences and demonstrate that both yield satisfactory results that are in good agreement with manual tracking method.

Robust Multi-Bernoulli Sensor Selection for Multi-Target Tracking in Sensor Networks

This letter addresses the sensor selection problem for tracking multiple dynamic targets within a sensor network. Since the bandwidth and energy of the sensor network are constrained, it would not be feasible to directly use the entire information of sensor nodes for detection and tracking of the targets and hence the need for sensor selection. Our sensor selection solution is formulated using the multi-Bernoulli random finite set framework. The proposed method selects a minimum subset of sensors which are most likely to provide reliable measurements. The overall scheme is a robust method that works in challenging scenarios where no prior information are available on clutter intensity or sensor detection profile. Simulation results demonstrate successful sensor selection in a challenging case where five targets move in a close vicinity to each other. Comparative results show the superior performance of our method in terms of accuracy of estimating the number of targets and their states.

Comments on "Joint Detection and Estimation of Multiple Objects From Image Observations

The above article [1] introduced an algorithm for multitarget track-before-detect based on a multi-Bernoulli random finite set model (MB-TBD). This new algorithm was compared with the Histogram Probabilistic Multi-Hypothesis Tracker (H-PMHT) on simulated data examples containing multiple targets with non-linear dynamics. The authors reported poor performance from H-PMHT and described several deficiencies of the algorithm. This note highlights unnecessary assumptions made in the assessment of H-PMHT and repeats two of the simulation examples after relaxing them. We demonstrate a substantial improvement in performance compared with the originally published results. The simulation example is also shown to be a relatively high signal to noise problem and good performance is obtained from a conventional detect-then-track algorithm.