This paper presents an efficient information-theoretic sensor management method to maximize the performance of the passive multi-sensor system for multi-target tracking. We model the multi-target state as a generalized labeled multi-Bernoulli (GLMB) random finite set and formulate the dynamic sensor selection process as a partially observable Markov decision process (POMDP). The optimization objective is to maximum the information gain obtained from the observed data, which is measured by the Cauchy-Schwarz divergence. This is accomplished with two main technical innovations. The first is a tractable decomposed POMDP based sensor selection solution, in which the informative sensors are selected sequentially from the candidates based on the Cauchy-Schwarz divergence. The second is a novel dual-stage multi-sensor fusion strategy based on the iterated-corrector GLMB filter. Since the uncertainty of the passive multi-sensor system is generally large, the performance of the iterated-corrector scheme can be greatly influenced by the order of sensor updates. To fix this problem, the selected sensors are ranked in order of the Cauchy-Schwarz divergence obtained in sensor selection, followed by the iterated-corrector update. For the multi-sensor fusion, the effect of poor performance sensors is weakened and that of better performance sensors is enhanced. Simulation studies demonstrate the effectiveness and efficiency of the proposed method in challenging passive multi-target tracking scenarios.

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.

The paper addresses the problem of tracking multiple targets with Doppler-only measurements in multi-sensor systems. It is well known that the observability of the target state measured using Doppler-only measurements is very poor, which makes it difficult to initialize the tracking target and produce the target trajectory in any tracking algorithm. Within the framework of random finite sets, we propose a novel constrained admissible region (CAR) based birth model that instantiates the birth distribution using Doppler-only measurements. By combining physics-based constraints in the unobservable subspace of the state space, the CAR based birth model can effectively reduce the ambiguity of the initial state. The CAR based birth model combines physics-based constraints in the unobservable subspace of the state space to reduce the ambiguity of the initial state. We implement the CAR based birth model with the generalized labeled multi-Bernoulli tracking filter to demonstrate the effectiveness of our proposed algorithm in Doppler-only tracking. The performance of the proposed approach is tested in two simulation scenarios in terms of the optimal subpattern assignment (OSPA) error, OSPA⁽²⁾ 
${}^{\left(2\right)}$error, and computing efficiency. The simulation results demonstrate the superiority of the proposed approach. Compared to the approach taken by the state-of-the-art methods, the proposed approach can at most reduce the OSPA error by 58.77%, reduce the OSPA⁽²⁾ error by 43.51%, and increase the computing efficiency by 9.56 times in the first scenario. In the second scenario, the OSPA error is reduced by 62.80%, the OSPA⁽²⁾ ${}^{\left(2\right)}$error is reduced by 43.65%, and the computing efficiency is increased by 2.61 times at most.

To deal with the track coalescence problem of the joint probabilistic data association (JPDA) filter, a novel approach based on the Kullback–Leibler divergence (KLD) is developed in this study. In JPDA, the posterior probability density function (PDF) is approximated by a single Gaussian PDF at each time step. The authors propose a novel method of optimising the posterior PDF to obtain a single Gaussian PDF that minimises the KLD from the posterior PDF. However, the KLD is intractable because the posterior PDF is a Gaussian mixture model. Hence, an approximation of the KLD is introduced as the cost function to simplify the problem. The cost function is a linear combination of multiple objective functions which are not conflicting. Therefore, the minimisation of the cost function is easier to operate, because all objective functions can be optimised simultaneously. In addition, an iterative method is adopted for minimising the cost function. In the iteration process, the tracking accuracy is improved with the monotonic decrease of the cost function. Theoretical analysis and example show the feasibility of the proposed approach. Simulation results demonstrate the advantages of the new approach over others when tracking closely spaced targets with contaminated sensor measurements.

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.

Conditioned on measurement data from sensors, the joint probabilistic data association (JPDA) filter is a popular methodology for tracking multiple objects in clutter. The JPDA filter, however, suffers from the severe track coalescence effect, i.e., tracks following objects in close proximity tend to coalesce. To improve the tracking accuracy, we propose a novel Cauchy–Schwarz set JPDA (CSSJPDA) filter by optimizing the posterior Gaussian mixture density with an iterative successive component-based optimization (ISCO) algorithm in the Cauchy–Schwarz sense. The posterior Gaussian mixture density is marginalized by Gaussian densities to estimate object states at each time step. To improve the marginalization accuracy, the posterior density is optimized in the random finite set (RFS) family. We derive a closed-form expression of the Cauchy–Schwarz divergence between the posterior density and its Gaussian approximation and use it as a cost function for density optimization. To improve the optimization efficiency, we propose the ISCO algorithm to minimize the cost function successively along one Gaussian component at a time and prove its monotone convergence. Two indicative examples are used to illustrate the effectiveness of the CSSJPDA filter. With the iteration, the cost function decreases and the Gaussian approximation becomes more accurate. Simulation results demonstrate that the CSSJPDA filter provides a good tradeoff between the tracking accuracy and the computational efficiency compared to the existing methods. Numerical experiments with a real-world dataset further verify the performances of the proposed method.