Label GM-PHD Filter Based on Threshold Separation Clustering

Gaussian mixture probability hypothesis density (GM-PHD) filtering based on random finite set (RFS) is an effective method to deal with multi-target tracking (MTT). However, the traditional GM-PHD filter cannot form a continuous track in the tracking process, and it is easy to produce a large number of redundant invalid likelihood functions in a dense clutter environment, which reduces the computational efficiency and affects the update result of target probability hypothesis density, resulting in excessive tracking error. Therefore, based on the GM-PHD filter framework, the target state space is extended to a higher dimension. By adding a label set, each Gaussian component is assigned a label, and the label is merged in the pruning and merging step to increase the merging threshold to reduce the Gaussian component generated by dense clutter update, which reduces the computation in the next prediction and update. After pruning and merging, the Gaussian components are further clustered and optimized by threshold separation clustering, thus as to improve the tracking performance of the filter and finally realizing the accurate formation of multi-target tracks in a dense clutter environment. Simulation results show that the proposed algorithm can form a continuous and reliable track in dense clutter environment and has good tracking performance and computational efficiency.

Bayesian multiple target tracking

<p>This thesis addresses several challenges in Bayesian target tracking, particularly for array signal processing applications, and for multiple targets. The optimal method for multiple target tracking is the Bayes’ joint filter that operates by hypothesising all the targets collectively using a joint state. As a consequence, the computational complexity of the filter increases rapidly with the number of targets. The probability hypothesis density and the multi-Bernoulli filters that overcome this complexity do not possess a suitable framework to operate directly on phased sensor array data. Instead, such data is converted into beamformer images in which close targets may not be effectively resolved and much information is lost. This thesis develops a multiple signal classification (MUSIC) based multi-target particle filter that improves upon the filters mentioned above. A MUSIC based multi-Bernoulli particle filter is also developed, that operates more directly on array data. The above mentioned particle filters require a resampling step which impedes information accumulation over successive observations, and affects the detection of very covert targets. This thesis develops soft resampling and soft systematic resampling to overcome this problem without affecting the accuracy of approximation. Additionally, modified Kolmogorov-Smirnov testing is proposed, to numerically evaluate the accuracy of the particle filter approximation.</p>

Bayesian multiple target tracking

<p>This thesis addresses several challenges in Bayesian target tracking, particularly for array signal processing applications, and for multiple targets. The optimal method for multiple target tracking is the Bayes’ joint filter that operates by hypothesising all the targets collectively using a joint state. As a consequence, the computational complexity of the filter increases rapidly with the number of targets. The probability hypothesis density and the multi-Bernoulli filters that overcome this complexity do not possess a suitable framework to operate directly on phased sensor array data. Instead, such data is converted into beamformer images in which close targets may not be effectively resolved and much information is lost. This thesis develops a multiple signal classification (MUSIC) based multi-target particle filter that improves upon the filters mentioned above. A MUSIC based multi-Bernoulli particle filter is also developed, that operates more directly on array data. The above mentioned particle filters require a resampling step which impedes information accumulation over successive observations, and affects the detection of very covert targets. This thesis develops soft resampling and soft systematic resampling to overcome this problem without affecting the accuracy of approximation. Additionally, modified Kolmogorov-Smirnov testing is proposed, to numerically evaluate the accuracy of the particle filter approximation.</p>

State Estimation and Smoothing for the Probability Hypothesis Density Filter

<p>Tracking multiple objects is a challenging problem for an automated system, with applications in many domains. Typically the system must be able to represent the posterior distribution of the state of the targets, using a recursive algorithm that takes information from noisy measurements. However, in many important cases the number of targets is also unknown, and has also to be estimated from data. The Probability Hypothesis Density (PHD) filter is an effective approach for this problem. The method uses a first-order moment approximation to develop a recursive algorithm for the optimal Bayesian filter. The PHD recursion can implemented in closed form in some restricted cases, and more generally using Sequential Monte Carlo (SMC) methods. The assumptions made in the PHD filter are appealing for computational reasons in real-time tracking implementations. These are only justifiable when the signal to noise ratio (SNR) of a single target is high enough that remediates the loss of information from the approximation. Although the original derivation of the PHD filter is based on functional expansions of belief-mass functions, it can also be developed by exploiting elementary constructions of Poisson processes. This thesis presents novel strategies for improving the Sequential Monte Carlo implementation of PHD filter using the point process approach. Firstly, we propose a post-processing state estimation step for the PHD filter, using Markov Chain Monte Carlo methods for mixture models. Secondly, we develop recursive Bayesian smoothing algorithms using the approximations of the filter backwards in time. The purpose of both strategies is to overcome the problems arising from the PHD filter assumptions. As a motivating example, we analyze the performance of the methods for the difficult problem of person tracking in crowded environments</p>

State Estimation and Smoothing for the Probability Hypothesis Density Filter

<p>Tracking multiple objects is a challenging problem for an automated system, with applications in many domains. Typically the system must be able to represent the posterior distribution of the state of the targets, using a recursive algorithm that takes information from noisy measurements. However, in many important cases the number of targets is also unknown, and has also to be estimated from data. The Probability Hypothesis Density (PHD) filter is an effective approach for this problem. The method uses a first-order moment approximation to develop a recursive algorithm for the optimal Bayesian filter. The PHD recursion can implemented in closed form in some restricted cases, and more generally using Sequential Monte Carlo (SMC) methods. The assumptions made in the PHD filter are appealing for computational reasons in real-time tracking implementations. These are only justifiable when the signal to noise ratio (SNR) of a single target is high enough that remediates the loss of information from the approximation. Although the original derivation of the PHD filter is based on functional expansions of belief-mass functions, it can also be developed by exploiting elementary constructions of Poisson processes. This thesis presents novel strategies for improving the Sequential Monte Carlo implementation of PHD filter using the point process approach. Firstly, we propose a post-processing state estimation step for the PHD filter, using Markov Chain Monte Carlo methods for mixture models. Secondly, we develop recursive Bayesian smoothing algorithms using the approximations of the filter backwards in time. The purpose of both strategies is to overcome the problems arising from the PHD filter assumptions. As a motivating example, we analyze the performance of the methods for the difficult problem of person tracking in crowded environments</p>

Multi-robot Cardinality Balanced Multi-Bernoulli Filter SLAM Method

In order to improve the Simultaneous Localization and Mapping (SLAM) accuracy of mobile robots in complex indoor environments, the multi-robot cardinality balanced Multi-Bernoulli filter SLAM method (MR-CBMber-SLAM) is proposed. First of all, this method introduces a Multi-Bernoulli filter based on the random finite set (RFS) theory to solve the complex data association problem. Besides, this method aims at the problem that the Multi-Bernoulli filter will overestimate in the aspect of SLAM map features estimation, and combines the strategy of cardinality balanced with the Multi-Bernoulli filter. What’s more, in order to further improve the accuracy and operating efficiency of SLAM, a multi-robot strategy and a multi-robot Gaussian information fusion (MR-GIF) method are proposed. In the experiment, the MR-CBMber-SLAM method is compared with the multi-vehicle Probability Hypothesis Density SLAM (MV-PHD-SLAM) method. The experimental results show that the MR-CBMber-SLAM method is better than MV-PHD-SLAM method. Therefore, it effectively verifies that the MR-CBMber-SLAM method is more adaptable to the complex indoor environment.

Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment

A major advantage of the use of passive sonar in the tracking multiple underwater targets is that they can be kept covert, which reduces the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the complexity of data association between measurements and targets make the problem of underwater passive multiple target tracking challenging. To deal with these problems, the cardinalized probability hypothesis density (CPHD) recursion, which is based on Bayesian information theory, is developed to handle the data association uncertainty, and to acquire existing targets’ numbers and states (e.g., position and velocity). The key idea of the CPHD recursion is to simultaneously estimate the targets’ intensity and the probability distribution of the number of targets. The CPHD recursion is the first moment approximation of the Bayesian multiple targets filter, which avoids the data association procedure between the targets and measurements including clutter. The Bayesian-filter-based extended Kalman filter (EKF) is applied to deal with the nonlinear bearing and Doppler measurements. The experimental results show that the EKF-based CPHD recursion works well in the underwater passive multiple target tracking system in cluttered and noisy environments.