Bayesian Multiple Target Tracking

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.