A second-order PHD filter with mean and variance in target number

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters

Poisson multi-Bernoulli conjugate prior for multiple extended object filtering

This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object filtering. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a conjugate prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter performs well in comparison to the extended target d-GLMB and LMB filters. An experiment with Lidar data illustrates the benefit of tracking both detected and undetected targets

Predicting Multiple Target Tracking Performance for Applications on Video Sequences

This dissertation presents a framework to predict the performance of multiple target tracking (MTT) techniques. The framework is based on the mathematical descriptors of point processes, the probability generating functional (p.g.fl). It is shown that conceptually the p.g.fls of MTT techniques can be interpreted as a transform that can be marginalized to an expression that encodes all the information regarding the likelihood model as well as the underlying assumptions present in a given tracking technique. In order to use this approach for tracker performance prediction in video sequences, a framework that combines video quality assessment concepts and the marginalized transform is introduced. The multiple hypothesis tracker (MHT), Joint Probabilistic Data Association (JPDA), Markov Chain Monte Carlo (MCMC) data association, and the Probability Hypothesis Density filter (PHD) are used as a test cases. We introduce their transforms and perform a numerical comparison to predict their performance under identical conditions. We also introduce the concepts that present the base for estimation in general and for applications in computer vision

Predicting Multiple Target Tracking Performance for Applications on Video Sequences

This dissertation presents a framework to predict the performance of multiple target tracking (MTT) techniques. The framework is based on the mathematical descriptors of point processes, the probability generating functional (p.g.fl). It is shown that conceptually the p.g.fls of MTT techniques can be interpreted as a transform that can be marginalized to an expression that encodes all the information regarding the likelihood model as well as the underlying assumptions present in a given tracking technique. In order to use this approach for tracker performance prediction in video sequences, a framework that combines video quality assessment concepts and the marginalized transform is introduced. The multiple hypothesis tracker (MHT), Joint Probabilistic Data Association (JPDA), Markov Chain Monte Carlo (MCMC) data association, and the Probability Hypothesis Density filter (PHD) are used as a test cases. We introduce their transforms and perform a numerical comparison to predict their performance under identical conditions. We also introduce the concepts that present the base for estimation in general and for applications in computer vision

Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA and association-based MeMBer

Recent developments in random finite sets (RFSs) have yielded a variety of tracking methods that avoid data association. This paper derives a form of the full Bayes RFS filter and observes that data association is implicitly present, in a data structure similar to MHT. Subsequently, algorithms are obtained by approximating the distribution of associations. Two algorithms result: one nearly identical to JIPDA, and another related to the MeMBer filter. Both improve performance in challenging environments.Comment: Journal version at http://ieeexplore.ieee.org/document/7272821. Matlab code of simple implementation included with ancillary file