We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multi-target tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the \delta-generalised labelled multi-Bernoulli (\delta-GLMB) filter, showing that a \delta-GLMB density represents a multi-Bernoulli mixture with labelled targets so it can be seen as a special case of PMBM. In addition, we propose an implementation for linear/Gaussian dynamic and measurement models and how to efficiently obtain typical estimators in the literature from the PMBM. The PMBM filter is shown to outperform other filters in the literature in a challenging scenario.

Poisson multi-Bernoulli mixture filter: direct derivation and implementation

The initiation of tracks for newly discovered objects presents unique challenges in space situational awareness. Recent work explores the use of admissible regions to initialize filters for space object tracking; however, these methods require follow-on measurements to refine the initial admissible region solution. This paper presents an approach to the joint search and track problem, designed to allow a single sensor to build and maintain a catalog of objects without requiring an a priori estimate.

Search-Detect-Track Sensor Allocation for Geosynchronous Space Objects

We propose an efficient sequential Monte Carlo probability hypothesis density (PHD) filter which employs the Kalman-gain approach during weight update to correct predicted particle states by minimizing the mean square error between the estimated measurement and the actual measurement received at a given time in order to arrive at a more accurate posterior. This technique identifies and selects those particles belonging to a particular target from a given PHD for state correction during weight computation. Besides the improved tracking accuracy, fewer particles are required in the proposed approach. Simulation results confirm the improved tracking performance when evaluated with different measures.

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Kalman-Gain Aided Particle PHD Filter for Multitarget Tracking

Authors’ addresses: B. K. Habtemariam, A. Aravinthan, R. Tharmarasa, and T. Kirubarajan, McMaster University, Hamilton, ON, Canada, E-mails: (habtembk@mcmaster.ca, aravinthan@ieee.org, tharman@mail.ece.mcmaster.ca, kiruba@mcmaster.ca); K. Punithakumar, GE Healthcare, London, ON, Canada, E-mail: (Kumaradevan. Punithakumar@ge.com); T. Lang, General Dynamics Canada, Ottawa, ON, Canada, E-mail: (tom.lang@gdcanada.com).

Distributed Tracking with a PHD Filter using Efficient Measurement Encoding.

Although the Gaussian mixture probability hypothesis density (GMPHD) filter is a multi-target tracker that can alleviate the computational intractability of the optimal multi-target Bayes filter and its computational complex is lower than that of sequential Monte Carlo probability hypothesis density (SMCPHD), its computational burden can be reduced further. In the standard GMPHD filter, each observation should be matched with each component when the PHD is updated. In practice, time cost of evaluating many unlikely measurements-to-components parings is wasteful, because their contribution is very limited. As a result, a substantial reduction in complexity could be obtained by directly setting relative value associated with these parings. A fast GMPHD algorithm is proposed in the paper based on gating strategy. Simulation results show that the fast GMPHD can save computational time by 60%~70% without any degradation in performance compared with standard GMPHD.

Jing Jiang

Papers

Fast Gaussian Mixture Probability Hypothesis Density Filter