Random finite set (RFS) based filters for superpositional observation model

The random finite set (RFS) modeling framework has been developed in the past couple of decades to model the multi-target state and observations. We are interested in developing RFS based computationally efficient filters when the observation model has a superpositional form. Specifically, the observations from multiple targets combine in an additive fashion. Examples of sensors which can be modeled in this manner are acoustic sensors, radio frequency sensors and antenna arrays in wireless communications. We have developed filters using RFS theory and the related finite set statistics. Approximate equations are derived for PHD, CPHD and multi-Bernoulli filters. Computationally tractable auxiliary particle filter implementations of these filters have also been developed. They are successfully applied to the problem of multi-target tracking in simulated RF tomography environment.

Related publications :

  1. Nannuru, S., and M. J. Coates"Particle filter implementation of the multi-Bernoulli filter for superpositional sensors", 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Saint Martin, Dec 2013.
  2. Nannuru, S., and M. J. Coates"Multi-Bernoulli filter for superpositional sensors", 16th International Conference on Information Fusion, Istanbul, Turkey, Jul 2013.
  3. Nannuru, S.M. J. Coates, and R. Mahler"Computationally-tractable approximate PHD and CPHD filters for superpositional sensors", IEEE Journal of Selected Topics in Signal Processing, vol. 7, Jun 2013.
  4. Thouin, F.S. Nannuru, and M. J. Coates"Multi-target Tracking for Measurement Models with Additive Contributions, Revised version", International Conference on Information Fusion, Chicago, Illinois, July 2011.


Superpositional observation model

The superpositional sensor observation model can be characterized as follows:

1. Each target can potentially affect multiple   sensor measurements

A single target can affect multiple sensors

2. Multiple targets can simultaneously affect a sensor measurement 

3. Multiple targets affect a sensor measurement  in additive fashion


PHD and CPHD filters

The probability hypothesis density (PHD) and the cardinalized probability hypothesis density (CPHD) filters are respectively based on Poisson process and independent and identically distributed cluster (IIDC) process modeling of the multi-target state. The PHD filter propagates the first moment (also called PHD) of the multi-target state. The CPHD filter propagates the first moment and the cardinality distribution of the multi-target state. The PHD function has a multi-modal form where the modes correspond to regions with high target occurance probability.

Multi-modal nature of PHD function.

Multi-Bernoulli filter

The multi-Bernoulli filter models the multi-target state using the multi-Bernoulli RFS. A multi-Bernoulli RFS is the union of multiple Bernoulli RFS each of which models the existance probability and state distribution of a single target. The multi-Bernoulli filter is realized by propagating the conditional PHD components corresponding to the Bernoulli sets. Thus the individual modes of the PHD are separately propagated allowing more accurate state estimation and tracking.

Decomposing the PHD into the conditional PHDs allows tracking of each target accurately.


Code for auxiliary particle filter implementation of CPHD filter, multi-Bernoulli filter and hybrid multi-Bernoulli CPHD filter