Campuses:

(Team 4) Problems in Nonlinear Filtering

Monday, August 9, 2004 - 11:00am - 11:20am
Keller 3-180
John Hoffman (Lockheed Martin)
Filtering is the process of estimating the state of a stochastic dynamical system over time from a sequence of noisy observations of the system. Filtering theory plays a vital role in navigation, air traffic control, and a variety of other signal processing applications. Our problem will focus on an aspect of filtering known as multi-target filtering. In multi-target filtering, there are multiple targets each moving, getting born, dieing, spawning new targets. Standard multi-target filtering techniques such as the Multi-Hypothesis Tracker Correlator, and the Joint Probabilistic Data Association algorithm are not able to handle situations where the targets are close to each other, and/or there is a large amount of noise without massive computational resources. Recently, Dr. Ron Mahler of Lockheed Martin has proposed an alternative approach called the Probability Hypothesis Density Function (PHD). The essential idea of the PHD is to track the first multi-target moment density function. That is, to track the function D(x) where the integral of D(x) over a set A, is the expected number of targets in that set. We will be investigating a topic associated with the PHD in our group.

References:

Mahler, A theoretical Foundation for the Stein-Winter Probability Hypothesis Density (PHD) Multitarget Tracking Approach, Proc. 2002 MSS Nat'l Symp. on Sensor and Data Fusion, Vol I (unclassified), San Antoni TX, June 2000.

Mahler, Approximate Multisensor-Multitarget joint Detection, Tracking and Identification Using a First Order Multitarget Moment Statistic, IEEE Trans. AES, to appear.

Goodman, Mahler and Nguyen, Mathematics of Data Fusion, Kluwer Academic Publishers 1997.

Doucet, Godsill, and Andrieu, On Sequential Monte Carlo Sampling Methods for Bayesian Filtering, Stat. Comp. No. 10, pp 197-208, 2000.

Bar-Shalom and Li, Multitarget-Multisensor Tracking: Principles and Techniques, Storrs, CT: YBS Publishing, 1995