Multiple target direction of arrival tracking

yy Abstract| A new algorithm is presented for estimating the directions of arrival of signals from an unknown number of moving signal sources. The parameter space is a countable union of cartesian products of the torus, each product space corresponding to a diierent number of signals reaching the sensor array. A Bayesian posterior probability measure is deened on this parameter space by combining the sensor array manifold models with the von-Mises prior on source motion. The estimates are generated empirically using a random sampling algorithm based on Jump-Diiusion processes 1] and the results are presented from an implementation on a DAP510 massively parallel computer. This correspondence focuses on tracking the directions of arrival (DOA's) of signals emitted from multiple sources in remotely sensed, dynamically changing scenes. There are an unknown number of signal sources assumed moving in a 2-D plane containing a uniform linear array of passive , isotropic sensors. The goal is to track their angular locations relative to the array. Taking the minimum mean squared error (MMSE) approach, we seek the conditional means of statistics of targets' positions under the posterior density. The posterior density being highly nonlinear in the track parameters, precludes the closed form analytic generation of conditional expectations. Therefore, we utilize recent advances in use of random sampling methods for empirically generating estimates from complicated distributions 2, 3]. The random samples are generated by simulating a Markov process with the ergodic property that the empirical distribution of the samples converges to the posterior distribution as described in 1, 4]. The algorithm searches through the connected parts of the parameter space (carte-sian products of the torus) with sample paths corresponding to the solutions of standard diiusion equations; across the disconnected parts of parameter space the jump process determines the transitions, satisfying jump-diiusion dynamics in such a way that the sample statistics converge to their expectation under the posterior. Such methods have been applied previously to the understanding of electron-microscope images containing sub-cellular structures such as mitochondrias and linear membranes 1]. There exists a substantial literature on estimating the DOA's of moving/stationary sources recorded by sensor arrays 5, 6] with the non-linear problem solved using gradient-based techniques and eigen-value analyses in mostly maximum-likelihood settings. Most of this work assumes knowledge of the number of targets which, in general, is time varying and unknown a-priori. The jump-diiusion based sampling algorithm jointly estimates the location parameters along with the …