Analog diffusion network architecture for solving data association problems in multitarget tracking

Abstract

The solution of the data association problem in a multi-target tracking scenario requires the computation of probabilities, (beta) <SUB>i</SUB><SUP>j</SUP>, of assigning the i-th measurement to the j-th target. Previously, we have suggested a parallel structure based on a layered, asynchronous (sequential) Boltzmann machine for the estimation of the association probabilities. An efficient analog realization of this structure with stochastic neurons is presented here. The dynamics of this network are described by a vector Langevin equation, and as a result, the network approximates a purely synchronous Boltzmann machine, with potentially rapid convergence. Asymptotically, the probability (beta) <SUB>i</SUB><SUP>j</SUP> equals the activation frequency of the quantized neuron output (upsilon) <SUB>ij</SUB>, in a layered two-dimensional network. Design criteria for approximating the true association probabilities are described. The transient and steady state behaviors of each stochastic neuron, shown to be a diffusion process in a bounded region, are analyzed. The performance of the layered diffusion network is compared with a theoretical bound and also with the performance of an asynchronous Boltzmann machine.