Subspace tracking in a sensor array using complex Bingham distribution

Abstract

This study presents a subspace-based tracking algorithm called Bingham filter using the outputs of a sensor array. Given n sensors in the sensor array with spatially and temporally white Gaussian noise in the outputs of the array, the Bingham filter estimates the signal subspaces generated by the targets based on the phased array observations, a priori information and previous estimates. Assuming the complex Bingham distribution as the probability distribution of the target subspace, the authors propose a closed-form solution to the problem of updating the predicted subspace using the phased array observations. Furthermore, the authors offer a closed-form solution for the prediction step of the tracking algorithm based on the relation between the complex Bingham distribution parameters and its covariance matrix. Combining these two steps, a new subspace tracking algorithm is derived that is similar to the Kalman filter. The algorithm is applied to track underwater targets and its efficiency is investigated using simulated phased array observations. Simulation results show that compared with the multiple signal classification (MUSIC) algorithm alone, the combination of the Bingham filter and MUSIC algorithm has better performance in low SNR scenarios.