Bayesian Inference for Multi-Line Spectra in Linear Sensor Array

Viet Hung Tran, Wenwu Wang, Yuhui Luo, Jonathon A. Chambers

Abstract: For a linear sensor array, using line spectra is a common technique for estimating directions of arrival (DOA) of single-tone sources. Yet, very few papers consider multitone sources. For the first time, we provide the optimal Bayesian inference for multi-line spectra, i.e. a superposition of line spectra, and estimate the DOAs of the multi-tone sources. For tractable computation via fast Fourier transform, we apply a grid-based method, in which source's tones and sensor's array measure are both uncorrelated. Exploiting this method, we interpret the superposition of sensor's data as a complex Gaussian mixture of multi-tone signals. We then estimate DOA via conjugate Von-Mises, also known as circular Gaussian distribution. Our simulation shows that the multitone method is superior to traditional single-tone method for detecting multi-tone source's frequencies, particularly for the sources with overlapping frequencies. The posterior DOA's resolution can be tuned via Von-Mises' parameter a priori, which enhances the sparsity of DOA's estimation.