Wideband Array Signal Processing Using MCMC Methods In Colored Noise

This paper proposes a novel Bayesian solution to a difficult problem of joint detection and estimation of wideband sources impinging on a linear array of sensors in spatially colored noise with arbitrary covariance matrix. The wideband signals are approximated by an interpolation function and the signal samples. With the appropriate choices of prior distribution functions of the parameters, nuisance parameters, including the unknown noise covariance matrix, are analytically integrated out, allowing the use of the reversible jump Markov chain Monte Carlo (MCMC) procedure to simulateneously detect the unknown model order and estimate the inter-sensor delays (ISDs) of the sources. Advantages of the proposed method include joint detection of model order and estimation of the ISD parameters, relaxation of the assumption of white Gaussian observation noise, and the fact that reliable performance can be obtained using significantly fewer observations than previous wideband methods. The ISD estimation performance of the proposed method is compared with the theoretical Cramér Rao lower bound (CRLB) for this problem. Simulation results demonstrate the effectiveness and robustness of the method.