Robust methods tailored for non-Gaussian narrowband array processing
Williams, Douglas Bennett
Johnson, Don H.
Doctor of Philosophy
Array processing algorithms generally assume that the received signal, composed of both narrowband signals and noise, is Gaussian, which is not true in general. In the context of the narrowband array processing problem, we develop robust methods to accurately estimate the spatial correlation matrix which also utilize a priori information about the matrix structure. For Gaussian processes, structured estimates have been developed which find the maximum likelihood covariance matrix estimate subject to structural constraints on the covariance matrix (8). However, further problems arise when the noise is non-Gaussian and the estimators for Gaussian processes may lead to grossly inaccurate estimates (17). By minimizing the worst asymptotic estimate variance, we obtain the robust structured maximum likelihood type estimates(M-estimates) of the spatial correlation matrix in the presence of noises with probability density functions (p.d.f.) in the $\epsilon$-contamination and Kolmogorov classes. These estimates are robust against variations in the amplitude distribution of the noise and take into account sensor placement. Given these estimates, existing array processing algorithms designed for Gaussian circumstances can be used on non-Gaussian problems. We also demonstrate a parametric structured estimate of the spatial correlation matrix which allows estimation of the arrival angles directly. A method of exactly determining the class of p.d.f.s is developed which only depends on the time domain noise amplitude distributions being second order processes. Knowledge of this p.d.f. class allows development of algorithms which can be used in the presence of any type of second-order noise process and which perform nearly as well as existing ones do with Gaussian noise. We examine the maximum number of signals whose parameters can be estimated with a linear array of M equally spaced sensors. Conventionally, when the signals are mutually uncorrelated, this number has been taken to be one less than the number of sensors. We show how to estimate the signals' directions and amplitudes with the number of signals equal to one less than twice the number of sensors. This increase in the number of signals is accomplished by using length 2$M$ real signal vectors rather than the usual length $M$ complex vectors. We show that 2$M$ of these real vectors are linearly independent with probability one, and, thus, in the presence of additive white noise, the parameters of 2$M$ $-$ 1 signals can be estimated. An algorithm for determining directions and amplitudes is presented. However, computational complexity limits this algorithm to small $M$ and low time-bandwidth products.
Electronics; Electrical engineering; Statistics