Adaptive estimation of eigensubspace and tracking the directions of arrival

Abstract

In this paper, we present an adaptive method to estimate the eigensubspace and directions-of-arrival (DOAs) of multiple narrowband plane waves. We first develop, for the arbitrary array and asymptotic case, an approximate complex Newton-update formula for recursively seeking the eigenvector corresponding to the minimum eigenvalue of the data covariance matrix of the underlying complex, stationary signal scenario. The development of the algorithm involves complex differentiation and use of exact gradient and a refined approximation to the Hessian of the cost function in the Newton-update formula derived by Abatzaglou et al. (1991). For seeking the complete noise subspace, we combine this algorithm with the matrix level inflation technique suggested by Mathew et al. (1995). Next, we consider nonstationary signal sources and present the adaptive procedure for tracking the noise subspace and directions of arrival of the moving sources. Tracking of angles of arrival is accomplished by computing the minimum-norm polynomial coefficients and deriving an elegant relationship between the changes in the values of the coefficients and the values of the roots of the polynomial on a snapshot basis. Computer simulations are included to demonstrate the quality of estimated noise subspace and accuracy in the estimates of DOAs. Results are compared with those obtained using some of the existing methods for adaptive subspace estimation (Yang and Kaveh, 1988 ; Yu, 1991) and tracking of angles (Yu, 1991).