A new state-space approach for direction finding

Direction-of-arrival estimation using state-space models in sensor array processing with a uniform Linear array can be reduced to finding a solution to the equation U˜₁F≈U˜₂ for F, where noises in both sides of the equation are highly correlated. Least squares or even total least squares solutions are not optimal, and the complicated covariance structure in U˜₁ and U˜₂ does not allow a weighted total least squares procedure to be carried out. The approach presented in this correspondence is to first solve a least squares problem to get an estimate of the underlying subspace represented by the noisy basis vectors in U˜₁ and U˜₂. An approximate error covariance matrix for the least squares problem is obtained using a first-order perturbation expansion. This covariance matrix is used to solve for the underlying subspace in a weighted least squares sense. Parameters are then extracted from the estimated subspace. Numerical examples show that the performance of the proposed method is very close to the Cramer-Rao bound