Adaptive eigensubspace algorithms for direction or frequency estimation and tracking

The authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator´s practical implementations. The general formulation of the proposed estimator results from an asymptotic argument, which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure. A highly parallel algorithm, denoted the inflation method, is introduced for the estimation of the noise subspace. The simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than P.A. Thompson´s (1980) adaptive version of V.F. Pisarenko´s technique (1973) in estimating frequencies or directions of arrival (DOA) of plane waves. For tracking nonstationary parameters, the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions