Subspace approximation based algorithms for adaptive high resolution spectrum estimate

In this paper, subspace approximation based algorithms are developed for adaptive high resolution spectrum estimation. Our approach is to adopt adaptive eigen-subspace computation algorithms into subspace approximation methods. Three subspace approximation methods are considered in this paper. They are the Multiple Signal Classification Method (MUSIC), Toeplitz Approximation Method (TAM) and Noise Subspace Approximation Method (NOSSAM). Given an eigen-subspace of a Hermitian covariance matrix, our goal is to update the eigen-subspace estimate when the original covariance matrix is undergone a rank one update. To facilitate real time computation, it is desired to avoid the eigen decomposition on the newly updated covariance matrix. Three algorithms, namely, the Adaptive Block Power method (ABPM), the Adaptive Subspace Iteration method (ASI), and the Adaptive Block Gradient Subspace Iteration method (BGSI) are derived. Among these three algorithms, the adaptive BGSI method stands out due to its superb performance. Sample simulation results will be reported to illustrate the methods presented in this paper.