ADAPTIVE ESTIMATION OF EIGENSUBSPACE

In a recent work we recast the problem of estimating the minimum eigen vector(eigenvector corresponding to the minimum eigenvalue) of a symme tric positive definite matrix into a neural network framework. We now extend this work using an inflation technique to estimate all or some of the orthogonal eigenvectors of the given matrix. Based on these res ults, we form a cost function for the finite data case and derive a Ne wton-based adaptive algorithm. The inflation technique leads to a high ly modular and parallel structure for implementation. The computationa l requirement of the algorithm is O(N-2), N being the size of the cova riance matrix. We also present a rigorous convergence analysis of this adaptive algorithm. The algorithm is locally convergent and the undes ired stationary points are unstable. Computer simulation results are p rovided to compare its performance with that of two adaptive subspace estimation methods proposed by Yang and Kaveh and an improved version of one of them, for stationary and nonstationary signal scenarios. The results show that the proposed approach performs identically to one o f them and is significantly superior to the remaining two.