A Unified Approach To Adaptive Subspace Estimation

We present a unified optimization approach to adaptively estimating the signal subspace of a covariance matrix. Two optimization criteria, namely the mean-square-error (MSE) minimization and the output variance maximization for the signal subspace estimation are shown to be equivalent, and thus yield the same algorithm when applied with a certain optimization technique. Our analysis shows that both the subspace algorithm with explicit weight orthonormalization and the unconstrained gradient descent algorithm to minimize the MSE can be approximated reasonably to the well-known Oja's subspace algorithm. The global convergence of Oja's subspace algorithm is established based on the Lyapunov function approach. Simulations are provided to confirm the analysis.