An Improved Adaptive Subspace Tracking Algorithm Based on Approximated Power Iteration

Abstract

A subspace tracking technique has drawn a lot of attentions due to its wide applications. The main objective of this approach is to estimate signal or noise subspace basis for the sample covariance matrix. In this paper we focus on providing a fast stable and adaptive subspace tracking algorithm that is implemented with low computational complexity. An alternative realization of the fast approximate power iteration (FAPI) method termed modified FAPI (MFAPI) is also presented. Rather than solving an inverse square root of a matrix employed in the FAPI the MFAPI applies the matrix product directly to ensure the orthonormality of the subspace basis matrix at each recursion. This approach yields a simpler derivation and is numerically stable while maintaining a similar computational complexity as compared with that of the FAPI. Furthermore we present a detailed mathematical proof of the numerical stability of our proposed algorithm. Computer simulation results indicate that the MFAPI outperforms many classical subspace tracking algorithms particularly at the transient-state step.