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.

Keywords

• Adaptive subspace tracking
• approximated power iteration
• orthonormal iteration
• projection approximation