1Fast Approximated Power Iteration Subspace Tracking

Abstract — This paper introduces a fast implementation of the power iteration method for subspace tracking, based on an approximation less restrictive than the well known projection approximation. This algorithm, referred to as the fast API method, guarantees the orthonormality of the subspace weighting matrix at each iteration. Moreover, it outperforms many subspace trackers related to the power iteration method, such as PAST, NIC, NP3 and OPAST, while having the same computational complexity. The API method is designed for both exponential windows and sliding windows. Our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations. Index Terms — Subspace tracking, projection approximation, power iteration