Bi-iterative least-square method for subspace tracking

Abstract—Subspace tracking is an adaptive signal processing technique useful for a variety of applications. In this paper, we introduce a simple bi-iterative least-square (Bi-LS) method, which is in contrast to the bi-iterative singular value decomposition (Bi-SVD) method. We show that for subspace tracking, the Bi-LS method is easier to simplify than the Bi-SVD method. The linear complexity algorithms based on Bi-LS are computationally more efficient than the existing linear complexity algorithms based on Bi-SVD, although both have the same performance for subspace tracking. A number of other existing subspace tracking algo-rithms of similar complexity are also compared with the Bi-LS algorithms. Index Terms—Adaptive signal processing, bi-iteration, low-rank approximation, projection approximation, QR decomposition, sin-gular value decomposition, subspace tracking