Bi-iteration recursive instrumental variable subspace tracking and adaptive filtering

In this paper, we propose a class of fast sequential bi-iteration singular value (Bi-SVD) subspace tracking algorithms for adaptive eigendecomposition of the cross covariance matrix in the recursive instrumental variable (RIV) method of system identification. These algorithms can be used for RIV subspace processing of signals in unknown correlated Gaussian noise. Realizations with O(Nr²) and O(Nr) operations per time step are described, where N is the input vector dimension, and r is the number of dominant singular values and vectors to be tracked. The algorithms are solely based on passive Givens plane rotations and standard matrix-vector multiplications. The matrix inversion lemma is not used. The application and performance of the algorithms is demonstrated in a low-rank RIV subspace adaptive filtering context