Bi-iteration Subspace Tracking

Two classical subspace estimation algorithms are MUSIC and ESPRIT, these traditional high resolution subspace algorithms show good performances in eigen subspace estimation, yet they have some disadvantages. On one side, both algorithms assume that the background noise is spatially white Gaussian noise. In real applications however, the noise is not always white Gaussian noise, this made these algorithms invalid; on the other side, these algorithms are batch methods, when all the observed data are received, they are disposed at one time. If the signals are time-variant, these methods are not suitable anymore. Based on the analysis of the existing adaptive subspace tracking algorithms, such as the projection approximation subspace tracking (PAST) algorithm and the power method, this paper proposes an algorithm which can be viewed as approximated power method and it is a bi-iterate rank-one update model. The signal subspace can be obtained through the recursive least square (RLS) solutions of two unconstrained weight functions. Introducing instrumental variable (IV) can make this algorithm used in colored noise environment. Two proper approximations are made in the deduction to reduce the computational complexity. Finally the tracking results are orthonormalized to obtain better performances. Simulation results proved the efficiency of the proposed algorithm.