Fast, rank adaptive subspace tracking and applications

High computational complexity and inadequate parallelism have deterred the use of subspace-based algorithms in real-time systems. We proposed a new class of fast subspace tracking (FST) algorithms that overcome these problems by exploiting the matrix structure inherent in multisensor processing. These algorithms simultaneously track an orthonormal basis for the signal subspace and preserve signal eigenstructure information while requiring only O(Nr) operations per update (where N is the number of channels, and r is the effective rank). Because of their low computational complexity, these algorithms have applications in both recursive and block data processing. Because they preserve the signal eigenstructure as well as compute an orthonormal basis for the signal subspace, these algorithms may be used in a wide range of sensor array applications including bearing estimation, beamforming, and recursive least squares. We present a detailed description of the FST algorithm and its rank adaptive variation (RA-FST) as well as a number of enhancements. We also demonstrate the FST's rapid convergence properties in a number of application scenarios.