An adaptive TQR-SVD for angle and frequency tracking

The transposed QR (TQR) iteration is a square root version of the symmetric QR iteration and defines the TQR algorithm. The authors review the TQR algorithm and extend it to incorporate weighting schemes and complex data. Geometrically, the algorithm breaks each QR iteration into least square regression fit followed by a rotation to the regression hyperplane. This basic insight leads to a rapidly converging adaptive algorithm for tracking the singular values and right singular vectors of an exponentially weighted and downward growing data matrix. The applications of high resolution angle and frequency tracking are developed using subspace averaging based deflation to reduce computation. Simulation results demonstrate the performance of the method, and it is compared to other SVD tracking schemes