A TQR-iteration based adaptive SVD for real time angle and frequency tracking

TLDR: The transposed VR (TQR) iteration is a square root version of the symmetric QR iteration that formulates a TQR-iteration based adaptive SVD algorithm, develops a real time systolic architecture, and analyzes performance.

Abstract: The transposed VR (TQR) iteration is a square root version of the symmetric QR iteration. The TQR algorithm converges directly to the singular value decomposition (SVD) of a matrix and was originally derived to provide a means to identify and reduce the effects of outliers for robust SVD computation. The paper extends the TQR algorithm to incorporate complex data and weighted norms, formulates a TQR-iteration based adaptive SVD algorithm, develops a real time systolic architecture, and analyzes performance. The applications of high resolution angle and frequency tracking are developed and the updating scheme is so tailored. A deflation mechanism reduces both the computational complexity of the algorithm and the hardware complexity of the systolic architecture, making the method ideal for real time applications. Simulation results demonstrate the performance of the method and compare it to existing SVD tracking schemes. The results show that the method is exceptional in terms of performance to cost ratio and systolic implementation. >