Updating the Jacobi SVD for nonstationary data
Flavio Lorenzelli, K. Yao · IEE Proceedings - Vision Image and Signal Processing · 1997
An effective updating algorithm for singular value decomposition (SVD), based on Jacobi rotations, has recently been proposed (Moonen et al., 1992). This algorithm is composed of two basic steps: QR updating and rediagonalisation. The authors are concerned with the behaviour of this algorithm for nonstationary data, and the effect of the updating rate on tracking accuracy. To overcome the trade-off between accuracy and updating rate intrinsic in the original algorithm, the authors propose two schemes which improve the overall performance when the rate of change of the data is high. In the ‘variable rotational rate’ scheme, the number of Jacobi rotations per update is dynamically determined. In the ‘variable forgetting factor’ approach, the effective width of the observation adjusts to the data nonstationarity. Behaviour and performance of the two schemes are discussed and compared. Applications to direction-of-arrival estimation and speech processing are given.