Numerical properties of a hyperbolic rotation method for windowed RLS filtering

Numerical properties of the hyperbolic rotation method for windowed RLS filtering are examined. This matrix-oriented approach is important from two standpoints: (1) it provides the LS predictor for a sliding-window block of data, and (2) it is amenable to parallel implementation. It is shown how a hyperbolic rotation matrix may be constructed to update the LS Cholesky factor as a function of the previous Cholesky factor and the data in the sliding window. Finally, it is shown that the hyperbolic rotation method is stable for observation matrices which are not rank-deficient.