FINITE-PRECISION ANALYSIS OF A COVARIANCE ALGORITHM FOR LEAST-SQUARESFIR FILTERING AND AR MODELING

In this paper a numerically stable, fast-order recursive algorithm for the solution of the covariance approach in signal modeling is describ ed. The propagation of finite arithmetic errors as well as data acquis ition errors are studied in detail. First, linearization of the main a lgorithmic recursions is carried out. Then, a suitable transformation converts the resulting state equations of the accumulated errors into their residual form. Subsequently, bounds for the residuals are comput ed. The derivation of these bounds heavily depends on the Levinson typ e structure of the algorithm and the low displacement rank of the prob lem. The main result of the paper then states that the proposed algori thm is numerically weakly stable. The proposed order recursive algorit hm is subsequently utilized as a block adaptive method. Its performanc e is also demonstrated by long run simulations.