FINITE-PRECISION ANALYSIS OF A COVARIANCE ALGORITHM FOR LEAST-SQUARES FIR 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 described. The propagation of finite arithmetic errors as well as data acquisition errors are studied in detail. First, linearization of the main algorithmic 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 computed. The derivation of these bounds heavily depends on the Levinson type structure of the algorithm and the low displacement rank of the problem. The main result of the paper then states that the proposed algorithm is numerically weakly stable. The proposed order recursive algorithm is subsequently utilized as a block adaptive method. Its performance is also demonstrated by long run simulations.