METHOD FOR STABLE AND ACCURATE SOLUTION FOR AN ILL-CONDITIONED SYSTEM OF NORMAL EQUATIONS ASSOCIATED WITH A PREDICTION FILTER WHOSE OUTPUT IS DEFINED AS A TIME ADVANCED VERSION OF THE INPUT

A method for obtaining a stable and accurate solution for an ill-conditioned system of normal equations associated with digital Weiner filter for a time invariant system and/or an autoregressive operator of an autoregressive model. A time invariant stochastic model, uses a Gram_Schmidt process of orthonormalisation to condition the coefficient matrix, a singular matrix associated with such a system of normal equations, to an identity matrix. The observed output of the digital Weiner filter and/or autoregressive operator is defined as a time advanced version of the input. The method has application in situations where digitized data at smaller sampling intervals are made available.