Infinite Precision Analysis of the Fast or Algorithms Based on Backward Prediction Errors

The conventional QR Decomposition Recursive Least Squares (QRD-RLS) method requires the order of X 2 multiplications-O[1\,JJ-per output sample. Nevertheless. a number of Fast QRD-RLS algorithms have been proposed with O[lYJ of complexity. Particularly thc Fast QRD-RLS al­ gorithms based on backward prediction enol'S are well known for their good numerical behaviors and low complexities. In such a scenario. considering a case where fixed-point arith­ metic is employed. an infinite precision analysis offering the mean square values of the internal variables becomes very at­ tractive for a practical implementation. In addition to this. a finite-precision analysis requires the estimates of these mean square values. In this work. we first present an overview of the main Fast QRD-RLS algorithms. followed by an infinite precision analysis concerning the steady state mean square values of the internal variables 01" four FQR-RLS algorithms. We stress the fact that the goal of this paper is the presentation of the infinite precision analysis results. the expressions for the mean square values of the internal variables. for all FQR algorithms based on backward prediction errors. The validity of these analytical expressions is verified through computer simulations. carried out in a system identification setup. In the appendixes. the pseudo-code detailed implementations of each algorithm are listed.