Computationally efficient adaptive identification algorithms

The Recursive Weighted Least-Squares (RWLS) identification algorithm is commonly used in adaptive systems. It is well-known that the conventionally mechanized RWLS algorithm is numerically unstable so that it is generally implemented in an algebraically equivalent matrix factorized form (square-root or U-D factorization techniques). In this paper we present two new factorized forms for the implementation of the RWLS algorithm with a forgetting factor. These factorized algorithms use orthogonal transformations such as Modified Gram-Schmidt (MGS) or Modified Weighted Gram-Schmidt (MWGS) transformations which are both numerically robust. The factorization techniques are then applied to a regularized Adaptive Least-Squares (ALS) algorithm. Moreover to handle abrupt parameter variations a new ALS algorithm, based on the use of a fault detection procedure is described.