On inverse factorization adaptive least-squares algorithms

This paper presents an adaptive exponentially weighted algorithm for least-squares (LS) system identification. The algorithm updates an inverse 'square root' factor of the input data correlation matrix, by applying numerically robust orthogonal Householder transformations. The scheme avoids, almost entirely, costly square roots and divisions (present in other numerically well-behaved adaptive LS schemes) and provides directly the estimates of the unknown system coefficients. Furthermore, it offers enhanced parallelism, which leads to efficient implementations. A square array architecture for implementing the new algorithm, which comprises simple operating blocks, is described. The numerically robust behavior of the algorithm is demonstrated through simulations. The algorithm is compared to the recently developed inverse factorization QR scheme (Alexander and Ghirnikar, 1993), in terms of computational complexity, parallel potential and numerical properties.