QR methods of O(N) complexity in adaptive parameter estimation

Recent attention in adaptive least squares parameter estimation has been focused on methods derived from the QR factorization owing to the fact that the QR-based algorithms are much more numerically stable and accurate than the traditional pseudo-inverse-based algorithms, also known as normal equation-based algorithms, even though the former is usually much slower than the latter. This paper presents a fast adaptive least squares algorithm for the parameter estimation of linear and some nonlinear time-varying systems. The algorithm is based on Householder transformations. As verified by simulation results, this algorithm exhibits good numerical stability and accuracy. In addition, the new algorithm requires computation and storage with order of O(N) rather than O(N²) where N is the number of unknown parameters to be estimated. This algorithm can be easily extended to construct other kinds of algorithms, such as the generalized adaptive least squares algorithm, the augmented matrix algorithm, and the maximum likelihood algorithm