Partially-coupled recursive least squares algorithm for multivariate systems based on the model transformation

This paper investigates the parameter estimation problem for multivariate output-error systems perturbed by autoregressive noises. To reduce the influence of the colored noises on parameter estimates, we turn the original model into the new model with white noises by using the model transformation. In consideration of the high dimensions of multivariate systems and different types of parameters, we decompose the transformed system model into several sub-models in accordance with the number of the outputs. However, the decomposition results in many redundant estimates. Here, we propose two algorithms to cut down the redundant estimates. By taking the average of the parameter estimation vectors, we develop a model transformation partially-coupled (MT-PC) recursive least squares algorithm. Moreover, an MT-PC recursive least squares algorithm is presented by means of the coupling identification concept. Compared with the multivariate recursive generalized least squares algorithm, the two algorithms have higher computational efficiencies and smaller estimation errors. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed algorithms.