On the Recursive Algorithm of Bias Compensated Weighted Least Squares Method

This paper investigates the problem of identifying errors-in-variables (EIV) models, where the both input and output measurements are corrupted by white noises, and addresses a new efficient recursive identification algorithm. The identification problem of EIV models with unknown noise variances has been studied extensively and several methods have been proposed. To be further developed in terms of estimation accuracy, the bias compensated weighted least squares (BCWLS) method with only requirement of input noise variance estimate has been proposed by using the biased weighted least squares estimate. However, the recursive form for the standard least squares estimate cannot be applied to recursively compute the BCWLS estimate because the weight matrix is not diagonal. To recursively compute the BCWLS estimate, the recursive forms for the WLS estimate and the input noise variance estimate are derived when the biased WLS estimate is two-stage least squares type estimate. The results of a simulated example indicate that the proposed recursive algorithm provides good results.