Unbiased recursive least squares identification methods for a class of nonlinear systems with irregularly missing data

Missing data often occur in industrial processes. In order to solve this problem, an auxiliary model and a particle filter are adopted to estimate the missing outputs, and two unbiased parameter estimation methods are developed for a class of nonlinear systems (e.g., bilinear systems) with irregularly missing data. Firstly, an auxiliary model is constructed to estimate the unknown output, and an auxiliary model-based multi-innovation recursive least squares algorithm is presented by expanding the scalar innovation to an innovation vector. Secondly, according to the bias compensation principle, an auxiliary model-based bias compensation multi-innovation recursive least squares algorithm is proposed to compensate the bias caused by the colored noise. Thirdly, for further improving the parameter estimation accuracy, the unknown true output is estimated by a particle filter, and a particle filtering-based bias compensation multi-innovation recursive least squares algorithm is developed. Finally, a numerical example is selected to validate the effectiveness of the proposed algorithms. The simulation results indicate that the proposed algorithms have good performance in identifying bilinear systems with irregularly missing data.