Recursive Least Squares Identification Methods For Pseudo-Linear Regressive Systems Using Data Filtering

In the space navigation, astronomical system, social and economic systems, indus-trial process and many other areas, the object of study is generally more complex, such as single-input pseudo-linear system. The existing theories are often difficult to directly obtain the corresponding mathematical model by using observational data to determine the mathematical model of the object and its parameters. Based on the National Na-ture Science Foundation of China, this thesis studies the two-stage identification methods for pseudo-linear systems with colored noises. After reading some relevant references, the author briefly reviews the history of system identification and overviews the existed parameter estimation methods in the exordium, and then derives the filtering based re-cursive least squares identification methods for different system models in detail in the next chapters. The main two results are as follows:1. For pseudo-linear moving average systems, filtering based recursive least squares esti-mation algorithm is developed. The main idea is to design a linear filter according to the structure of noise model, and to transform the system model into a model with white noise by filtering the inputs and outputs of the system by the corresponding filter designed, and then to identify the transformed system model and noise model by using the least squares principle, at the same time, the method is applied to pseudo-linear auto-regressive systems and pseudo-linear Box-Jenkins systems, The simulation results show that the proposed algorithms are effective.2. For pseudo-linear output error moving average systems, parameter identification metho based on auxiliary model and filtering technique is developed, this section presents a auxiliary model based recursive least squares parameter estimation algorithm through constructing an auxiliary model and replacing the unknown inner variables with the outputs of the auxiliary model. Furthermore, through filtering the observation data with the estimated transfer function of the noise model and using the filtered data, we present a data filtrating based recursive least squares parameter estimation algo-rithm. Compared with the auxiliary model based recursive least squares parameter estimation algorithm. The filtering based recursive least squares parameter estimation algorithm requires less computational effort and has higher computational efficiency, at the same time, the method is applied to pseudo-linear output error auto-regressive systems and pseudo-linear output error Box-Jenlins systems, The simulation results indicate that the proposed algorithms are effective. In summary, this thesis proposes estimation algorithms for pseudo-linear regressive systems and pseudo-linear output error regressive systems, the performances of the algo-rithms are illustrated by computer simulations.