Bias Compensation Based Recursive Least Squares Identification Based On Latest Estimation For Output Error Model

The least square algorithm is widely used in the field of system identification, but it is not unbiased for output error model. Bias compensation is named by adding bias to the estimation result. With the development of industry, systems are more and more complex, the dimension of models and the order are rising, and the calculation quantity is increasing. The traditional two-stage identification algorithm can reduce the computational load, but it will cause the problem of slow convergence speed. This paper, based on bias compensation based recursive least squares identification algorithm, in order to reduce the calculation amount and improve the convergence characteristics, will be from the following aspects.For the OE model with white noise, the system is decomposed into two subsystems which are input and output parameters respectively by using hierarchical identification principle. Two subsystems are identified by using the bias compensation principle. The two-stage bias compensation based recursive least squares identification algorithm is established. Taking into account the latest estimation is more close to the true value of the parameter, the estimation of a subsystem is applied to the parameter estimation of the other, and a modified bias compensation based recursive least square identification algorithm based on latest estimation is proposed. Compared with the BCRLS algorithm, the new algorithm can get smaller computation. Simulation result in MATLAB shows that the new algorithm can improve the convergence speed of the two-stage identification algorithm and has good convergence accuracy and anti-interference ability.In order to be able to identify the parameters of time-varying system, combining the principle of hierarchical identification and the forgetting factor, two-stage bias compensation based recursive least square algorithm with forgetting factor is obtained. To make full use of latest estimation, a new identification algorithm named the bias compensation recursive least square algorithm based on latest estimation with forgetting factor is proposed. The computational load of new proposed identification algorithm is smaller. The simulation experiment shows that the algorithm has better tracking capability than the two-stage identification algorithm, and estimation of constant parameters of time-varying system are more precise by choosing proper forgetting factor of the two subsystems.In summary, identification algorithms based on latest estimation for the output error model are derived. It is proved that it can reduce calculation quantity and improve the convergence speed of the two-stage algorithm.