Bias Compensation Based Recursive Least Squares Identification For ARMAX Model

Establishing a corresponding mathematical model is the primary factor of researching questions in industrial production. System identification is an effective method of mathematical modeling. The least squares method is the simplest and most widely used in system identification methods to get the system parameter estimation. The least squares estimation with colored noises is biased for equation error models. With the increase of the sampled data, the least squares method prone to "data saturation" phenomenon if the old data has the same influence factor with the new data. The main research contents and results in the dissertation are listed as follows:In order to deal with the problem that the least squares estimation of ARMAX model is biased, the principle of bias compensation is used to establish a new least squares identification algorithm for this equation error models with moving average noises. This dissertation presents a bias compensation based recursive least squares algorithm(BCRLS) for equation error models with colored noises. In the proposed algorithm, a term of bias compensation is firstly formulated and the weighted average variance of the white noise is estimated in order to obtain unbiased parameter estimations.On the other hand, a forgetting factor is introduced to restrain the ―data saturation‖ phenomenon. This dissertation presents a bias compensation based forgetting factor recursive least squares identification algorithm(FF-BCRLS) for equation error model with colored noises to weaken the old data and strengthen the new one.Finally, a numerical example is employed to show the advantages of the two proposed identification algorithms by Matlab. The time-invariant system for BCRLS identification algorithm and the time-varying system for FF-BCRLS identification algorithm are considered for ARMAX. Compared the simulation results, the proposed BCRLS algorithm is better than the recursive least squares(RLS) algorithm and FF-BCRLS algorithm has advantage to restrain the ―data saturation‖ phenomenon in time-varying system.