Decomposition Based Iterative Estimation Methods For Output Error Type Systems

In the study of linear system identification problem, the least square iterative methodcan be applied to identify the output error type model, which can obtain a relativelyhigher estimation accuracy in just a few iterations. However, the computational burdenof the traditional algorithm will be heavy when the covariance matrices have a largedimension or the quantity of collected input-output data is huge. Therefore, based on thedecomposition-coordination identification theory and the least square iterative method,this paper study the estimation method for the output error type model, and solve thecomputation problem, and this idea has theoretical significance and application prospects.This paper gets some achievements and listed as follows:1. For the output error model, an identification model is derived, which decomposedthe original identification model into two fictitious subsystems, and use the leastsquare iterative method to estimate the parameter of each subsystems, and derivedthe decomposition based iterative algorithm. The proposed algorithm has a lesscomputational burden.2. For the output error moving average system which contain colored noise, the identi-fication models are derived, which decomposed the original identification model intothree fictitious subsystems, and derived the decomposition based least square iterativeidentification algorithm. The proposed algorithm is more efcient than the traditionalone.3. For the output error autoregressive system which contain another type of colorednoise, using the decomposition and data filtering technique to convert the originalsystems into several subsystems, and derived the filtering decomposition based leastsquare iterative algorithm. The proposed algorithm has obvious advantage comparewith the traditional one.4. For Box-Jenkins model, the identification model is derived, which use the linear filterto convert the original model to an output error model with moving average noise,then derived the filtering decomposition based least square iterative identificationalgorithm the proposed algorithm has a less computational burden.5. Through multiple simulations verify the validity of the algorithms, and the algorithmcomputation analysis, demonstrate that in the case of large number of identificationparameter or huge quantity of the collected input-output data the proposed algorithmhas obvious advantage compare with the traditional one. This paper researches the decomposition iterative estimation method for output errortype models and derived the parameter estimate algorithm for each system respectively.Simulation experiment and computation analysis shows the validity of the proposed algo-rithm, the estimation accuracy is close to the least square based iterative algorithm andit has a better computational efciency.