Bias Compensation Based Least Squares Identification For Equation Error Model With Input Noise

Equation error model is a class of stochastic system model in which the output of the system is disturbed by noise.When the system input of this model is also subject to noise interference,the standard recursive least squares identification algorithm cannot obtain the unbiased estimation of the system parameter vector,there exists a deviation term in the estimation expression of the system noise.In order to improve the algorithm,based on the idea of bias compensation,first the author calculate the expression of the error term,then use the bias term to compensate the standard least squares algorithm.The main work is as follows:This paper introduces four specific models of error model,controlled autoregressive model,controlled autoregressive moving average model,equation error autoregressive model and equation error autoregressive moving average model.The author analyzes the first two models with input white noise,deduces the concrete expression of the deviation term.For controlled autoregressive model with white noise input,the author analyzes the deviation term and decomposes it into the expression of the input white noise autocorrelation function matrix and the system parameter vector matrix defined in this paper.Then,based on the idea of augmented least squares algorithm,the author introduces new parameter vector,information vector and the system least squares norm function,establishes the system of equations about the matrix defined in this paper,obtains the estimate of the deviation term.On this basis,the author establishes recursive least square identification algorithm based on bias compensation.For controlled autoregressive moving average model with input white noise,which is very similar to the controlled autoregressive model,the author emphatically analyzes the difference from the controlled autoregressive model.A new system noise autocorrelation function matrix is defined.The similarity principle is used to establish the equations of the noise matrix,and the estimation of the deviation term is obtained.The bias compensation least squares algorithm is established.The author defines a new system noise autocorrelation function matrix,uses the similarity principle to establish the equations of the noise matrix,then obtains the estimation of the deviation term.Finally establishes the bias compensation least squares algorithm.The author uses MATLAB to simulate the identification algorithm and set the contrast experiment.For the CAR model,different SNRs are set for comparison simulation.For the CARMA model,different lengths of parameter vectors are set for comparison simulation.The effectiveness of the algorithm,the influence of signal-to-noise ratio and parameter vector length on the identification performance are analyzed.