Parameter Estimation of Static Multi-Input Model with Noisy Inputs and Output

This paper deals with identification of a group of multi-input static systems with noisy inputs and output. This group includes static models y=∑_ (i=1) ^n▒〖a_i u_i 〗 where u_is are contaminated by noise. It is assumed that we know which inputs are the contaminated ones. To reach the goal، the PEM which is an efficient classical system identification method is implemented. Then، by combining it with the IV method which is commonly used for identification of the intended group of systems، a new method is proposed. We call the new method as compensated PEM. Since both PEM and IV methods are recursively implementable، the proposed method could be implemented recursively as well. It is proved that the new method results in an unbiased estimation. Simulation results are provided to verify the given theorems and compare the proposed method with its competitors in mean and variance of the estimation. Finally a practical application of the method is investigated.