Estimating the Parameters of a Dynamic Model from Noisy Input and Output Measurements

摘要

An algorithm to compute least squares estimates for the parameters of a dynamic model from noisy measurements of inputs and outputs is provided. Estimating the unknown parameters of a dynamic model with errors in all variables by means of the least squares method gives an object function which contains an inverse matrix. A Q - R decomposition to evaluate object function and gradient is proposed. These are used in an iterative procedure in order to obtain estimates. Though in general the object function cannot be written as a sum of independent random variables weak consistency under mild conditions on input, system and noise can be proved.