Parameter estimation for a special class of nonlinear systems by using the over-parameterisation method and the linear filter

This paper studies the parameter estimation issues of a special class of nonlinear systems (i.e. bilinear-in-parameter systems) utilising the measurement input-output data. The estimation idea is based on the data filtering technique and the over-parameterisation method to represent the system as a linearly parameterised form. Then, by means of the filtered model and the noise model, a filtering based over-parameterisation generalised extended gradient iterative (F-O-GEGI) algorithm is developed for estimating all the parameters. For purpose of improving the precision of parameter estimation, a filtering based over-parameterisation generalised extended least squares iterative (F-O-GELSI) algorithm is derived by formulating and minimising two separate criterion functions. By these foundations, the F-O-GEGI algorithm and the F-O-GELSI algorithm with finite measurement data are presented. The simulation example is provided to test and compare the presented approaches.