System parameter estimation with input/output noisy data andmissing measurements

An investigation is undertaken to examine the parameter estimation problem of linear systems when some of the measurements are unavailable (i.e., missing data) and the probability of occurrence of missing data is unknown a priori. The system input and output data are also assumed to be corrupted by measurement noise, and the knowledge of the noise distribution is unknown. Under the unknown noise distribution and missing measurements, a consistent parameter estimation algorithm [which is based on an l_p norm iterative estimation algorithm-iteratively reweighted least squares (IRLS)] is proposed to estimate the system parameters. We show that if the probability of missing measurement is less than one half, the parameter estimates via the proposed estimation algorithm will converge to the true parameters as the number of data tends to infinity. Finally, several simulation results are presented to illustrate the performance of the proposed l _p norm iterative estimation algorithm. Simulation results indicate that under input/output missing data and noise environment, the proposed parameter estimation algorithm is an efficient approach toward the system parameter estimation problem