Identification of multiple inputs single output errors-in-variables system using cumulant

A higher-order cumulant-based weighted least square (HOCWLS) and a higher-order cumulant-based iterative least square (HOCILS) are derived for multiple inputs single output (MISO) errors-in-variables (EIV) systems from noisy input/output data. Whether the noises of the input/output of the system are white or colored, the proposed algorithms can be insensitive to these noises and yield unbiased estimates. To realize adaptive parameter estimates, a higher-order cumulant-based recursive least square (HOCRLS) method is also studied. Convergence analysis of the HOCRLS is conducted by using the stochastic process theory and the stochastic martingale theory. It indicates that the parameter estimation error of HOCRLS consistently converges to zero under a generalized persistent excitation condition. The usefulness of the proposed algorithms is assessed through numerical simulations.