An innovative parameter estimation for fractional order systems with impulse noise.

This paper investigates the problem of parameter estimation for fractional order linear systems when the output signal is polluted by impulse noise. The conventional least square error objective function is replaced by a new approximate least absolute error (ALAE) function to restrain the influence of impulse noise. Then a novel parameter estimation approach is designed based on the stochastic gradient method, the fractional order parameter update law and the ALAE criterion, which improves estimation accuracy and enhances robustness at the same time. It is shown that the adoption of the fractional order parameter update law ensures larger selection range of update order and smoother convergence of the algorithm. The effectiveness and superiority of the proposed method are verified by strict mathematical analysis and detailed numerical examples.