An innovative parameter estimation for fractional-order systems in the presence of outliers

This paper investigates the problem of parameter estimation for fractional-order linear systems when output signal is polluted by noise and outliers. Different from conventional filtering and semi-definite programming methods, the outliers detection problem is formulated as amatrix decomposition problem based on a novel nuclear norm method, which can not only make exact detection of outliers, but also estimate measurement noise at the same time. Then, a new parameter estimation approach is developed via a modified fractional-order gradient method with variable initial value mechanism and fractional-order parameter update law. With the adoption of recovered output signal, the proposed approach can obtain much better estimation performance, whose effectiveness and superiority are verified by strict mathematical analysis and detailed numerical examples.