Hamed H. Afshari, Andrew S. Lee, S. Andrew Gadsden, and Saeid R. Habibi


Estimation theory, faulty systems, Kalman filter, signal processing,sliding modes


This paper introduces a novel second-order state estimation method that is applied to linear systems dealing with modelling uncertainties. This method produces state estimates by decreasing the innovation sequence (measurement error) and its time difference which results in preserving smoothness and stability against modelling uncertainties. This filter is referred to as the second-order filter since it updates state estimates based on values of the measurement error and its incremental change. The corrective gain of this filter is designed based on a time-varying manifold that is a linear combination of the measurement error and its time difference. This manifold introduces a cut-off frequency coefficient into the filter formulation. The optimal version of the dynamic second-order filter is then calculated by finding the optimal value of this coefficient at each time step such that the state error covariance matrix is minimised. It is shown that the corrective gain of the optimal second-order filter collapses to the Kalman filter’s gain for a known model with white noise. In order to verify the accuracy of the method, it is implemented on an aerospace electro-hydrostatic actuator setup under the normal and faulty scenarios.

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