The extended Luenberger sliding innovation filter

The sliding innovation filter is a newly developed filter that was derived in 2020 to be a predictor-corrector filter. The filter uses the measurement as a hyperplane, and then applies a force that makes the estimates fluctuating around it. The filter works on systems with full ranked measurement matrix (all states are measured). However, once the rank becomes partial, the filter depends highly on the pseudo inverse of the measurement matrix. This means that if the measurement matrix does not have a direct link to the hidden states, then these states will not be correctly estimated. When the system is nonlinear, the problem becomes worse as the Jacobean matrix must be calculated for the measurement matrix before the pseudo inverse is applied. To solve this issue, this paper proposes a new formulation of the SIF that is based on the extended Luenberger filter. The proposed method is tested on extracting the damping ration for a third order system.