Offline state estimation for hybrid systems via nonsmooth variable projection. (May 2020) - Zhang, Jize; Pace, Andrew M.; Burden, Samuel A.; Aravkin, Aleksandr
Abstract: We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system's state. We formulate state estimation as a continuous optimization problem by relaxing the discrete component and using a robust loss function to accommodate large changes in the continuous component during switching events. Subsequently, we develop a novel nonsmooth variable projection algorithm with Gauss–Newton updates to solve the state estimation problem and prove the algorithm's global convergence to stationary points. We demonstrate the effectiveness of our approach by comparing it to a state-of-the-art filter bank method, and by applying it to simple piecewise-linear and -nonlinear mechanical systems undergoing intermittent impact.