Offline state estimation for hybrid systems via nonsmooth variable projection

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. (C) 2020 Elsevier Ltd. All rights reserved.