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A hybrid dynamical system switches between dynamic regimes at time- orstate-triggered events. We propose an offline algorithm that simultaneouslyestimates discrete and continuous components of a hybrid system's state. Weformulate state estimation as a continuous optimization problem by relaxing thediscrete component and use a robust loss function to accommodate large changesin the continuous component during switching events. Subsequently, we develop anovel nonsmooth variable projection algorithm with Gauss-Newton updates tosolve the state estimation problem and prove the algorithm's global convergenceto stationary points. We demonstrate the effectiveness of our approach onsimple piecewise-linear and -nonlinear mechanical systems undergoingintermittent impact.

Offline state estimation for hybrid systems via nonsmooth variable projection