The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Many state estimation and control algorithms require knowledge of how probability distributions propagate through dynamical systems. However, despite hybrid systems becoming increasingly important in many fields, there has been little work on utilizing the map transitions. Here, we make use a propagation law that employs saltation matrix (a first-order update to sensitivity equation) create Salted Kalman Filter (SKF), natural extension Extended Away from events, SKF is standard filter. When event occurs, plays an analogous role as system dynamics, subsequently inducing discrete modification both prediction steps. The outperforms naive variational – Jacobian reset by having reduced mean squared error estimation, especially immediately after transition event. Compared against particle filter, filter only when large number particles are used, likely due more accurate accounting split distribution near transition.