A Quantised State Systems Approach for Jacobian Free Extended Kalman Filtering

Model based methods for control of intelligent autonomous systems rely on a state estimate being available. One of the most common methods to obtain a state estimate for non-linear systems is the Extended Kalman Filter (EKF) algorithm. In order to apply the EKF an expression must be available for the Jacobian of the driving function; for complex systems this can be difficult to obtain. This paper presents an EKF variation that makes use of integrated quantised state simulation to propagate the state and obtain a backward difference estimate of the Jacobian at a small computational cost. A simulation case study involving a deep space probe is presented.