Tracking nonlinear systems using higher order moments

A sub-optimal nonlinear time-recursive filter is developed which considers an arbitrary number of moments of the conditional density. The filter assumes a quadratic truncation of the system dynamics and measurement functions and retains N moments, thus requiring knowledge of up to 2N+2 a priori moments and N+1 moments of the measurement noise process, which may be non-Gaussian. Prediction and update relations are given for moments of arbitrary order along with mechanisms which facilitate their closed forms. Numerical examples are given for both scalar and vector systems and show promising results.