Kalman Filter provides the optimal estimate of the states of a stochastic dynamical system if the system is linear, the measurements are also linear functions of states and the errors in system modeling and the measurements are Gaussian white noise. However, for a nonlinear system, the use of Extended kalman Filter (EKF) or Unscented Kalman Filter(UKF) provides a sub-optimal estimate. In general, for a nonlinear system, EKF gives a less accurate measure of covariance than UKF. In order to correct the covariance, higher order EKF have been proposed. Similarly, higher order UKF also leads to a more accurate covariance. My queries are:
- Apart from improvement in the covariance, do higher order filters provide any other advantage?
- Can we capture skewness or kurtosis using these high order filters?