Comparison of JML, EKF and SDDRE Filters of Nonlinear Dynamic Systems

The Joint Maximum Likelihood filter, also called Least Mean Square Error filter, has been recently derived for the state estimation of nonlinear dynamic systems. It is an exact, explicit, closed form and recursive optimal filter. In this paper performances of this new Least Mean Square Error filter, the Extended Kalman Filter and the State Dependent Differential Riccati equation based Filter are compared. The Van der Pol equation is used in this comparison. It is demonstrated by simulations that although the performances are not so different that the Least Mean Square Error filter is the fastest filter to reach for the first time zero tracking error.