Maximum Likelihood-Based Iterated Divided Difference Filter for Nonlinear Systems from Discrete Noisy Measurements

A new filter named the maximum likelihood-based iterated divided difference filter (MLIDDF) is developed to improve the low state estimation accuracy of nonlinear state estimation due to large initial estimation errors and nonlinearity of measurement equations. The MLIDDF algorithm is derivative-free and implemented only by calculating the functional evaluations. The MLIDDF algorithm involves the use of the iteration measurement update and the current measurement, and the iteration termination criterion based on maximum likelihood is introduced in the measurement update step, so the MLIDDF is guaranteed to produce a sequence estimate that moves up the maximum likelihood surface. In a simulation, its performance is compared against that of the unscented Kalman filter (UKF), divided difference filter (DDF), iterated unscented Kalman filter (IUKF) and iterated divided difference filter (IDDF) both using a traditional iteration strategy. Simulation results demonstrate that the accumulated mean-square root error for the MLIDDF algorithm in position is reduced by 63% compared to that of UKF and DDF algorithms, and by 7% compared to that of IUKF and IDDF algorithms. The new algorithm thus has better state estimation accuracy and a fast convergence rate.