Abstract
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.
Highlights
The problem of estimating the state of a nonlinear stochastic system from noisy measurement data has been the subject of considerable research interest during the past few years
Emboldened by the superiority of divided difference filter (DDF), the basic idea of the Iterated Extended Kalman filter (IEKF) and the iteration termination condition based on maximum likelihood, we propose a new filter named the maximum likelihood based iterated divided difference Kalman filter (MLIDDF)
Enlightened by the development of IEKF and the superiority of DDF, we can derive the maximum likelihood based iterated divided difference filter (MLIDDF) which involves the use of the iteration measurement update and the current measurement
Summary
The problem of estimating the state of a nonlinear stochastic system from noisy measurement data has been the subject of considerable research interest during the past few years. The second–order EKF generally improves estimation accuracy, but at the expense of an increased computational burden [5] Another attempt to improve the performance of the EKF involves the use of an iterative measurement update; the resulting algorithm is called the Iterated Extended Kalman filter (IEKF) [6]. The FDF uses the first-order difference to approximate the derivative of the nonlinear function; it may introduce large state estimation errors due to a high nonlinearity, similar to the EKF. The parameters used in the UKF are required to tune finely in order to prevent the propagation of non-positive definite covariance matrix for a state vector’s dimension higher than three Another Gaussian filter, named the divided difference filter (DDF) was introduced in [14] using multidimensional Stirling’s interpolation formula.
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