- Steady-discrete derivative-free prolonged Kalman filter primarily based on Euler-Maruyama and Itô-Taylor discretizations: Standard and square-root implementations
Authors: Maria V. Kulikova, Gennady Yu. Kulikov
Summary: On this paper, we proceed to review the derivative-free prolonged Kalman filtering (DF-EKF) framework for state estimation of continuous-discrete nonlinear stochastic methods. Having thought of the Euler-Maruyama and Itô-Taylor discretization schemes for fixing stochastic differential equations, we derive the associated filters’ second equations primarily based on the derivative-free EKF principal. In distinction to the lately derived MATLAB-based continuous-discrete DF-EKF methods, the novel DF-EKF strategies protect an details about the underlying stochastic course of and supply the estimation process for a hard and fast variety of iterates on the propagation steps. Moreover, the DF-EKF strategy is especially efficient for working with stochastic methods with extremely nonlinear and/or nondifferentiable drift and remark capabilities, however the worth to be paid is its degraded numerical stability (to roundoff) in comparison with the usual EKF framework. To eradicate the talked about pitfall of the derivative-free EKF methodology, we develop the standard algorithms along with their steady square-root implementation strategies. In distinction to the printed DF-EKF outcomes, the brand new square-root methods are derived inside each the Cholesky and singular worth decompositions. A efficiency of the novel filters is demonstrated on plenty of numerical checks together with well- and ill-conditioned situations.
