- Regular-discrete derivative-free extended Kalman filter based totally on Euler-Maruyama and Itô-Taylor discretizations: Customary and square-root implementations
Authors: Maria V. Kulikova, Gennady Yu. Kulikov
Abstract: On this paper, we proceed to assessment the derivative-free extended Kalman filtering (DF-EKF) framework for state estimation of continuous-discrete nonlinear stochastic strategies. Having considered the Euler-Maruyama and Itô-Taylor discretization schemes for fixing stochastic differential equations, we derive the related filters’ second equations based totally on the derivative-free EKF principal. In distinction to the currently derived MATLAB-based continuous-discrete DF-EKF strategies, the novel DF-EKF methods defend an particulars concerning the underlying stochastic course of and provide the estimation course of for a tough and quick number of iterates on the propagation steps. Furthermore, the DF-EKF technique is particularly environment friendly for working with stochastic strategies with extraordinarily nonlinear and/or nondifferentiable drift and comment capabilities, nevertheless the value to be paid is its degraded numerical stability (to roundoff) compared with the same old EKF framework. To eradicate the talked about pitfall of the derivative-free EKF methodology, we develop the usual algorithms together with their regular square-root implementation methods. In distinction to the printed DF-EKF outcomes, the model new square-root strategies are derived inside every the Cholesky and singular value decompositions. A effectivity of the novel filters is demonstrated on loads of numerical checks along with well- and ill-conditioned conditions.
