- Regular-discrete derivative-free extended Kalman filter based mostly totally on Euler-Maruyama and Itô-Taylor discretizations: Typical and square-root implementations
Authors: Maria V. Kulikova, Gennady Yu. Kulikov
Abstract: On this paper, we proceed to test the derivative-free extended Kalman filtering (DF-EKF) framework for state estimation of continuous-discrete nonlinear stochastic packages. Having thought-about the Euler-Maruyama and Itô-Taylor discretization schemes for fixing stochastic differential equations, we derive the related filters’ second equations based mostly totally on the derivative-free EKF principal. In distinction to the not too way back derived MATLAB-based continuous-discrete DF-EKF strategies, the novel DF-EKF methods defend an particulars in regards to 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 packages with extraordinarily nonlinear and/or nondifferentiable drift and commentary options, nonetheless the value to be paid is its degraded numerical stability (to roundoff) as 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 revealed 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 fairly a couple of numerical exams along with well- and ill-conditioned conditions.
