An FEM-Based State Estimation Approach to Nonlinear Hybrid Positioning Systems. (12th June 2013)

• Record Type: Journal Article
• Authors: Zhao, Yu-Xin; Chen, Li-Juan; Ma, Yan
• Other Names: Su Xiaojie Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-06-12
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/175425
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : For hybrid positioning systems (HPSs), the estimator design is a crucial and important problem. In this paper, a finite-element-method- (FEM-) based state estimation approach is proposed to HPS. As the weak solution of hybrid stochastic differential model is denoted by the Kolmogorov's forward equation, this paper constructs its interpolating point through the classical fourth-order Runge-Kutta method. Then, it approaches the solution with biquadratic interpolation function to obtain a prior probability density function of the state. A posterior probability density function is gained through Bayesian formula finally. In theory, the proposed scheme has more advantages in the performance of complexity and convergence for low-dimensional systems. By taking an illustrative example, numerical experiment results show that the new state estimator is feasible and has good performance than PF and UKF.