An FEM-Based State Estimation Approach to Nonlinear Hybrid Positioning Systems

Zhao, Yang; Chen, Lijuan; Ma, Yan

doi:10.1155/2013/175425

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…In recent years, the state estimation problems of the dynamic system have become very important in various applications of nonlinear systems (NLSs), such as underwater navigation positioning, mechanical equipment fault diagnosis, signal processing, space target orbit prediction, target tracking, etc. [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

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Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation

Chen

Zhang

et al. 2021

Symmetry

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For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.

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Section: Introductionmentioning

confidence: 99%

“…(2) The deviation of the reference state trajectory must small. (3) The conditional Probability Density Function (PDF) should satisfy the Gaussian distribution. Otherwise, the performance of UKF will become unstable.…”

Section: Introductionmentioning

confidence: 99%

Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation

Chen

Zhang

et al. 2021

Symmetry

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show abstract

“…Using a complex exponential basis as approximating elements, we show that the nonlinear filter can be implemented efficiently (for low-order systems) using discrete cosine transforms (DCT) resulting in a fast nonlinear filter that could be implemented in real time on a digital signal processor. Sinusoidal bases have been used before to implement PFM based Bayes algorithms, but in much different contexts [14].…”

Section: Introductionmentioning

confidence: 99%

Projection Filter Method Based on State Estimation to Nonlinear Systems

Chen¹,

Sang²,

Du³

et al. 2015

Proceedings of the 2015 International Conference on Modeling, Simulation and Applied Mathematics

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For nonlinear systems (NLS), the estimator design is a crucial and important problem. In this paper, projection-filtermethod (PFM) based state estimation approach is proposed to NLS. As the weak solution of stochastic differential model of NLS is denoted by the Kolmogorov's forward equation, this paper presents a new finite-dimensional approximating filter for nonlinear filtering problem. By using the differential geometrical approach to statistical manifold onto which the stochastic partial differential equation of the probability density is projected, a finite-dimensional stochastic ordinary differential equation of the associating parameters is gained. The arithmetic of the projection filter can be predigested in the case of exponential family. Combining with the Bayes rule, the posterior density of the states is obtained By taking an illustrative example, numerical experiment results show that the new state estimator is feasible and has good performance than PF.

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A novel initial method of fuzzy wavelet network in once-through steam generator control

Zhao

Yuan

et al. 2014

Proceedings of the 33rd Chinese Control Conference

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An FEM-Based State Estimation Approach to Nonlinear Hybrid Positioning Systems

Cited by 3 publications

References 21 publications

Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation

Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation

Projection Filter Method Based on State Estimation to Nonlinear Systems

A novel initial method of fuzzy wavelet network in once-through steam generator control

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