Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter

AbstractIn this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.

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A Kalman filter for a class of nonlinear stochastic systems

Numerical Studies in Nonlinear Filtering - Lecture Notes in Control and Information Sciences ◽

10.1007/bfb0037757 ◽

2006 ◽

pp. 103-129

Keyword(s):

Kalman Filter ◽

Stochastic Systems ◽

Nonlinear Stochastic Systems

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A novel cubature statistically linearized Kalman filter for fractional-order nonlinear discrete-time stochastic systems

Journal of Vibration and Control ◽

10.1177/1077546317692943 ◽

2017 ◽

Vol 24 (24) ◽

pp. 5880-5897 ◽

Cited By ~ 1

Author(s):

Hamed Torabi ◽

Naser Pariz ◽

Ali Karimpour

Keyword(s):

Kalman Filter ◽

State Estimation ◽

Extended Kalman Filter ◽

Fractional Order ◽

Discrete Time ◽

Stochastic Systems ◽

Taylor Series Expansion ◽

The State ◽

Nonlinear Functions ◽

Measurement Models

In this paper, the state estimation problem for fractional-order nonlinear discrete-time stochastic systems is considered. A new method for the state estimation of fractional nonlinear systems using the statistically linearized method and cubature transform is presented. The fractional extended Kalman filter suffers from two problems. Firstly, the dynamic and measurement models must be differentiable and, secondly, nonlinearity is approximated by neglecting the higher order terms in the Taylor series expansion; by the proposed method in this paper, these problems can be solved using a statistically linearized algorithm for the linearization of fractional nonlinear dynamics and cubature transform for calculating the expected values of the nonlinear functions. The effectiveness of this proposed method is demonstrated through simulation results and its superiority is shown by comparing our method with some other present methods, such as the fractional extended Kalman filter.

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Stochastic Minimax Vibration Control for Uncertain Nonlinear Quasi-Hamiltonian Systems with Noisy Observations

10.20855/ijav.2019.24.41446 ◽

2019 ◽

Vol 24 (4) ◽

pp. 707-716

Author(s):

Zu-guang Ying ◽

Rong-chun Hu ◽

Rong-hua Huan

Keyword(s):

Kalman Filter ◽

Hamiltonian System ◽

Hamiltonian Systems ◽

Extended Kalman Filter ◽

Control Strategy ◽

Stochastic Systems ◽

Uncertain Parameters ◽

Dynamical Programming ◽

Worst Case ◽

Minimax Control

A stochastic minimax control strategy for uncertain nonlinear quasi-Hamiltonian systems with noisy observations under random excitations is proposed based on the extended Kalman filter and minimax stochastic dynamical programming principle. A structure system with smart sensors and actuators is modeled as a controlled, excited and dissipative Hamiltonian system with noisy observations. The differential equations for the uncertain nonlinear quasi-Hamiltonian system with control and observation under random excitation are given first. The estimated nonlinear stochastic control system with uncertain parameters is obtained from the uncertain quasi-Hamiltonian system with noisy observation. In this case, the optimally estimated state is determined by the observation based on the extended Kalman filter. The dual dynamical programming equation for the estimated uncertain system is then obtained based on the minimax stochastic dynamical programming principle. The worst-case disturbances are determined for bounded uncertain parameters and the optimal control law is determined for the worst case by the programming equation. The proposed minimax control strategy is applied to two uncertain nonlinear stochastic systems with controls and noisy observations. The control effectiveness for the stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed minimax control strategy is applicable to general uncertain nonlinear multi-degree-of-freedom structure systems with noisy observations under random excitations.

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The accurate continuous-discrete extended Kalman filter for continuous-time stochastic systems

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2015-0021 ◽

2015 ◽

Vol 30 (4) ◽

Cited By ~ 4

Author(s):

Gennady Yu. Kulikov ◽

Maria V. Kulikova

Keyword(s):

Kalman Filter ◽

Extended Kalman Filter ◽

Nonlinear Filtering ◽

Stochastic Systems ◽

Total Error ◽

Stochastic Dynamic ◽

Extended Kalman Filtering ◽

New Approach ◽

Error Covariance ◽

The Moment

AbstractThis paper elaborates a new approach to nonlinear filtering based on an accurate implementation of the continuous-discrete extended Kalman filter. It implies that the moment differential equations for calculating the predicted state mean of stochastic dynamic system and the corresponding error covariance matrix are solved accurately, i.e. with negligible error. The latter allows the total error of the extended Kalman filter to be reduced significantly and results in a new Accurate Continuous-Discrete Extended Kalman Filtering method. The developed technique is compared theoretically and numerically with other implementations of the extended Kalman filter to conform its outstanding performance on test examples.

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