scholarly journals Design Method of High-Order Kalman Filter for Strong Nonlinear System Based on Kronecker Product Transform

Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 653
Author(s):  
Xiaohan Liu ◽  
Chenglin Wen ◽  
Xiaohui Sun
Keyword(s):  
Kalman Filter ◽  
Kronecker Product ◽  
Design Method ◽  
Digital Simulation ◽  
Gaussian White Noise ◽  
High Order ◽  
Stochastic Dynamic ◽  
Strongly Nonlinear ◽  
Intermediate Variables ◽  
Stochastic Dynamic Systems

In this paper, a novel design idea of high-order Kalman filter based on Kronecker product transform is proposed for a class of strong nonlinear stochastic dynamic systems. Firstly, those augmenting systems are modeled with help of the Kronecker product without system noise. Secondly, the augmented system errors are illustratively charactered by Gaussian white noise. Thirdly, at the expanded space a creative high-order Kalman filter is delicately designed, which consists of high-order Taylor expansion, introducing magical intermediate variables, representing linear systems converted from strongly nonlinear systems, designing Kalman filter, etc. The performance of the proposed filter will be much better than one of EKF, because it uses more information than EKF. Finally, its promise is verified through commonly used digital simulation examples.

scholarly journals A Simple And Novel Algorithm For State Estimation Of Continuous Time Linear Stochastic Dynamic Systems Excited By Random Inputs

2019 ◽  
Vol 8 (10) ◽  
pp. 3559-3563
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Continuous Time ◽  
Stochastic Dynamic ◽  
Time Dynamic ◽  
Time Dynamics ◽  
Hardware Realization ◽  
Aerial Vehicle ◽  
Non Linear System ◽  
Stochastic Dynamic Systems

The major goal of this paper is to explore the effective state estimation algorithm for continuous time dynamic system under the lossy environment without increasing the complexity of hardware realization. Though the existing methods of state estimation of continuous time system provides effective estimation with data loss, the real time hardware realization is difficult due to the complexity and multiple processing. Kalman Filter and Particle Filer are fundamental algorithms for state estimation of any linear and non-linear system respectively, but both have its limitation. The approach adopted here, detect the expected state value and covariance, existed by random input at each stage and filtered the noisy measurement and replace it with predicted modified value for the effective state estimation. To demonstrate the performance of the results, the continuous time dynamics of position of the Aerial Vehicle is used with proposed algorithm under the lossy measurements scenario and compared with standard Kalman filter and smoothed filter. The results show that the proposed method can effectively estimate the position of Aerial Vehicle compared to standard Kalman and smoothed filter under the non-reliable sensor measurements with less hardware realization complexity.

SUBSPACE METHOD FOR ANALYZING LARGE-SCALE NONLINEAR STOCHASTIC DYNAMIC SYSTEMS WITH POLYNOMIAL TYPE OF NONLINEARITES

2012 ◽  
Vol 09 (01) ◽  
pp. 1240017 ◽  
Author(s):  
G. K. ER ◽  
V. P. IU
Keyword(s):  
Dynamic Systems ◽  
Large Scale ◽  
Gaussian White Noise ◽  
The State ◽  
Stochastic Dynamic ◽  
Subspace Method ◽  
State Variables ◽  
Polynomial Type ◽  
Fpk Equation ◽  
Stochastic Dynamic Systems

In this paper, the probabilistic solutions of the multi-degree-of-freedom (MDOF) or large-scale stochastic dynamic systems with polynomial type of nonlinearity and excited by Gaussian white noise excitations are obtained and investigated with the subspace method proposed recently by the authors. The space of the state variables of large-scale nonlinear stochastic dynamic (NSD) system excited by white noises is separated into two subspaces. Both sides of the Fokker–Planck–Kolmogorov (FPK) equation corresponding to the NSD system is then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in another subspace is formulated. Therefore, the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of large-scale NSD systems solvable with the exponential polynomial closure (EPC) method. A simple flexural beam on nonlinear elastic springs is analyzed with the subspace method to show the effectiveness of the subspace-EPC method in this case.

The continuous–discrete extended Kalman filter revisited

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Gennady Yu. Kulikov ◽  
Maria V. Kulikova
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Total Error ◽  
Waiting Times ◽  
Stochastic Dynamic ◽  
Extended Kalman Filtering ◽  
Gaussian Density ◽  
The Moment ◽  
Stochastic Dynamic Systems

AbstractThis paper elaborates a new approach to nonlinear filtering grounded in an accurate implementation of the continuous–discrete extended Kalman filter for estimating stochastic dynamic systems. It implies that the moment differential equations for calculation of the predicted state mean and error covariance of propagated Gaussian density are solved accurately, i.e., with negligible errors. 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. In addition, this filter exploits the scaled local and global error controls to avoid any comparison of different physical units. The designed state estimator is compared numerically with continuous–discrete unscented and cubature Kalman filters to expose its practical efficiency. The problem of long waiting times (i.e., infrequent measurements) arisen in chemical and other engineering is also addressed.

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