Density Difference Grid Design in a Point-Mass Filter

The paper deals with the Bayesian state estimation of nonlinear stochastic dynamic systems. The stress is laid on the point-mass filter, solving the Bayesian recursive relations for the state estimate conditional density computation using the deterministic grid-based numerical integration method. In particular, the grid design is discussed and the novel density difference grid is proposed. The proposed grid design covers such regions of the state-space where the conditional density is significantly spatially varying, by the dense grid. In other regions, a sparse grid is used to keep the computational complexity low. The proposed grid design is thoroughly discussed, analyzed, and illustrated in a numerical study.

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Conditional Density Driven Grid Design in Point-Mass Filter

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ◽

10.1109/icassp40776.2020.9052962 ◽

2020 ◽

Author(s):

Jindrich Dunik ◽

Ondrej Straka ◽

Jakub Matousek

Keyword(s):

Point Mass ◽

Conditional Density ◽

Mass Filter ◽

Grid Design

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Grid Design for Efficient and Accurate Point Mass Filter-Based Terrain Referenced Navigation

IEEE Sensors Journal ◽

10.1109/jsen.2017.2779463 ◽

2018 ◽

Vol 18 (4) ◽

pp. 1731-1738 ◽

Cited By ~ 10

Author(s):

Hyun Cheol Jeon ◽

Woo Jung Park ◽

Chan Gook Park

Keyword(s):

Point Mass ◽

Mass Filter ◽

Terrain Referenced Navigation ◽

Grid Design

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The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems

Communications in Computational Physics ◽

10.4208/cicp.140710.210111a ◽

2011 ◽

Vol 10 (5) ◽

pp. 1241-1256 ◽

Cited By ~ 1

Author(s):

Guo-Kang Er ◽

Vai Pan Iu

Keyword(s):

Large Scale ◽

Joint Probability ◽

Approximate Solutions ◽

The State ◽

Stochastic Dynamic ◽

State Variables ◽

High Dimensions ◽

Polynomial Type ◽

Fpk Equation ◽

Stochastic Dynamic Systems

AbstractThe probabilistic solutions of the nonlinear stochastic dynamic (NSD) systems with polynomial type of nonlinearity are investigated with the subspace-EPC method. The space of the state variables of large-scale nonlinear stochastic dynamic 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 method. Examples about the NSD systems with polynomial type of nonlinearity are given to show the effectiveness of the subspace-EPC method in these cases.

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

International Journal of Computational Methods ◽

10.1142/s0219876212400178 ◽

2012 ◽

Vol 09 (01) ◽

pp. 1240017 ◽

Cited By ~ 2

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.

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Application of Wavelets in Modeling Stochastic Dynamic Systems

Journal of Vibration and Acoustics ◽

10.1115/1.2893895 ◽

1998 ◽

Vol 120 (3) ◽

pp. 763-769 ◽

Cited By ~ 7

Author(s):

O. P. Agrawal

Keyword(s):

Dynamic Systems ◽

Stochastic Systems ◽

Random Coefficients ◽

The State ◽

Stochastic Dynamic ◽

State Variables ◽

Algebraic Equations ◽

Random Forcing ◽

Forcing Function ◽

Stochastic Dynamic Systems

This paper presents a wavelet based model for stochastic dynamic systems. In this model, the state variables and their variations are approximated using truncated linear sums of orthogonal polynomials, and a modified Hamilton’s law of varying action is used to reduce the integral equations representing dynamics of the system to a set of algebraic equations. For deterministic systems, the coefficients of the polynomials are constant, but for stochastic systems, the coefficients are random variables. The external forcing functions are treated as stationary Gaussian processes with specified mean and correlation functions. Using Karhunen-Loeve (K-L) expansion, the random input processes are represented in terms of linear sums of finite number of orthonormal eigenfunctions with uncorrelated random coefficients. A wavelet based technique is used to solve the integral eigenvalue problem. Application of wavelets and K-L expansion reduces the infinite dimensional input force vector to one with finite dimensions. Orthogonal properties of the polynomials and the wavelets are utilized to make the algebraic equations sparse and computationally efficient. A method to compute the mean and the variance functions for the state processes is developed. A single degree of freedom spring-mass-damper system subjected to a random forcing function is considered to show the feasibility and effectiveness of the formulation. Studies show that the results of this formulation agree well with those obtained using other schemes.

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