Splitting-up Spectral Method for Nonlinear Filtering Problems with Correlation Noises

Zhang, Fengshan; Zou, Yongkui; Chai, Shimin; Zhang, Ran; Cao, Yanzhao

doi:10.1007/s10915-022-01994-6

Splitting-up Spectral Method for Nonlinear Filtering Problems with Correlation Noises

Journal Article · 05 September 2022 · Journal of Scientific Computing

DOI:https://doi.org/10.1007/s10915-022-01994-6· OSTI ID:2422115

Zhang, Fengshan ^[1]; Zou, Yongkui; Chai, Shimin; Zhang, Ran;

OSTI

Not provided.

Research Organization:: Auburn Univ., AL (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0022253

OSTI ID:: 2422115

Journal Information:: Journal of Scientific Computing, Journal Name: Journal of Scientific Computing Journal Issue: 1 Vol. 93; ISSN 0885-7474

Publisher:: Springer

Country of Publication:: United States

Language:: English

References (50)

Convergence of a Branching Particle Method to the Solution of the Zakai Equation Crisan, Dan; Gaines, Jessica; Lyons, Terry SIAM Journal on Applied Mathematics, Vol. 58, Issue 5 https://doi.org/10.1137/S0036139996307371	journal	October 1998
Solving Nonlinear Filtering Problems in Real Time by Legendre Galerkin Spectral Method Dong, Wenhui; Luo, Xue; Yau, Stephen S. -T. IEEE Transactions on Automatic Control, Vol. 66, Issue 4 https://doi.org/10.1109/TAC.2020.3002979	journal	April 2021
Exact rates of convergeance for a branching particle approximation to the solution of the Zakai equation Crisan, Dan The Annals of Probability, Vol. 31, Issue 2 https://doi.org/10.1214/aop/1048516533	journal	April 2003
Approximation of the Zakai Equation for Nonlinear Filtering Ito, Kazufumi SIAM Journal on Control and Optimization, Vol. 34, Issue 2 https://doi.org/10.1137/S0363012993254783	journal	March 1996
A Multiscale Data Assimilation with the Ensemble Kalman Filter Zou, Yu; Ghanem, Roger Multiscale Modeling & Simulation, Vol. 3, Issue 1 https://doi.org/10.1137/030601168	journal	January 2005
On the optimal filtering of diffusion processes Zakai, Moshe Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 11, Issue 3 https://doi.org/10.1007/BF00536382	journal	January 1969
Error analysis for numerical formulation of particle filter Han, Xiaoying; Li, Jinglai; Xiu, Dongbin Discrete and Continuous Dynamical Systems - Series B, Vol. 20, Issue 5 https://doi.org/10.3934/dcdsb.2015.20.1337	journal	May 2015
Particle Filtering for Stochastic Navier--Stokes Signal Observed with Linear Additive Noise Llopis, Francesc Pons; Kantas, Nikolas; Beskos, Alexandros SIAM Journal on Scientific Computing, Vol. 40, Issue 3 https://doi.org/10.1137/17M1151900	journal	January 2018
Particle filtering for a class of cyber-physical systems under Round-Robin protocol subject to randomly occurring deception attacks Song, Weihao; Wang, Zidong; Wang, Jianan Information Sciences, Vol. 544 https://doi.org/10.1016/j.ins.2020.07.047	journal	January 2021
Distributed extended Kalman filtering for state-saturated nonlinear systems subject to randomly occurring cyberattacks with uncertain probabilities Li, Jiaxing; Hu, Jun; Chen, Dongyan Advances in Difference Equations, Vol. 2020, Issue 1 https://doi.org/10.1186/s13662-020-02896-3	journal	August 2020
Robust extended Kalman filtering for nonlinear systems with multiplicative noises Kai, Xiong; Liangdong, Liu; Yiwu, Liu Optimal Control Applications and Methods, Vol. 32, Issue 1 https://doi.org/10.1002/oca.928	journal	January 2011
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning E., Weinan; Han, Jiequn; Jentzen, Arnulf Nonlinearity, Vol. 35, Issue 1 https://doi.org/10.1088/1361-6544/ac337f	journal	December 2021
A Hybrid Sparse-Grid Approach for Nonlinear Filtering Problems Based on Adaptive-Domain of the Zakai Equation Approximations Bao, Feng; Cao, Yanzhao; Webster, Clayton SIAM/ASA Journal on Uncertainty Quantification, Vol. 2, Issue 1 https://doi.org/10.1137/140952910	journal	January 2014
Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics Evensen, Geir Journal of Geophysical Research, Vol. 99, Issue C5 https://doi.org/10.1029/94JC00572	journal	January 1994
On the splitting-up method and stochastic partial differential equations Gyöngy, István; Krylov, Nicolai The Annals of Probability, Vol. 31, Issue 2 https://doi.org/10.1214/aop/1048516528	journal	April 2003
Resampling algorithms and architectures for distributed particle filters Bolic, M.; Djuric, P. M. IEEE Transactions on Signal Processing, Vol. 53, Issue 7 https://doi.org/10.1109/TSP.2005.849185	journal	July 2005
Unbiased estimation of the solution to Zakai’s equation Ruzayqat, Hamza M.; Jasra, Ajay Monte Carlo Methods and Applications, Vol. 26, Issue 2 https://doi.org/10.1515/mcma-2020-2061	journal	April 2020
On Kalman Filtering With Nonlinear Equality Constraints Julier, Simon J.; LaViola, Joseph J. IEEE Transactions on Signal Processing, Vol. 55, Issue 6 https://doi.org/10.1109/TSP.2007.893949	journal	June 2007
Linear filtering of systems with memory and application to finance Inoue, A.; Nakano, Y.; Anh, V. International Journal of Stochastic Analysis, Vol. 2006, Issue 1 https://doi.org/10.1155/JAMSA/2006/53104	journal	January 2006
Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs Chen, Jing; Zhu, Quanmin; Liu, Yanjun Automatica, Vol. 118 https://doi.org/10.1016/j.automatica.2020.109034	journal	August 2020
Particle Filtering for Nonlinear/Non-Gaussian Systems With Energy Harvesting Sensors Subject to Randomly Occurring Sensor Saturations Song, Weihao; Wang, Zidong; Wang, Jianan IEEE Transactions on Signal Processing, Vol. 69 https://doi.org/10.1109/TSP.2020.3042951	journal	January 2021
Numerical Analysis of Spectral Methods: Theory and Applications Gottlieb, David; Orszag, Steven A. CBMS-NSF Regional Conference Series in Applied Mathematics https://doi.org/10.1137/1.9781611970425	book	January 1977
Complete Real Time Solution of the General Nonlinear Filtering Problem Without Memory Luo, Xue; Yau, Stephen S. -T. IEEE Transactions on Automatic Control, Vol. 58, Issue 10 https://doi.org/10.1109/TAC.2013.2264552	journal	October 2013
Stochastic partial differential equations and filtering of diffusion processes Pardouxt, E. Stochastics, Vol. 3, Issue 1-4 https://doi.org/10.1080/17442507908833142	journal	January 1980
Particle filters with random resampling times Crisan, D.; Obanubi, O. Stochastic Processes and their Applications, Vol. 122, Issue 4 https://doi.org/10.1016/j.spa.2011.12.012	journal	April 2012
An adaptive extended Kalman filtering approach to nonlinear dynamic gene regulatory networks via short gene expression time series ÖZbek, Levent Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, Vol. 69, Issue 2 https://doi.org/10.31801/cfsuasmas.749624	journal	December 2020
Kernel-based collocation methods for Zakai equations Nakano, Yumiharu Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 7, Issue 3 https://doi.org/10.1007/s40072-019-00132-y	journal	January 2019
Filtering in Pairwise Markov Model With Student's t Non-Stationary Noise With Application to Target Tracking Zhang, Guanghua; Lan, Jian IEEE Transactions on Signal Processing, Vol. 69 https://doi.org/10.1109/TSP.2021.3062170	journal	January 2021
Nonlinear filtering in target tracking using cooperative mobile sensors Hu, Jiangping; Hu, Xiaoming Automatica, Vol. 46, Issue 12 https://doi.org/10.1016/j.automatica.2010.08.016	journal	December 2010
Discretization and Simulation of the Zakai Equation Gobet, Emmanuel; Pagès, Gilles; Pham, Huyên SIAM Journal on Numerical Analysis, Vol. 44, Issue 6 https://doi.org/10.1137/050623140	journal	January 2006
Exact finite-dimensional filters for certain diffusions with nonlinear drift BeneŠ, V. E. Stochastics, Vol. 5, Issue 1-2 https://doi.org/10.1080/17442508108833174	journal	June 1981
Performance of Ensemble Kalman Filters in Large Dimensions Majda, Andrew J.; Tong, Xin T. Communications on Pure and Applied Mathematics, Vol. 71, Issue 5 https://doi.org/10.1002/cpa.21722	journal	November 2017
Hermite Spectral Method to 1-D Forward Kolmogorov Equation and Its Application to Nonlinear Filtering Problems Luo, Xue; Yau, Stephen S. -T. IEEE Transactions on Automatic Control, Vol. 58, Issue 10 https://doi.org/10.1109/TAC.2013.2259975	journal	October 2013
Error analysis of the Schmidt Kalman filter Nagata, Motoyasu; Sawaragi, Yoshikazu International Journal of Systems Science, Vol. 7, Issue 7 https://doi.org/10.1080/00207727608941963	journal	July 1976
Équations du filtrage non linéaire de la prédiction et du lissage Pardoux, E. Stochastics, Vol. 6, Issue 3-4 https://doi.org/10.1080/17442508208833204	journal	January 1982
New Results in Linear Filtering and Prediction Theory Kalman, R. E.; Bucy, R. S. Journal of Basic Engineering, Vol. 83, Issue 1 https://doi.org/10.1115/1.3658902	journal	March 1961
Approximation of the Zakaï Equation by the Splitting up Method Bensoussan, A.; Glowinski, R.; Rascanu, A. SIAM Journal on Control and Optimization, Vol. 28, Issue 6 https://doi.org/10.1137/0328074	journal	November 1990
Approximations to solutions of the zakai filtering equation Elliott, Robert J.; Glowinski, Roland Stochastic Analysis and Applications, Vol. 7, Issue 2 https://doi.org/10.1080/07362998908809174	journal	January 1989
Kalman Filtering for Discrete Stochastic Systems with Multiplicative Noises and Random Two-Step Sensor Delays Chen, Dongyan; Yu, Yonglong; Xu, Long Discrete Dynamics in Nature and Society, Vol. 2015 https://doi.org/10.1155/2015/809734	journal	January 2015
Robust Kalman Filtering With Probabilistic Uncertainty in System Parameters Kim, Sunsoo; Deshpande, Vedang M.; Bhattacharya, Raktim IEEE Control Systems Letters, Vol. 5, Issue 1 https://doi.org/10.1109/LCSYS.2020.3001490	journal	January 2021
On Galerkin Approximations for the Zakai Equation with Diffusive and Point Process Observations Frey, Rüdiger; Schmidt, Thorsten; Xu, Ling SIAM Journal on Numerical Analysis, Vol. 51, Issue 4 https://doi.org/10.1137/110837395	journal	January 2013
Spectral Methods: Algorithms, Analysis and Applications Shen, Jie; Tang, Tao; Wang, Li-Lian Springer Series in Computational Mathematics, Vol. 41 https://doi.org/10.1007/978-3-540-71041-7	book	August 2011
An improved constraint filtering technique for inferring hidden states and parameters of a biological model Murtuza Baker, Syed; Poskar, C. Hart; Schreiber, Falk Bioinformatics, Vol. 29, Issue 8 https://doi.org/10.1093/bioinformatics/btt097	journal	February 2013
Data Assimilation Evensen, Geir https://doi.org/10.1007/978-3-642-03711-5	book	January 2009
On a general class of stochastic partial differential equations Bensoussan, A. Stochastic Hydrology and Hydraulics, Vol. 1, Issue 4 https://doi.org/10.1007/BF01543101	journal	December 1987
Robust bayesian estimation for the linear model and robustifying the Kalman filter Masreliez, C.; Martin, R. IEEE Transactions on Automatic Control, Vol. 22, Issue 3 https://doi.org/10.1109/TAC.1977.1101538	journal	June 1977
Time-discretization of the zakai equation for diffusion processes observed in correlated noise Florchinger, Patrick; Gland, FranÇois le Stochastics and Stochastic Reports, Vol. 35, Issue 4 https://doi.org/10.1080/17442509108833704	journal	June 1991
A variable neighborhood search particle filter for bearings-only target tracking Djogatović, Marko S.; Stanojević, Milorad J.; Mladenović, Nenad Computers & Operations Research, Vol. 52 https://doi.org/10.1016/j.cor.2013.11.013	journal	December 2014
Well posedness and convergence analysis of the ensemble Kalman inversion Blömker, Dirk; Schillings, Claudia; Wacker, Philipp Inverse Problems, Vol. 35, Issue 8 https://doi.org/10.1088/1361-6420/ab149c	journal	July 2019
Optimal Consumption and Portfolio Decisions with Partially Observed real Prices Bensoussan, Alain; Keppo, Jussi; Sethi, Suresh P. Mathematical Finance, Vol. 19, Issue 2 https://doi.org/10.1111/j.1467-9965.2009.00362.x	journal	March 2009

Similar Records

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Journal Article · 2024 · Advances in Computational Mathematics · OSTI ID:2576228

Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables

Journal Article · 2003 · Applied Mathematics and Optimization · OSTI ID:21064235

Nonlinear inverse filtering in the presence of noise

Journal Article · 1996 · AIP Conference Proceedings · OSTI ID:401089

Related Subjects

Mathematics

Splitting-up Spectral Method for Nonlinear Filtering Problems with Correlation Noises

Citation Formats

References (50)

Similar Records

Related Subjects