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Convergence Analysis of Splitting-Up Algorithm of the Zakai’s Equation with correlated noises

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Journal of Systems Science & Complexity 2023年第3期36卷 922-946页

作者： LUO Xue PAN Ting DONG Wenhui School of Mathematical Sciences Beihang University(Shahe Campus)Beijing 102206China Key Laboratory of Mathematics Informatics and Behavioral Semantics(LMIB)Beihang UniversityBeijing 100191China School of Mathematics and Statistics Shaanxi Normal UniversityXi’an 710119China

In the field of nonlinear filtering(NLF),it is well-known that the unnormalized conditional density of the states satisfies the Zakai’s *** splitting-up algorithm has been first studied in the independent noises case by Bensoussan,et al.(1990).In this paper,the authors extend this convergence analysis of the splitting-up algorithm to the correlated noises’*** a time discretization,one splits the solution of the Zakai’s equation into two interlacing processes(with possibly computational advantage).These two processes correspond respectively to the prediction and *** certain conditions,the authors show that both processes tend to the solution of the Zakai’s equation,as the time step goes to *** authors specify the conditions imposed on the way of splitting-up to guarantee the *** major technical difficulty in the correlated noises’case,compared with the independent case,is to control the gradient of the second process in some *** illustrate the potentially computational advantage of the schemes based on the splitting-up ways,the authors experiment on a toy NLF model using the feedback particle filter(FPF)developed based on the splitting-up method and the sampling importance and resampling(SIR)as *** FPF outperforms in both accuracy and efficiency.

关键词： Convergence analysis correlated noises nonlinear filtering splitting-up algorithm

Optimal filtering for uncertain systems with stochastic nonlinearities, correlated noises and missing measurements

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1052-1059页

作者： Shuo Zhang Yan Zhao Min Li Jianhui Zhao School of Instrument Science and Opto-electronics Engineering Beihang University

The globally optimal recursive filtering problem is studied for a class of systems with random parameter matrices,stochastic nonlinearities, correlated noises and missing measurements. The stochastic nonlinearities are presented in the system model to reflect multiplicative random disturbances, and the additive noises, process noise and measurement noise, are assumed to be one-step autocorrelated as well as two-step cross-correlated.A series of random variables is introduced as the missing rates governing the intermittent measurement losses caused by unfavorable network conditions. The aim of the addressed filtering problem is to design an optimal recursive filter for the uncertain systems based on an innovation approach such that the filtering error is globally minimized at each sampling time. A numerical simulation example is provided to illustrate the effectiveness and applicability of the proposed algorithm.

关键词： globally optimal recursive filtering random parameter matrices stochastic nonlinearities correlated noises missing measurements

Current transport and mass separation for an asymmetric fluctuation system with correlated noises

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Chinese Physics B 2018年第1期27卷 289-293页

作者：王杰宁丽娟 School of Mathematics and Information Science Shaanxi Normal University

We discuss the transport of an underdamped particle driven by an external fluctuation force in a spatially periodic asymmetric potential with correlated noises. The corresponding mathematical model is established. The movement of the steady current of an underdamped particle is presented by the method of the numerical simulation. It is indicated that the value of the current may be negative, zero, or positive. The external fluctuation force and correlated noises can effect the current direction. Under the appropriate parameters, the correlated noises intensity may even raise a reversal of the current. Besides, we have noticed a phenomenon that particles with different weight have different directions during movement by the impact of the correlated noises and external fluctuation force. Therefore, the Brownian particles can be effectively separated according to their masses.

关键词： current transport correlated noises fluctuation force Brownian motion

A novel multi-sensor multiple model particle filter with correlated noises for maneuvering target tracking

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High Technology Letters 2014年第4期20卷 355-362页

作者：胡振涛 Fu Chunling Institute of Image Processing and Pattern Recognition Henan University School of Physics and Electronics Henan University

Aiming at the effective realization of particle filter for maneuvering target tracking in multi-sensor measurements,a novel multi-sensor multiple model particle filtering algorithm with correlated noises is *** with the kinetic evolution equation of target state,a multi-sensor multiple model particle filter is firstly constructed,which is also used as the basic framework of a new *** the new algorithm,in order to weaken the adverse influence from random measurement noises in the measuring process of particle weight,a weight optimization strategy is introduced to improve the reliability and stability of particle *** addition,considering the correlated noise existing in the practical engineering,a decoupling method of correlated noise is given by the rearrangement and transformation of the state transition equation and measurement *** the weight optimization strategy and noise decoupling method adopt respectively the center fusion structure and the off-line way,it improves the adverse effect effectively on computational complexity for increasing state dimension and sensor ***,the theoretical analysis and experimental results show the feasibility and efficiency of the proposed algorithm.

关键词： multi-sensor information fusion weight optimization correlated noises maneuvering target tracking

WMF full-order Kalman smoother for multisensor Descriptor systems with correlated noises 36

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WMF full-order Kalman smoother for multisensor Descriptor sy...

Statistical fluctuations in a saturation laser model with correlated noises

第36届中国控制会议

作者： Chenjian Ran Yinfeng Dou Yuan Gao Department of Automation Heilongjiang University

ISBN: (纸本)9781538629185

For the multisensor descriptor systems with correlated noises,the WMF full-order Kalman smoother is ***,the centralized fusion descriptor system is *** this centralized fusion descriptor system is transformed to the descriptor system with uncorrelated ***,the weighted measurement fusion（WMF） descriptor system is ***,the WMF full-order Kalman and smoother and its smoothering error variance are presented,based on the maximum likelihood（ML） estimation and extended state method.A simulation example of a 3-sensor descriptor systems with common distribute noises verifies its effectiveness and the accuracy relation of the presented WMF full-order Kalman smoother.

关键词： multisensor descriptor systems correlated noises weighted measurement fusion full-order Kalman smoother

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Chinese Physics B 2006年第12期15卷 2861-2866页

作者：陈世波梅冬成 Department of Physics Yunnan University Kunming 650091 China

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker-Planck equation and analytic expressions of the steady-state probability distribution function （SPD） of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that （i） the correlation strength A of correlated noises always enhances the fluctuation of laser intensity; （ii） the correlation time v of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.

关键词： saturation laser model correlated noises fluctuation phenomena

Optimal filtering for uncertain systems with stochastic nonlinearities, correlated noises and missing measurements

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Journal of Systems Science & Complexity 2015年第5期28卷 1052-1059页

作者： Shuo Zhang Yan Zhao Min Li Jianhui Zhao School of Instrument Science and Opto-electronics Engineering Beihang University

关键词： globally optimal recursive filtering random parame- ter matrices stochastic nonlinearities correlated noises missing measurements

Two-stage Kalman Filter for Linear System with correlated noises

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Two-stage Kalman Filter for Linear System with Correlated No...

Decoupling Strong Tracking Cubature Kalman Filter for Nonlinear Systems with One-step Randomly Delayed Measurements and correlated noises

第37届中国控制会议

作者： Hong Wang Institute of System Science and Control Engineering School of AutomationHangzhou Dianzi University

The two-stage method is greatly effective to deal with state estimation for systems with unknown bias because it can improve the computation performance. Unfortunately, the current two-stage Kalman filters have some obvious limitations on noise formulation, for example, uncorrelated noises and white Gaussian noises and so on. The study on the common Kalman filtering methods has indicated that the simple noise assumptions cannot satisfy characteristics of practical systems. This paper designs a kind of two-stage Kalman estimator under the case with correlated noises. The idea is to introduce the Kalman filtering method with correlated noises to the design process of the two-stage Kalman filter with bias estimation. The purpose is to obtain an improved two-stage Kalman filter, which can deals with a kind of correlated noises, and extends practical application ***, changes on filtering formulas are clearly discovered after the noise correlation is considered compared to the current linear two-stage Kalman filters. The proposed method will be beneficial to the engineers and researches of corresponding *** effectiveness of this method can be verified by simulation.

关键词： Unknown Bias correlated noises Augmented State Kalman Filter Two-stage Kalman Filter Model Transformation

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Decoupling Strong Tracking Cubature Kalman Filter for Nonlin...