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Journal of Systems Engineering and Electronics 2022年第6期33卷 1140-1150页

作者： LI Lifu CHENG Ting School of Information and Communication Engineering University of Electronic Science and Technology of ChinaChengdu 611731China

Phased array radar’s measurements include two direction cosine and range measurements,which can be obtained in the direction cosine coordinates.State equation of the target is nonlinear with the measurements and in order to solve the nonlinear problem,debiased conversion measurements based target tracking with direction cosine and range measurements in direction cosine coordinates named DCMKFPreDcos is proposed first in this paper,where the predicted information is introduced to calculate the converted measurement errors’statistical characteristics to eliminate the correlation between measurement noise and the converted measurement errors covariance.When range rate information can be obtained further,based on the above DCMKF-PreDcos’filtering result,the sequential filtering is adopted to process the additional range rate measurement and the DCMKF-PreDcos algorithm with extra range rate information is given.The predicted information is also introduced to calculate the involved statistical characteristics of converted measurements.The effectiveness of the proposed algorithms is shown in simulation results.

关键词： nonlinear filtering range rate information target tracking direction cosine coordinates predicted information

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 equation.The 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’case.Given 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 updating.Under certain conditions,the authors show that both processes tend to the solution of the Zakai’s equation,as the time step goes to zero.The authors specify the conditions imposed on the way of splitting-up to guarantee the convergence.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 sense.To 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 comparison.The FPF outperforms in both accuracy and efficiency.

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

Measure of nonlinearity for underwater target tracking using hull-mounted sensor

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International Journal of Intelligent Computing and Cybernetics 2022年第3期15卷 333-344页

作者： B.Omkar Lakshmi Jagan S.Koteswara Rao Department of Electrical and Electronics Engineering Koneru Lakshmaiah Education FoundationGunturIndia Department of Electronics and Communication Engineering Koneru Lakshmaiah Education FoundationGunturIndia

Purpose-Doppler-Bearing Tracking(DBT)is commonly used in target tracking applications for the underwater environment using the Hull-Mounted Sensor(HMS).It is an important and challenging problem in an underwater environment.Design/methodology/approach-The system nonlinearity in an underwater environment increases due to several reasons such as the type of measurements taken,the speeds of target and observer,environmental conditions,number of sensors considered for measurements and so on.Degrees of nonlinearity(DoNL)for these problems are analyzed using a proposed measure of nonlinearity(MoNL)for state estimation.Findings-In this research,the authors analyzed MoNL for state estimation and computed the conditional MoNL(normalized)using different filtering algorithms where measurements are obtained from a single sensor array(i.e.HMS).MoNL is implemented to find out the system nonlinearity for different filtering algorithms and identified how much nonlinear the system is,that is,to measure nonlinearity of a problem.Originality/value-Algorithms are evaluated for various scenarios with different angles on the target bow(ATB)in Monte-Carlo simulation.Computation of root mean squared(RMS)errors in position and velocity is carried out to assess the state estimation accuracy using MATLAB.

关键词： nonlinear filtering Statistical signal processing Underwater target tracking Estimation theory Hull-mounted sensor

Ice bottom evolution derived from thermistor string-based ice mass balance buoy observations

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International Journal of Digital Earth 2023年第1期16卷 3085-3104页

作者： Zeliang Liao Yubing Cheng Ying Jiang Mengmeng Li Bin Cheng Stein Sandven School of Computer Science and Engineering Sun Yat-Sen UniversityGuangzhouPeople’s Republic of China Institute of Atmospheric Physics Chinese Academy of SciencesBeijingPeople’s Republic of China Henan Academy of Big Dat1 Zhengzhou UniversityZhengzhouPeople’s Republic of China Meteorological Department Finnish Meteorological InstituteHelsinkiFinland Acoustic and Oceanography Department Nansen Environmental and Remote Sensing CenterBergenNorway

Digital information on sea ice extent,thickness,volume,and distribution is crucial for understanding Earth's climate system.The Snow and Ice Mass Balance Apparatus(SIMBA)is used to determine snow and ice temperatures in Arctic,Antarctic,ice-covered seas,and boreal lakes.Snow depth and ice thickness are derived from SIMBA temperature regimes(SIMBA_ET and SIMBA_HT).In warm conditions,SiMBA_ET temperature-based ice thickness may have errors due to the isothermal vertical profile.SIMBA_HT provides a visible ice-bottom interface for manual quantification.We propose an unmanned approach,combining neural networks,wavelet analysis,and Kalman filtering(NWK),to mathematically establish NwK and retrieve ice bottoms from various SIMBA_HT datasets.In the Arctic,NWK-derived total thickness showed a bias range of-5.64 cm to 4.01 cm and a correlation coefficient of 95%-99%.For Baltic Sea ice,values ranged from 1.31 cm to 2.41 cm(88%-98%correlation),and for boreal lake ice,-0.7 cm to 2.6 cm(75%-83%correlation).During ice growth,thermal equilibrium,and melting,the bias varied from-3.93 cm to 2.37 cm,-1.92 cm to 0.04 cm,and-4.90 cm to 3.96 cm,with correlation coefficients of 76%-99%.These results demonstrate NWK's robustness in retrieving ice bottom evolution in different water environments.

关键词： Sea ice thickness lake ice thickness ice-bottom evolution nonlinear filtering

Scaling parameters selection principle for the scaled unscented Kalman filter

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Journal of Systems Engineering and Electronics 2018年第3期29卷 601-610页

作者： NIE Yongfang ZHANG Tao Department of Automation Tsinghua University Department of Strategic Missile and Underwater Weapon Naval Submarine Academy

The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.

关键词： nonlinear filtering scaled unscented Kalman filter scaling parameter selection principle

Modified unscented particle filter for nonlinear Bayesian tracking

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Journal of Systems Engineering and Electronics 2008年第1期19卷 7-14页

作者： Zhan Ronghui Xin Qin Wan Jianwei School of Electronic Science and Engineering National Univ. of Defense Technology. Changsha 410073 P. R. China

A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conventional unscented particle filter （UPF） confronted in practice. Specifically, a different derivation of the importance weight is presented in detail. The proposed method can avoid the calculation of the prior and reduce the effects of the impoverishment problem caused by sampling from the proposal distribution, Simulations have been performed using two illustrative examples and results have been provided to demonstrate the validity of the modified UPF as well as its improved performance over the conventional one.

关键词： Bayesian estimation modified unscented particle filter nonlinear filtering unscented Kalman filter

Robust H2/H∞ global linearization filter design for nonlinear stochastic time-varying delay systems

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Science China(Information Sciences) 2016年第3期59卷 187-203页

作者： Weihua MAO Feiqi DENG Anhua WAN College of Mathematics and Informatics South China Agricultural University College of Automation Science and Engineering South China University of Technology School of Mathematics and Computational Science Sun Yat-Sen University

One can design a robust H∞filter for a general nonlinear stochastic system with external disturbance by solving a second-order nonlinear stochastic partial Hamilton-Jacobi inequality(HJI), which is difficult to be solved. In this paper, the robust mixed H2/H∞globally linearized filter design problem is investigated for a general nonlinear stochastic time-varying delay system with external disturbance, where the state is governed by a stochastic It?-type equation. Based on a globally linearized model, a stochastic bounded real lemma is established by the Lyapunov–Krasovskii functional theory, and the robust H∞globally linearized filter is designed by solving the simultaneous linear matrix inequalities instead of solving an HJI. For a given attenuation level,the H2globally linearized filtering problem with the worst case disturbance in the H∞filter case is known as the mixed H2/H∞globally linearized filtering problem, which can be formulated as a linear programming problem with simultaneous LMI constraints. Therefore, this method is applicable for state estimation in nonlinear stochastic time-varying delay systems with unknown exogenous disturbance when state variables are unavailable.A simulation example is provided to illustrate the effectiveness of the proposed method.

关键词： global linearization method mixed H2/H∞ filtering nonlinear filtering Hamilton-Jacobi inequal ity Lyapunov–Krasovskii functional nonlinear stochastic time-varying delay system

A novel strong tracking cubature Kalman filter and its application in maneuvering target tracking

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Chinese Journal of Aeronautics 2019年第11期32卷 2489-2502页

作者： An ZHANG Shuida BAO Fei GAO Wenhao BI School of Aeronautics Northwestern Poly technical UniversityXi’an 710072China School of Electronics and Information Northwestern Poly technical UniversityXi’an 710129China

The fading factor exerts a significant role in the strong tracking idea. However, traditional fading factor introduction method hinders the accuracy and robustness advantages of current strong-tracking-based nonlinear filtering algorithms such as Cubature Kalman Filter(CKF) since traditional fading factor introduction method only considers the first-order Taylor expansion. To this end, a new fading factor idea is suggested and introduced into the strong tracking CKF method.The new fading factor introduction method expanded the number of fading factors from one to two with reselected introduction positions. The relationship between the two fading factors as well as the general calculation method can be derived based on Taylor expansion. Obvious superiority of the newly suggested fading factor introduction method is demonstrated according to different nonlinearity of the measurement function. Equivalent calculation method can also be established while applied to CKF. Theoretical analysis shows that the strong tracking CKF can extract the thirdorder term information from the residual and thus realize second-order accuracy. After optimizing the strong tracking algorithm process, a Fast Strong Tracking CKF(FSTCKF) is finally established. Two simulation examples show that the novel FSTCKF improves the robustness of traditional CKF while minimizing the algorithm time complexity under various conditions.

关键词： Algorithm time complexity Cubature Kalman filter nonlinear filtering Robustness Strong tracking filter

Major Development Under Gaussian filtering Since Unscented Kalman Filter

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IEEE/CAA Journal of Automatica Sinica 2020年第5期7卷 1308-1325页

作者： Abhinoy Kumar Singh IEEE Department of Electrical Engineering Indian Institute of Technology Indore

filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring.A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering.The early Gaussian filters used a derivative-based implementation,and suffered from several drawbacks,such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF),was introduced in the nineties,which offered several advantages over the derivativebased Gaussian filters.Since the proposition of UKF,derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF.The review is particularly focused on three categories of developments:i)advancing the numerical approximation methods;ii)modifying the conventional Gaussian approach to further improve the filtering performance;and iii)constrained filtering to address the problem of discrete-time formulation of process dynamics.This review highlights the computational aspect of recent developments in all three categories.The performance of various filters are analyzed by simulating them with real-life target tracking problems.

关键词： Bayesian framework cubature rule-based filtering Gaussian filters Gaussian sum and square-root filtering nonlinear filtering quadrature rule-based filtering unscented transformation