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cubature Formula and Interpolation on the Cubic Domain

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Numerical Mathematics(Theory,Methods and Applications) 2009年第2期2卷 119-152页

作者： Huiyuan Li Jiachang Sun Yuan Xu Institute of Software Chinese Academy of Sciences Beijing 100190 China Department of Mathematics University of Oregon Eugene Oregon 97403-1222 USA.

Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [-1,1]^2, as well as new results on [-1, 1]^3. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on n3/4 ＋ O（n^2） nodes of a cubature formula on [-1,1]^3.

关键词： Lattice cubature interpolation discrete Fourier series.

Marginalized cubature Kalman filtering algorithm based on linear/nonlinear mixed-Gaussian model

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High Technology Letters 2018年第4期24卷 362-368页

作者： Hu Yumei Hu Zhentao Jin Yong School of Automation Northwestern Polytechnical University College of Computer and Information Engineering Henan University

Aiming at improving the estimation accuracy and real-time of nonlinear system with linear Gaussian sub-structure,a novel marginalized cubature Kalman filter is proposed in Bayesian estimation framework. Firstly,the marginalized technique is adopted to model the target system dynamics with nonlinear state and linear state separately,and the two parts are estimated by cubature Kalman filter and standard Kalman filter respectively. Therefore,the linear part avoids the generation and propagation process of cubature points. Accordingly,the computational complexity is ***,the accuracy of state estimation is improved by taking the difference of nonlinear state estimation as the measurement of linear state. Furthermore,the computational complexity of marginalized cubature Kalman filter is discussed by calculating the number of floating-point operation. Finally,simulation experiments and analysis show that the proposed algorithm can improve the performance of filtering precision and real-time effectively in target tracking system.

关键词： state estimation marginalized modeling mixed-Gaussian model cubature Kalman filter

Adaptive “cubature and Sigma Points” Kalman Filtering Applied to MEMS IMU/GNSS Data Fusion during Measurement Outlier

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Journal of Sensor Technology 2013年第4期3卷 115-125页

作者： Hamza Benzerrouk Hassen Salhi Alexander Nebylov International Institute for Advanced Aerospace Technologies of Saint-Petersburg State University of Aerospace Instrumentation 67 Bolshaya Morskaya Saint Petersburg Russia SET Laboratory (Systèmes Electriques et Télecommande) of Electronic Department of Saad Dahlab University of Blida Soumaa Algeria

In this paper, adaptive sensor fusion INS/GNSS is proposed to solve specific problem of non linear time variant state space estimation with measurement outliers, different algorithms are used to solve this specific problem generally occurs in intentional and non-intentional interferences caused by other radio navigation sources, or by the GNSS receiver’s deterioration. Non linear approximation techniques such as Extended Kalman filter EKF, Sigma Point Kalman Filters such as UKF and CDKF are computed to estimate the navigation states for UAV flight control. Several comparisons are conduced and analyzed in order to compare the accuracy and the convergence of different approaches usually applied in navigation data fusion purposes. The last non linear filter algorithm developed is the cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application. In this work, CKF is compared with SPKF and EKF in ideal conditions and during GNSS outliers supposed to occur during specific interval of time, innovation based adaptive approach is selected and used to modify the covariance calculation of the non linear filters performed in this paper. Interesting results are observed, discussed with real perspectives in navigation data fusion for real time applications. Three parallel modified algorithms are simulated and compared to non-adaptive forms according to Root Mean Square Error (RMSE) criteria.

关键词： IMU MEMS GPS GNSS Kalman Filtering cubature Rule Sigma Points Unscented Kalman Filter

Short-term mixed electricity demand and price forecasting using adaptive autoregressive moving average and functional link neural network

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Journal of Modern Power Systems and Clean Energy 2019年第5期7卷 1241-1255页

作者： Sujit Kumar DASH Pradipta Kishore DASH Siksha O Anusandhan Deemed to be University Bhubaneswar 751030India

A new hybrid adaptive autoregressive moving average(ARMA)and functional link neural network(FLNN)trained by adaptive cubature Kalman filter(ACKF)is presented in this paper for forecasting day-ahead mixed short-term demand and electricity prices in smart *** hybrid forecasting framework is intended to capture the dynamic interaction between the electricity consumers and the forecasted prices resulting in the shift of demand curve in electricity *** proposed model comprises a linear ARMA-FLNN obtained by using a nonlinear expansion of the weighted *** nonlinear functional block helps introduce nonlinearity by expanding the input space to higher dimensional space through basis *** train the ARMA-FLNN,an ACKF is used to obtain faster convergence and higher forecasting *** proposed method is tested on several electricity markets,and the performance metrics such as the mean average percentage error(MAPE)and error variance are compared with other forecasting methods,indicating the improved accuracy of the approach and its suitability for a real-time forecasting.

关键词： Mixed demand and price forecasting cubature Kalman filter Price spikes Smart grids

A multi-rate sensor fusion approach using information filters for estimating aero-engine performance degradation

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Chinese Journal of Aeronautics 2019年第7期32卷 1603-1617页

作者： Feng LU Chunyu JIANG Jinquan HUANG Xiaojie QIU Jiangsu Province Key Laboratory of Aerospace Power System College of Energy and Power EngineeringNanjing University of Aeronautics and AstronauticsNanjing210016China Aviation Motor Control System Institute Aviation Industry Corporation of ChinaWuxi214063China

Gas-path performance estimation plays an important role in aero-engine health management, and Kalman Filter(KF) is a well-known technique to estimate performance degradation. In previous studies, it is assumed that different kinds of sensors are with the same sampling rate, and they are used for state estimation by the KF simultaneously. However, it is hard to achieve state estimation using various kinds of sensor measurements at the same sampling rate due to a complex network and physical characteristic differences between sensors, especially in an advanced multisensor architecture. For this purpose, a multi-rate sensor fusion using the information filtering approach is proposed based on the square-root cubature rule, which is called Multi-rate Squareroot cubature Information Filter(MSCIF) to track engine performance degradation. Soft measurement synchronization of the MSCIF is designed to provide a sensor fusion condition for multiple sampling rates of measurement, and a fault sensor is isolated by maximum likelihood validation before state estimation. The contribution of this paper is to supply a novel multi-rate informationfilter approach for sensor fault tolerant health estimation of an aero-engine in a multi-sensor system. Tests are conducted for aero-engine performance degradation estimation with multiple sampling rates of sensor measurement on both digital simulation and semi-physical *** results illustrate the superiority of the proposed algorithm in terms of degradation estimation accuracy and robustness to sensor failure in a multi-sensor system.

关键词： Aero-engine cubature information filter Performance degradation Sensor fusion State estimation

A SET OF SYMMETRIC QUADRATURE RULES ON TRIANGLES AND TETRAHEDRA

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Journal of Computational Mathematics 2009年第1期27卷 89-96页

作者： Linbo Zhang Tao Cui Hui Liu LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

We present a program for computing symmetric quadrature rules on triangles and tetrahedra. A set of rules are obtained by using this program. Quadrature rules up to order 21 on triangles and up to order 14 on tetrahedra have been obtained which are useful for use in finite element computations. All rules presented here have positive weights with points lying within the integration domain.

关键词： Finite element Numerical integration Quadrature cubature Triangle Tetrahedron.

Sigma-Point Filters in Robotic Applications

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Intelligent Control and Automation 2015年第3期6卷 168-183页

作者： Mohammad Al-Shabi Department of Mechatronics Engineering Philadelphia University Amman Jordan

Sigma-Point Kalman Filters (SPKFs) are popular estimation techniques for high nonlinear system applications. The benefits of using SPKFs include (but not limited to) the following: the easiness of linearizing the nonlinear matrices statistically without the need to use the Jacobian matrices, the ability to handle more uncertainties than the Extended Kalman Filter (EKF), the ability to handle different types of noise, having less computational time than the Particle Filter (PF) and most of the adaptive techniques which makes it suitable for online applications, and having acceptable performance compared to other nonlinear estimation techniques. Therefore, SPKFs are a strong candidate for nonlinear industrial applications, i.e. robotic arm. Controlling a robotic arm is hard and challenging due to the system nature, which includes sinusoidal functions, and the dependency on the sensors’ number, quality, accuracy and functionality. SPKFs provide with a mechanism that reduces the latter issue in terms of numbers of required sensors and their sensitivity. Moreover, they could handle the nonlinearity for a certain degree. This could be used to improve the controller quality while reducing the cost. In this paper, some SPKF algorithms are applied to 4-DOF robotic arm that consists of one prismatic joint and three revolute joints (PRRR). Those include the Unscented Kalman Filter (UKF), the cubature Kalman Filter (CKF), and the Central Differences Kalman Filter (CDKF). This study gives a study of those filters and their responses, stability, robustness, computational time, complexity and convergences in order to obtain the suitable filter for an experimental setup.

关键词： Sigma Point Unscented Kalman Filter cubature Kalman Filter Centeral Difference Kalman Filter Filtering Estimation Robotic Arm PRRR

管道地理坐标测量中低精度IMU初始对准技术

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沈阳工业大学学报 2013年第6期35卷 687-691页

作者：杨洋杨理践董梅沈阳工业大学大学信息科学与工程学院沈阳110870 辽宁大学物理学院沈阳110036 中国民用航空局东北地区空中交通管理局沈阳110043

针对管道地理坐标测量系统低精度惯性测量单元(inertial measurment unit,IMU)初始对准问题,提出一种管道定位的初始对准方法.针对大角度情况进行粗对准,然后在小角度范围内再进行精对准.在精对准过程中,对测量信号采用一阶马尔科夫模型... 详细信息

针对管道地理坐标测量系统低精度惯性测量单元(inertial measurment unit,IMU)初始对准问题,提出一种管道定位的初始对准方法.针对大角度情况进行粗对准,然后在小角度范围内再进行精对准.在精对准过程中,对测量信号采用一阶马尔科夫模型,提取出符合kalman滤波模型的白噪声分量,随后建立13维状态量的kalman状态方程以及观测方程.对于较大方位误差角引起的非线性,采用cubature Kalman滤波(cubature Kalman filtering,CKF)算法对非线性模型进行状态估计,解决了滤波模型的非线性问题并进行了静态对准实验.实验结果表明,设计的算法在计算时间上优于Unscented粒子滤波(Unsented particle filtering,UPF)算法,适于作为管道地理坐标测量的初始对准算法.

关键词：捷联惯导初始对准地理坐标测量姿态角一阶马尔科夫惯性测量单元 Unscented粒子滤波 cubature Kalman滤波