Mixed‐Degree Spherical Simplex‐Radial Cubature Kalman Filter

Wang, Shiyuan; Yang, Feng; Duan, Shukai; Wang, Lidan

doi:10.1155/2017/6969453

Cited by 7 publications

(5 citation statements)

References 24 publications

(50 reference statements)

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“…Liu et al [11] proposed a interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF) by integrating the interacting multiple model (IMM) filter with the fifth-degree spherical simplex-radial cubature Kalman filter (5thSSRCKF). Wang et al [12] proposed a mixed-degree spherical simple-x-radial cubature Kalman filter (MSSRCKF), and analyzed its accuracy. Simulations results showed that the algorithm can achieve performance improvement of fifth-degree SSRCKF and has higher accuracy under less computational burden.…”

Section: Introductionmentioning

confidence: 99%

A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot

Liu

Wang

Guo

et al. 2020

Sensors

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The motion state of a quadruped robot in operation changes constantly. Due to the drift caused by the accumulative error, the function of the inertial measurement unit (IMU) will be limited. Even though multi-sensor fusion technology is adopted, the quadruped robot will lose its ability to respond to state changes after a while because the gain tends to be constant. To solve this problem, this paper proposes a strong tracking mixed-degree cubature Kalman filter (STMCKF) method. According to system characteristics of the quadruped robot, this method makes fusion estimation of forward kinematics and IMU track. The combination mode of traditional strong tracking cubature Kalman filter (TSTCKF) and strong tracking is improved through demonstration. A new method for calculating fading factor matrix is proposed, which reduces sampling times from three to one, saving significantly calculation time. At the same time, the state estimation accuracy is improved from the third-degree accuracy of Taylor series expansion to fifth-degree accuracy. The proposed algorithm can automatically switch the working mode according to real-time supervision of the motion state and greatly improve the state estimation performance of quadruped robot system, exhibiting strong robustness and excellent real-time performance. Finally, a comparative study of STMCKF and the extended Kalman filter (EKF) that is commonly used in quadruped robot system is carried out. Results show that the method of STMCKF has high estimation accuracy and reliable ability to cope with sudden changes, without significantly increasing the calculation time, indicating the correctness of the algorithm and its great application value in quadruped robot system.

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Section: Introductionmentioning

confidence: 99%

A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot

Liu

Wang

Guo

et al. 2020

Sensors

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“…A significant observation is that a cubature rule over spherical surface that is constituted by the dth-degree spherical rule and the dth-degree radial rule can achieve a dth-degree estimation accuracy. Nevertheless, the degree of the spherical rule as shown in Algorithm 1 is not necessarily equal to the radial rule degree which facilitates and motivates the mixture-degree of cubature rules over the spherical surface [23,35].…”

Section: Efficient Cubature Rule Over the Entire N-d Spacementioning

confidence: 99%

Fault Diagnosis of Nonlinear Systems Using a Hybrid-Degree Dual Cubature-based Estimation Scheme

Shen¹,

Khorasani²

2021

Preprint

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In this paper, a novel hybrid-degree dual estimation approach based on cubature rules and cubature-based nonlinear filters is proposed for fault diagnosis of nonlinear systems through simultaneous state and time-varying parameter estimation. Our proposed dual nonlinear filtering scheme is developed based on case-dependent cubature rules that are motivated by the following observations and facts, namely (i) dynamic characteristics of nonlinear system states and parameters generally are distinct and posses different degrees of complexities, and (ii) performance of cubature rules depend on the system dynamics and vary due to handling of high-dimensional integrations approximations. For improving the robustness capability of our proposed methodologies a modified cubature point propagation method is incorporated. The performance of our proposed dual estimation strategy is demonstrated and evaluated by application to a nonlinear gas turbine engine for addressing the component fault diagnosis problem within an integrated fault detection, isolation and identification framework. Robustness analysis is implemented to verify the capability of our proposed approaches to deal with parametric uncertainties and unmodeled dynamics. Extensive simulation case studies and discussions with respect to component fouling, erosion or abrupt faults are provided to substantiate and justify the superiority of our proposed fault diagnosis methodology when compared to other well-known alternative diagnostic techniques such as the Unscented Kalman Filters (UKF) and Particle Filters (PF) that are commonly available in the literature.

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“…The MACNCKF algorithm is commonly used in CKF and its various derivative algorithms. This section provides a discretized approximation algorithm flow based on Mixeddegree Spherical Simplex-Radial Cubature Kalman Filter (MSSRCKF) [24]. MSSRCKF is a CKF algorithm adopting mixed-order simplest phase-path sampling strategy.…”

Section: Macnckf Implementation Based On Mssrckfmentioning

confidence: 99%

“…First, there is need to calculate i ξ according to equations (24) and (25), and perform the first volume point calculation:…”

Section: Macnckf Implementation Based On Mssrckfmentioning

confidence: 99%

A Multiplicative Noises and Additive Correlated Noises Cubature Kalman Filter and Its Application in Quadruped Robot

Liu

Wang

et al. 2020

IEEE Access

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The traditional Cubature Kalman Filter (CKF) and its derived algorithms cannot work without the two hypotheses of Kalman Filter (KF), one is that the system model is accurate and the other is the system is only influenced by independent white noise with known statistical characteristics. However, it is difficult to fully guarantee the above hypotheses in actual operation. The presence of multiplicative noise undermines the first hypothesis, while the additive noise correlation undermines the second hypothesis. Given invalid hypotheses, the estimated performances of CKF and its derivative algorithms are degraded drastically. To solve this issue, this paper proposes Multiplicative Noises and Additive Correlated Noises Cubature Kalman Filter (MACNCKF), which solves state estimation problems involving multiplicative noise and additive noise while maintaining CKF advantages. Moreover, this algorithm has been testified to be correct and easy to be transplanted to CKF and its derivative algorithm after strict mathematical derivation. When the system lacks multiplicative noise and additive noise, the algorithm is degraded to corresponding algorithm in a general form, which helps extend the application environment of CKF and its derivative algorithms, thus improving robustness. Numerical simulation and experiments on quadruped robot system indicate that MACNCKF can effectively solve state estimation problem involving both multiplicative noise and additive noise. Given time consumption in MACNCKF basically comparable to that in CKF, MACNCKF has improved estimation accuracy, robustness and reliability.

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Mixed‐Degree Spherical Simplex‐Radial Cubature Kalman Filter

Cited by 7 publications

References 24 publications

A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot

A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot

Fault Diagnosis of Nonlinear Systems Using a Hybrid-Degree Dual Cubature-based Estimation Scheme

A Multiplicative Noises and Additive Correlated Noises Cubature Kalman Filter and Its Application in Quadruped Robot

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