A Variational Bayesian Based Robust Cubature Kalman Filter under dynamic model mismatch and outliers interference

An accurate state of charge (SOC) estimation is vital for safe operation and efficient management of lithium-ion batteries. To improve the accuracy and robustness, an adaptive and robust square root cubature Kalman filter based on variational Bayesian approximation and Huber’s M-estimation (VB-HASRCKF) is proposed. The variational Bayesian (VB) approximation is used to improve the adaptivity by simultaneously estimating the measurement noise covariance and the SOC, while Huber’s M-estimation is employed to enhance the robustness with respect to the outliers in current and voltage measurements caused by adverse operating conditions. A constant-current discharge test and an urban dynamometer driving schedule (UDDS) test are performed to verify the effectiveness and superiority of the proposed algorithm by comparison with the square root cubature Kalman filter (SRCKF), the VB-based SRCKF, and the Huber-based SRCKF. The experimental results show that the proposed VB-HASRCKF algorithm outperforms the other three filters in terms of SOC estimation accuracy and robustness, with a little higher computation complexity.

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Analysis of a variational Bayesian adaptive cubature Kalman filter tracking loop for high dynamic conditions

GPS Solutions ◽

10.1007/s10291-015-0510-0 ◽

2016 ◽

Vol 21 (1) ◽

pp. 111-122 ◽

Cited By ~ 11

Author(s):

Zhi-yong Miao ◽

Yun-long Lv ◽

Ding-jie Xu ◽

Feng Shen ◽

Shun-wan Pang

Keyword(s):

Kalman Filter ◽

Tracking Loop ◽

Dynamic Conditions ◽

Variational Bayesian ◽

Cubature Kalman Filter ◽

High Dynamic

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Square-root algorithms for robust modifications of the continuous-discrete cubature Kalman filter

Вычислительные технологии ◽

10.25743/ict.2020.25.3.010 ◽

2020 ◽

pp. 88-98

Author(s):

Владимир Михайлович Чубич ◽

Светлана Олеговна Кулабухова

Keyword(s):

Kalman Filter ◽

Nonlinear Filtering ◽

Measurement Data ◽

Parametric Identification ◽

Positive Definiteness ◽

Square Root ◽

Rounding Errors ◽

Variational Bayesian ◽

Stochastic Dynamical System ◽

Cubature Kalman Filter

Предложены две устойчивые к ошибкам машинного округления и к аномальным данным квадратно-корневые модификации непрерывно-дискретного кубатурного фильтра Калмана, основанные на вариационном байесовском и коррентропийном подходах. Апробация разработанных алгоритмов на модельной задаче со случайным характером расположения аномальных наблюдений показала их работоспособность при сопоставимом качестве фильтрации. Подтверждена алгебраическая эквивалентность представленных квадратно-корневых и стандартных версий Rounding errors due to the finite length of machine word can significantly affect the quality of estimation and filtering when solving the corresponding problems in various subject areas. In this regard, to improve the reliability of the obtained results, it is advisable to develop and then apply square-root modifications of the used algorithms. Purpose: developing the square-root modifications of the continuous-discrete cubature Kalman filter on the basis of variational Bayesian and correntropy approaches. Methodology: matrix orthogonal QR decomposition. Findings: two robust (resistant to the possible presence of anomalous data and to machine rounding errors) modifications of the continuous-discrete cubature Kalman filter have been developed. The first (variational Bayesian) algorithm is obtained by extending the known discrete equations of the extrapolation stage to the continuous-discrete case. The second algorithm, based on the maximum correntropy criterion, is proposed in this paper for the first time. The developed square-root algorithms for nonlinear filtering are validated on the example of one stochastic dynamical system model with the random location of anomalous observations. In doing so, the filtering quality, estimated by the value of the accumulated mean square error, was quite comparable for both modifications during equivalent results obtained for the corresponding root-free analogues. Value: the proposed square-root versions of robust modifications of the continuous-discrete cubature Kalman filter are algebraically equivalent to their standard analogues. Meanwhile, positive definiteness and symmetry of covariance matrices of the state vector estimates at the extrapolation and the filtration stages are provided. The developed algorithms will be used to develop software and mathematical support for parametric identification of stochastic nonlinear continuous-discrete systems in the presence of anomalous observations in the measurement data

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Robust cubature Kalman filter based on variational Bayesian and transformed posterior sigma points error

ISA Transactions ◽

10.1016/j.isatra.2018.11.005 ◽

2019 ◽

Vol 86 ◽

pp. 18-28 ◽

Cited By ~ 3

Author(s):

Bingbo Cui ◽

Xinhua Wei ◽

Xiyuan Chen ◽

Jinyang Li ◽

Aichen Wang

Keyword(s):

Kalman Filter ◽

Variational Bayesian ◽

Cubature Kalman Filter

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Cooperative Space Object Tracking Based on Distributed Adaptive Variational Bayesian Cubature Kalman Filter

2018 IEEE CSAA Guidance, Navigation and Control Conference (CGNCC) ◽

10.1109/gncc42960.2018.9018929 ◽

2018 ◽

Author(s):

Chen Hu ◽

Gang Liu ◽

Jingqi Huang ◽

Haoshen Lin ◽

Xibin An

Keyword(s):

Kalman Filter ◽

Object Tracking ◽

Space Object ◽

Variational Bayesian ◽

Cubature Kalman Filter ◽

Space Object Tracking

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A tracking algorithm of hypersonic target based on dynamic model and square-root cubature Kalman filter

Journal of Physics Conference Series ◽

10.1088/1742-6596/1074/1/012094 ◽

2018 ◽

Vol 1074 ◽

pp. 012094

Author(s):

Xiangke Guo ◽

Rongke Liu ◽

Changyun Liu ◽

Qiang Fu ◽

Yafei Song

Keyword(s):

Kalman Filter ◽

Dynamic Model ◽

Tracking Algorithm ◽

Square Root ◽

Cubature Kalman Filter

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Real-Time Disturbances Estimating and Compensating of Nonlinear Dynamic Model for Underwater Vehicles

Mathematical Problems in Engineering ◽

10.1155/2018/3073072 ◽

2018 ◽

Vol 2018 ◽

pp. 1-16

Author(s):

Yuexin Zhang ◽

Lihui Wang

Keyword(s):

Kalman Filter ◽

Dynamic Model ◽

Navigation System ◽

Nonlinear Dynamic ◽

Model Parameters ◽

System State ◽

Nonlinear Dynamic Model ◽

External Disturbances ◽

Cubature Kalman Filter ◽

Nonlinear Disturbances

To reduce the deviation caused by the stochastic environmental disturbances, estimating these disturbances is required to compensate the navigation system. Based on the idea of Kalman filter using least-squares algorithm for optimal estimation, a nonlinear disturbances estimator which can be perfectly integrated with cubature Kalman filter (CKF) is proposed. For the nonlinear disturbances estimator, the disturbances are estimated by gain matrix, innovation sequences, and innovation covariance generated by CKF. The disturbances estimating and compensating algorithm consists of three parts. Firstly, the navigation system state space model is established based on nonlinear dynamic model of six degrees of freedom. Secondly, the external disturbances are estimated by using CKF and a nonlinear estimator. Finally, the disturbances compensation is carried out by improving the system state equation. In view of the uncertainty of the dynamic model and the randomness of external disturbances, numerical simulation experiments are conducted in the circumstances of sinusoidal disturbances, random disturbances, and uncertain model parameters. The results demonstrate that the proposed method can estimate disturbances effectively and improves navigation accuracy significantly.

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