UKF Based on Maximum Correntropy Criterion in the Presence of Both Intermittent Observations and Non-Gaussian Noise

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

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Maximum Correntropy Criterion Kalman Filter for α-Jerk Tracking Model with Non-Gaussian Noise

Entropy ◽

10.3390/e19120648 ◽

2017 ◽

Vol 19 (12) ◽

pp. 648 ◽

Cited By ~ 15

Author(s):

Bowen Hou ◽

Zhangming He ◽

Xuanying Zhou ◽

Haiyin Zhou ◽

Dong Li ◽

...

Keyword(s):

Kalman Filter ◽

Gaussian Noise ◽

Tracking Model ◽

Maximum Correntropy Criterion ◽

Non Gaussian

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Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise

2016 Annual Conference on Information Science and Systems (CISS) ◽

10.1109/ciss.2016.7460553 ◽

2016 ◽

Cited By ~ 45

Author(s):

Reza Izanloo ◽

Seyed Abolfazl Fakoorian ◽

Hadi Sadoghi Yazdi ◽

Dan Simon

Keyword(s):

Kalman Filtering ◽

Gaussian Noise ◽

Maximum Correntropy Criterion ◽

Non Gaussian

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Diffusion Generalized MCC with a Variable Center Algorithm for Robust Distributed Estimation

Electronics ◽

10.3390/electronics10222807 ◽

2021 ◽

Vol 10 (22) ◽

pp. 2807

Author(s):

Wentao Ma ◽

Panfei Cai ◽

Fengyuan Sun ◽

Xiao Kou ◽

Xiaofei Wang ◽

...

Keyword(s):

Adaptive Filtering ◽

Gaussian Noise ◽

Distributed Estimation ◽

Filtering Algorithms ◽

Combine Strategy ◽

Stable Performance ◽

The Mean ◽

Maximum Correntropy Criterion ◽

Non Gaussian ◽

Variable Center

Classical adaptive filtering algorithms with a diffusion strategy under the mean square error (MSE) criterion can face difficulties in distributed estimation (DE) over networks in a complex noise environment, such as non-zero mean non-Gaussian noise, with the object of ensuring a robust performance. In order to overcome such limitations, this paper proposes a novel robust diffusion adaptive filtering algorithm, which is developed by using a variable center generalized maximum Correntropy criterion (GMCC-VC). Generalized Correntropy with a variable center is first defined by introducing a non-zero center to the original generalized Correntropy, which can be used as robust cost function, called GMCC-VC, for adaptive filtering algorithms. In order to improve the robustness of the traditional MSE-based DE algorithms, the GMCC-VC is used in a diffusion adaptive filter to design a novel robust DE method with the adapt-then-combine strategy. This can achieve outstanding steady-state performance under non-Gaussian noise environments because the GMCC-VC can match the distribution of the noise with that of non-zero mean non-Gaussian noise. The simulation results for distributed estimation under non-zero mean non-Gaussian noise cases demonstrate that the proposed diffusion GMCC-VC approach produces a more robustness and stable performance than some other comparable DE methods.

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Diffusion Maximum Correntropy Criterion Based Robust Spectrum Sensing in Non-Gaussian Noise Environments

Entropy ◽

10.3390/e20040246 ◽

2018 ◽

Vol 20 (4) ◽

pp. 246 ◽

Cited By ~ 2

Author(s):

Xiguang Xu ◽

Hua Qu ◽

Jihong Zhao ◽

Feiyu Yan ◽

Weihua Wang

Keyword(s):

Spectrum Sensing ◽

Gaussian Noise ◽

Maximum Correntropy Criterion ◽

Non Gaussian

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Robust Kalman-Type Filter for Non-Gaussian Noise: Performance Analysis With Unknown Noise Covariances

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4043054 ◽

2019 ◽

Vol 141 (9) ◽

Cited By ~ 3

Author(s):

Seyed Fakoorian ◽

Alireza Mohammadi ◽

Vahid Azimi ◽

Dan Simon

Keyword(s):

Kalman Filter ◽

Gaussian Noise ◽

Optimality Criterion ◽

Minimum Mean Square Error ◽

Mean Square ◽

Process Noise ◽

Noise Covariance ◽

Maximum Correntropy Criterion ◽

Non Gaussian ◽

Mean Square Errors

The Kalman filter (KF) is optimal with respect to minimum mean square error (MMSE) if the process noise and measurement noise are Gaussian. However, the KF is suboptimal in the presence of non-Gaussian noise. The maximum correntropy criterion Kalman filter (MCC-KF) is a Kalman-type filter that uses the correntropy measure as its optimality criterion instead of MMSE. In this paper, we modify the correntropy gain in the MCC-KF to obtain a new filter that we call the measurement-specific correntropy filter (MSCF). The MSCF uses a matrix gain rather than a scalar gain to provide better selectivity in the way that it handles the innovation vector. We analytically compare the performance of the KF with that of the MSCF when either the measurement or process noise covariance is unknown. For each of these situations, we analyze two mean square errors (MSEs): the filter-calculated MSE (FMSE) and the true MSE (TMSE). We show that the FMSE of the KF is less than that of the MSCF. However, the TMSE of the KF is greater than that of the MSCF under certain conditions. Illustrative examples are provided to verify the analytical results.

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