Huber-Based Adaptive Unscented Kalman Filter with Non-Gaussian Measurement Noise

Zhu, Bing; Chang, Lubin; Xu, Jiangning; Zha, Feng; Li, Jingshu

doi:10.1007/s00034-017-0736-x

Cited by 27 publications

(15 citation statements)

References 33 publications

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“…24,25 Heavy-tailed distribution imitated by compound Gaussian distribution is one of the typical non-Gaussian distributions, and it is widely used in research works. 25–27 Therefore, we employ the heavy-tail distribution imitated by compound Gaussian distribution to study the polar alignment. Its probability density function is…”

Section: The Bds Measurement Noise Characteristics In the Polar Regiomentioning

confidence: 99%

A new polar alignment algorithm based on the Huber estimation filter with the aid of BeiDou Navigation Satellite System

Zhao

Zeng

Liu

et al. 2021

International Journal of Distributed Sensor Networks

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For aircrafts equipped with BeiDou Navigation Satellite System/Strapdown Inertial Navigation System integrated navigation system, BeiDou Navigation Satellite System information can be used to achieve autonomous alignment. However, due to the complex polar environment and multipath effect, BeiDou Navigation Satellite System measurement noise often exhibits a non-Gaussian distribution that will severely degrade the estimation accuracy of standard Kalman filter. To address this problem, a new polar alignment algorithm based on the Huber estimation filter is proposed in this article. Considering the special geographical conditions in the polar regions, the dynamic model and the measurement model of BeiDou Navigation Satellite System/Strapdown Inertial Navigation System integrated alignment system in the grid frame are derived in this article. The BeiDou Navigation Satellite System measurement noise characteristics in the polar regions are analyzed and heavy-tailed characteristics are simulated, respectively. Since the estimation accuracy of standard Kalman filter can be severely degraded under non-Gaussian noise, a Kalman filter based on the Huber estimation is designed combining grid navigation system and generalized maximum likelihood estimation. The simulation and experiment results demonstrate that the proposed algorithm has better robustness under non-Gaussian noise, and it is effective in the polar regions. By employing the proposed algorithm, the rapidity and accuracy of the alignment process can be improved.

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Section: The Bds Measurement Noise Characteristics In the Polar Regiomentioning

confidence: 99%

A new polar alignment algorithm based on the Huber estimation filter with the aid of BeiDou Navigation Satellite System

Zhao

Zeng

Liu

et al. 2021

International Journal of Distributed Sensor Networks

View full text Add to dashboard Cite

show abstract

“…A method based on fuzzy logic was proposed to improve the fractional-order UKF with the adaptive noise covariance in Ramezani and Safarinejadian (2018), and the convergence and accuracy of the state estimation was improved. The application of UKF in non-Gaussian measurement noises for nonlinear systems was studied in Zhu et al (2018). Meanwhile, fractional-order UKF was investigated to estimate the state of charge, and the static and dynamic discharge experiments of the battery in Sun et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises

Chen

Gao

et al. 2020

Transactions of the Institute of Measurement and Control

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Hybrid extended-unscented Kalman filters (HEUKFs) for continuous-time nonlinear fractional-order systems with process and measurement noises are investigated in this paper. The Grünwald-Letnikov difference and the fractional-order average derivative (FOAD) method are adopted to discretize the investigated nonlinear fractional-order system, and the nonlinear functions in the system description are coped with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The first-order Taylor expansion used in the EKF method is performed for the nonlinear function at the current time. Meanwhile, the unscented transformation used in the UKF is also concerned for the nonlinear function at the previous time. By using the HEUKF designed in this paper, the third-order approximations for the nonlinear function can be achieved to enhance the accuracy of state estimation and estimation error matrix. Finally, numerical examples are provided to illustrate the effectiveness of the proposed HEUKF for nonlinear fractional-order systems.

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“…The estimation theory of non-Gaussian systems has become more and more influential in many technical fields, and therefore numerous meaningful attempts have been devoted to it [15,[20][21][22][23]. The non-Gaussian input noise and system state joint estimator was presented for discrete-time nonlinear non-Gaussian systems in [20], where the state posterior distribution was iteratively computed by utilizing the Gaussian sum filtering, and the noise parameter posterior distribution was calculated by applying the variational Bayesian method, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…By selecting a suitable system noise a particle estimator with higher efficiency was constructed for nonlinear non-Gaussian systems in [21]. Based on the mixed l 1 and l 2 norm minimum performance index, an adaptive filter was presented for a class of systems in non-Gaussian and nonlinear manner in [22], where the tuning factor γ was determined by using the projection statistics algorithm. A Tobit Kalman-like estimator was proposed by converting the system with time-correlated and non-Gaussian noises into a Gaussian system with unknown noises covariances in [23].…”

Section: Introductionmentioning

confidence: 99%

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

Zhao

et al. 2020

Adv Differ Equ

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We investigate non-Gaussian noise second-order filtering and fixed-order smoothing problems for non-Gaussian stochastic discrete systems with packet dropouts. We present a novel Kalman-like nonlinear non-Gaussian noise estimation approach based on the packet dropout probability distribution and polynomial filtering technique. By means of properties of Kronecker product we first introduce a second-order polynomial extended system and then analyze the means and variances of the Kronecker powers of the extended system noises. To generate noise estimators in forms of filtering and smoothing, we use the innovation approach. We give an example to illustrate that the presented algorithm has better robustness against packet dropouts than conventional linear minimum variance estimation.

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Huber-Based Adaptive Unscented Kalman Filter with Non-Gaussian Measurement Noise

Cited by 27 publications

References 33 publications

A new polar alignment algorithm based on the Huber estimation filter with the aid of BeiDou Navigation Satellite System

A new polar alignment algorithm based on the Huber estimation filter with the aid of BeiDou Navigation Satellite System

Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

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