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Robust M–M unscented Kalman filtering for GPS/IMU navigation

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Abstract

In this paper, a robust unscented Kalman filter (UKF) based on the generalized maximum likelihood estimation (M-estimation) is proposed to improve the robustness of the integrated navigation system of Global Navigation Satellite System and Inertial Measurement Unit. The UKF is a variation of Kalman filter by which the Jacobian matrix calculation in a nonlinear system state model is not necessary. The proposed robust M–M unscented Kalman filter (RMUKF) applies the M-estimation principle to both functional model errors and measurement errors. Hence, this robust filter attenuates the influences of disturbances in the dynamic model and of measurement outliers without linearizing the nonlinear state space model. In addition, an equivalent weight matrix, composed of the bi-factor shrink elements, is proposed in order to keep the original correlation coefficients of the predicted state unchanged. Furthermore, a nonlinear error model is used as the dynamic equation to verify the performance of the proposed RMUKF with a simulation and field test. Compared with the conventional UKF, the impacts of measurement outliers and system disturbances on the state estimation are both controlled by RMUKF.

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Acknowledgements

This work is supported by the National Science Foundation of China (No. 41804036) and Fundamental Research Funds for the Central Universities (No. 2652018032). Special thanks to the editor and anonymous reviewers. Their constructive comments and suggestions for amendment have significantly improved the article.

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Authors and Affiliations

  1. School of Land Science and Geomatics, China University of Geosciences, Beijing, People’s Republic of China

    Cheng Yang

  2. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China

    Wenzhong Shi & Wu Chen

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  1. Cheng Yang
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  2. Wenzhong Shi
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  3. Wu Chen
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Correspondence to Cheng Yang.

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Yang, C., Shi, W. & Chen, W. Robust M–M unscented Kalman filtering for GPS/IMU navigation. J Geod 93, 1093–1104 (2019). https://doi.org/10.1007/s00190-018-01227-5

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  • DOI: https://doi.org/10.1007/s00190-018-01227-5

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