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

Cheng Yang, Wenzhong Shi, Wu Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

18 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1093-1104
Number of pages12
JournalJournal of Geodesy
Issue number8
Publication statusPublished - 1 Aug 2019


  • Integrated navigation
  • M-estimation
  • Nonlinear filter
  • Robust estimation
  • Unscented Kalman filter

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology
  • Computers in Earth Sciences

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