GPS Solutions

, Volume 12, Issue 4, pp 273–279 | Cite as

Adaptive estimation of multiple fading factors in Kalman filter for navigation applications

  • Yanrui Geng
  • Jinling Wang
Original Article


Kalman filter is the most frequently used algorithm in navigation applications. A conventional Kalman filter (CKF) assumes that the statistics of the system noise are given. As long as the noise characteristics are correctly known, the filter will produce optimal estimates for system states. However, the system noise characteristics are not always exactly known, leading to degradation in filter performance. Under some extreme conditions, incorrectly specified system noise characteristics may even cause instability and divergence. Many researchers have proposed to introduce a fading factor into the Kalman filtering to keep the filter stable. Accordingly various adaptive Kalman filters are developed to estimate the fading factor. However, the estimation of multiple fading factors is a very complicated, and yet still open problem. A new approach to adaptive estimation of multiple fading factors in the Kalman filter for navigation applications is presented in this paper. The proposed approach is based on the assumption that, under optimal estimation conditions, the residuals of the Kalman filter are Gaussian white noises with a zero mean. The fading factors are computed and then applied to the predicted covariance matrix, along with the statistical evaluation of the filter residuals using a Chi-square test. The approach is tested using both GPS standalone and integrated GPS/INS navigation systems. The results show that the proposed approach can significantly improve the filter performance and has the ability to restrain the filtering divergence even when system noise attributes are inaccurate.


Adaptive Kalman filter Fading factors Inertial navigation system (INS) Global positioning system (GPS) 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Surveying and Spatial Information SystemsUniversity of New South WalesSydneyAustralia

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