GPS navigation processing using the quaternion-based divided difference filter |
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Authors: | Dah-Jing Jwo Mei-Ying Hsieh Shih-Yao Lai |
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Institution: | (1) Department of Communications, Navigation and Control Engineering, National Taiwan Ocean University, 2 Peining Rd., Keelung, 202-24, Taiwan |
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Abstract: | Divided difference filter (DDF) with quaternion-based dynamic process modeling is applied to global positioning system (GPS)
navigation. Using techniques similar to those of the unscented Kalman filter (UKF), the DDF uses divided difference approximations
of derivatives based on Stirling’s interpolation formula which results in a similar mean but different posterior covariance
compared to the extended Kalman filter (EKF) solutions. The second-order divided difference is obtained from the mean and
covariance in second-order polynomial approximation. The quaternion-based dynamic model is adopted for avoiding the singularity
problems encountered in the Euler angle method and enhancing the computational efficiency. The proposed method is applied
to GPS navigation to increase the navigation estimation accuracy at high-dynamic regions while preserving (without sacrificing)
the precision at low-dynamic regions. For the illustrated example, the second-order DDF can deliver about 41–82% accuracy
improvement as compared to the EKF. Some properties and performance are assessed and compared to those of the EKF and UKF
approaches. |
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