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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Acknowledgments
This work has been supported in part by the National Science Council of the Republic of China under grant numbers NSC 96-2221-E-019-007 and NSC 97-2221-E-019-012. Valuable suggestions and detailed comments by Professor Alfred Leick, and the anonymous reviewers are gratefully acknowledged. Efforts made by Fong-Chi Chung of NTOU on simulation implementation for the revised version is also greatly appreciated.
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Jwo, DJ., Hsieh, MY. & Lai, SY. GPS navigation processing using the quaternion-based divided difference filter. GPS Solut 14, 217–228 (2010). https://doi.org/10.1007/s10291-009-0136-1
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DOI: https://doi.org/10.1007/s10291-009-0136-1