| Citation: | XU Qiang, WANG Hongli, HE Yiyang, et al. Improved pulsar navigation measurement equation based on truncation errors[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(9): 1974-1981. doi: 10.13700/j.bh.1001-5965.2017.0807(in Chinese)
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Considering that the traditional extended Kalman filter (EKF) algorithm has to neglect the higher order terms of the measurement model because of linearization, which causes the problem of large truncation errors in X-ray pulsar navigation, an improved linear measurement equation suitable for pulsar navigation is proposed. First, the paper analyzes the physical meaning of annual parallax effect and Shapiro effect which cause the truncation error in the process of simplifying the measurement equation. The two higher order terms' mathematical models are established and numerical analysis is conducted. Then, using the method of Taylor expansion, the two higher order terms are linearized to establish an improved linear measurement equation. Finally, using the earth satellite orbit data, the two measurement equations are respectively applied to the EKF algorithm of the pulsar navigation to verify the validity of the improved measurement equation. The results show that the improved linear measurement equation can guarantee the position and velocity estimation error within 250 m and 2 m/s under the consideration of the higher order terms, and that the improved linear measurement equation has some robustness to the higher order term changes. However, the traditional simplified measurement equation can cause divergence.
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