RKF method for pulsar based navigation with emphasis error correction

In order to reduce the influence of the emphasis error to the X-ray pulsar navigation system performance, a RKF based method for dealing the emphasis error is proposed. Through analyzing the emphasis error, the relationship between emphasis error and time is obtained. The measurement model with emphasis error is established and calculated with the principle of Kalman filter. The estimation error covariance is dealing with the matrix inequality due to the emphasis error is contained in the estimation error covariance. The proposed RKF method is tested on the Earth and Mars rotation orbit and compared with UKF and other filtering method which can deal with the emphasis error. The simulation results shows the proposed method can achieve higher positioning accuracy than UKF and the other two filtering methods, the RKF based method can greatly reduce the impact of emphasis error for XNAV.