Estimation Method And Application Of X-ray Pulsar Signal Phase Difference

As a new method of autonomous navigation and with good autonomy, high reliability and wide applicability, the relative navigation system based on X-ray pulsar forms complementary advantages to existing navigation systems and gradually gets great attention and favor in the field of aerospace. It is mainly through the proportional relation between the measured delay of the pulse arrival time and the distance increment of two spacecrafts along the pulsar direction vector to estimate the states of relative motion. In general, the delay of the pulse arrival time is obtained by the phase difference of the pulse signals, whose measurement accuracy directly determines the relative navigation and positioning accuracy. Therefore, how to obtain the high accuracy of the phase difference has become an urgent problem to be solved.In the X-ray pulsar relative navigation and positioning system, the integrated pulse profile or the measured pulse arrival time can be chosen as the research objects to estimate the phase difference. A new phase difference estimation algorithm called weighted FFT is proposed in this paper, which selects photons intensity series obtained by sampling with equal interval from photons arrival time series as the research object and gets the phase retardation in time domain through accumulating the phase difference between two photons intensity series and Energy weighting the ratio of phase difference to each frequency in frequency domain. This method can not only prevent losing of the effective signal in the process of accumulation to improve the signal-to-noise ratio, but also speed up operation rate with lesser data compared with pulse arrival time. In addition, combining three-dimensional relative position and velocity equation with orbital dynamics model of relative motion, a relative navigation system of Extended Kalman Filter is given to estimate the states of relative motion between two spacecrafts, which can validate the feasibility and optimal effect of the weighted FFT algorithm.To compare differences in the estimated accuracy of phase difference and computational complexity, comparative simulations of the proposed weighted FFT phase difference estimation algorithm, the nonlinear least squares(NLS) method and the maximum likelihood(ML) method are made. The effects of observation time and sampling interval on the weighted FFT algorithm are analyzed. The states of relative motion on relative navigation and positioning system are estimated by these algorithms. Results show that:(1) The computational complexity of weighted FFT algorithm is between ML and NLS, and the weighted FFT algorithm can get higher estimation precision of phase difference compared with NLS and ML algorithm.(2) The root mean square error of the phase difference estimated by the weighted FFT algorithm is an power function of the observation time or the sampling interval. With the extension of observation time and the decrease of the sampling interval, the impact is no longer significant.(3) In the relative navigation and positioning system, the weighted FFT algorithm can get more accurate estimation of relative position and velocity than NLS and ML algorithm.