Research On X-ray Pulsar Navigation Algorithms

This thesis deals with the X-ray pulsar navigation algorithms including data processing, error corrections, phase ambiguity resolution, and navigation and positioning methods. The main works and contributions are summarized as follows.1. Necessary qualifications of pulsars for the X-ray pulsar navigartion are proposed through the analysis of pulsar character. The principle and basic elements and navigation algorithmic flow of the X-ray pulsar navigation are described. The comparisions between the X-ray pulsar navigation and other navigation systems are made. Differential observation equations are derived and their ability of eliminating and reducing observation errors is investigated. The X-ray pulsar navigation algorithms about the timing correction, attitude determination, velocity determination and positioning are generally summarized.2. Aimed at data processing for ground radio observations and timing model setting-up, the transformation of the time of arrival(TOA) observed onboard spacecraft to the TCB/TDB time at the barycenter of the solar system and the pulsar timing model refining are researched. The magnitude of order and variations of Einstein delay, Shapiro delay, Roemer delay, dispersion delay and atmospheric delay are statistically analysed. The influences of varying timing models for binary pulsars and of planetary ephemeris on pulsar parameter fitting are compared. These analyses constitute a reference for henceforth data processing.3. The X-ray surveying data processing flows from data selection to time transformation are expounded. Computing method for the period search is educed. And the pulse profile folding is realized using real data of Crab pulsar. The results show that pulse profile can not exactly formed if the period of pulse is not known to a certain precision due to the insufficiency of observed photons. The influence of profile subinterval numbers and total number of observed photons on the signal-noise ratio and time resolution of profile are analysed.4. Equations judging whether a pulsar is sheltered by itself or by the third celestial body are given. Variations in pulsar visibility are analysed by means of calculation. It is pointed out that the main factor which affects pulsar visibility is the spacecraft itself, and that a proper detector setting can improve the visibility from 50% to 92%.5. GPS satellite navigation system ususlly selects satellites by a factor called the dilution of precision(DOP) based on the assumption that all satellite measurements have equal observation error. Pulsar's observation error are calculated using the SNR estimation method. Results show that various pulsar has normally a large observation error, from several tens of meters to thousands of kilometers. The DOP formula is deduced considering both unequal observation errors for various pulsars and their geometry configuration. Changes of DOP with the pulsar configuration are also summarized. Finally the best navigation pulsar configurations including three to six pulsars are selected through analysis, which provide a reference for the application of X-ray pulsar navigation.6. A library of phase ambiguity resolution algorithms is furnished. The situation about ambiguity searching are analysed which are affected by the observation error, number of pulsars, clock error, pulsar position error, pulse period, and pulsars'geometry configuration. In the single difference checkout method the ambiguity resolution correctness is severely influenced by the phase error. Using double-difference measurements followed by using single-difference measurements or using the spacecraft-clock-offset-aided single difference checkout method can solve this problem. These two methods can efficiently reduce the number of ambiguity combination that pass the threshold and improve the success ratio. Using the ambiguity resolution method based on the full-period number relation formula can avoid calculating spacecraft position. This method can effectively speed up searching and is convenient for implement, but fails to adjust observation errors during spacecraft position computation. So it suffer severely the influence of observation error.7. Geometric orbit determination is useful when spacecraft has a failure or in maneuver. Equations associated with the geometric orbit determination are derived and related software is developed. It is pointed out that the influence of pulsar ephemeris error is severer if the distance between the spacecraft and the point to which the timing model refers is very large. So we should manage to set the timing model reference point to the position closer to the running spacecraft. The phase error severely affects position precision. Increasing observing pulsars can reduce orbit determination error if the observation error is small. However if observation error is large, increasing observing pulsars may not benefit the orbit determination precision.8. Equations for the speed determination using triple-difference measurements are given. Random measurement error may bring severe influence on the triple-difference speed determination due to high sampling data rate. The higher the sampling rate the severer the influence on speed determination precision, and the results are more unstable. On the other hand the lower sampling rate may not reflect the instantaneous speed of spacecraft.9. Pulsar relative positioning based on the cross correlation method is presented. The spacecraft position can be determined through observing any celestial body which radiates variable signal. Thus it breaks away from the limitation of having to use pulsars that have stable period in absolute positioning. This method can use a wide range of pulsar sources. It also can simplify the calculation process and reduce the detector area as well.10. For the relative positioning, cross correlation calculation is carried out using simulated and real data. Results show that the amplitude of temporal signal is the main factor limiting the time delay determination precision. An improved time delay calculation method is presented. Using combined bins of observations can raise the signal-noise ratio of data and improve the time delay precision to such a level at which precision of time of arrival can be achieved. It avoid the influence of data sampling interval on time delay determination precision.11. A dynamic orbit determination software package is developed. The influence of all kinds of error sources on the orbit determination is assessed. It is found that the estimation of clock parameters with a second order polynomial for each pulsar in conjunction with the spacecraft position determination can absorb partial systematic errors and improve orbit determination precision. But because this method will increase the number of estimated parameters, the possibility of orbit determination matrix becoming singular is increased. The influence of observation error on the orbit determination precision is significantly reduced because of the dynamic equations. The orbit determination precision is improved from several kilometers to one hundred meters.12. The orbit determination by a single pulsar is very useful in the test phase of X-ray pulsar navigation. But in this case the orbit precision is not stable, varying from several kilometer to tens of kilometers. In trying to solve this problem the relationship between the palsar geometry and orbit determination precision is analysed. It is found that in RTN coordinate system the errors in R and T direction and position determination become larger when the angle between the unit vector in pulsar direction and Z-axis of orbit plane gets closer to 90°. While the errors will decrease when the angle is apart from 90°. And that the variation in T direction precision is opposite. Then the selecting pulsar problem with the single pulsar orbit determination error is investigated. A quasi-multiple pulsar orbit determination method is put forward which can improve the orbit determination precision. This method can effectively overcome the disadvantage of bad geometry configuration. And yield a precision comparable with that of the multi-pulsar orbit determination.