Theoretical Research On Timing And Autonomous Positioning Based On X-Ray Pulsars

Pulsars are a unique class of neutron stars that spin rapidly and stably, being of super-nuclear density, strong electro-magnitic field and strong gravitational field. They have been broadly used in the study on celestial bodies evolution, gravitational wave detection and many other frontiers. The most attractive observation characteristic of pulsars is their pulsed emission with a highly stable repetition rate in the radio, infrared and higher energy regions of the electromagnetic spectrum. The period between pulse peaks is equal to the spin period of the pulsar, whose timing stability rivals that of conventional atomic clocks, thus having tremendous potential in timing and navigation. Compared to the satellite navigation system and the earth-based tracking network that have restrictions of huge maintenance cost, limited coverage area and vulnerable anti-destroy ability, pulsars can determine time, attitude, position and velocity information for satellites, spacecrafts and explorers flying in near-ground space and deep-space, and demonstrate the potentiality of providing 3D navigation service with autonomous, safe, precise and high price-performance ratio properties, whcih not only is of important value in military, but can suit the demand in deep space detection. For X-ray pulsars are advantageous when considering the detector size and signal detection compared to radio pulsars, in the last few years, the X-ray pulsar-based navigation (XNAV) technology is having been paid close attention by many countries. However, the new technology is still on the stage of theory exploration and feasibility validation with many challenges to be handled. Especially, the substantive research has just started in China. Based on the background, the thesis commences on the system framework and the process of using X-ray pulsars to implement vehicle positioning, involving the following aspects:selection of X-ray detectors and detection of X-ray photons, measurement of time of arrival (TOA), establishment of pulsar resources database, derivation of light-time equations, design of navigation algorithms and so on. Some of key technologies are analysed in theory and simulation, and several required mathematics principles are explored and deduced appropriately. Since the precise TOAs information of received pulses is the foundation of the pulsar navigation, the thesis places emphasis on the research about TOA estimation and its accuracy analysis, and feasible positioning algorithms.The main work presented in the dissertation can be summarized as follows:1. Beginning from the needs of deep space explore, the limits of satellite navigation system and the advantages of the celestial navigation, the necessities of the pulsar navigation are discussed. The specialties and merits of this technology are analysed and especially, the application prospect of the autonomous formation flyer orbiting Mars or other target bodies is expected. Meanwhile, the development of XNAV is reviewed and some of challenges existed are described.2. Through comparing the performances of several kinds of X-ray detector and refering to the style of instruments on X-ray observation satellites owned by different countries, the view that silicon-microstrip detector and calorimeter should be taken as detector prototype for XNAV is proposed. Based on this consideration, an integrated detector system with the coded-aperture mask and collimator is conceived and the protection technologies for microelectronic devices under nuclear radiation environment are discussed. All of these works are of reference value for detector selection and composite detector design.3. Starting from the demands and particularities of XNAV, Many characteristic parameters of pulsars including position, distance, flux, period, pulse profile and so on that should be bright into onboard database are proposed, among which, flux and 1st period derivative of more over 100 X-ray pulsars are analysed statistically. Based on the analysis,15 pulsars are recommended as navigation resources for their good performance when considering comprehensively both the period stability and the high flux. Additionally, the navigation advantages of X-ray pulsars with period on the order of several milliseconds are discussed for reason of their excellent timing ability. This work may help to establish the database in engineering effectively.4. The ML estimate for pulse TOA based on nonhomogeneous stationary poission process is proposed and its approximate expression under low SNR is presented. The feasibility and effectiveness are verified using pulsar B1921-24 and Crab respectively on two conditions of defferent observation time and different SNRs. Moreover, the estimation of TOA accuracy considering the specific shape of the pulse is proposed, and a comparative study among different types of pulse which is in analytical form got by fitting the observed pulses, including the gaussian pulse, the double-gaussian pulse and the exponential pulse, is performed. Theoretical research and simulation experiment results show that the error of TOA measurement depends tightly on the shape of pulses. So to establish an analytical profile template for one pulsar is necessary to ensure the accuracy estimation of TOA more exact, thus improving range estimate.5. A novel method called maximum correction variance search algorithm to estimate the period of radio pulsar signal is proposed based on the second-order cyclostationary process, which is totally applicable to X-ray pulsars if the receiving process for photons is ignored. Analysis and simulation results indicate that the method is of low computation complexity, loose demand for data quantity but obvious effect, which can be popularized in real-time period estimate for weak pulsar signal. Meanwhile, a new profile cumulation method using Wavelet-Modulus-Maxima correlation information is proposed, which don't need to estimate one approximate pulse template and can get a standard profile with high quality even under the condition of low SNR and less pulses cumulated.6. The steps of TOA measurement for pulsars are discussed in a deepgoing way and the time transfer model to Solar System Barycentre is provided with high-order general relativistic corrections including Roemer time delay, Shapiro time delay and other delay effects, whose numerical contributions to the simplified light-time model are computed and evaluated for some space position.7. An iterative error correction method for spacecraft position is developed based on pulsar timing model and the linear form of the position offset equation is evolved. Modeling errors and other factors influencing the positioning error are also discussed. Additionally, An improved method for the ambiguity resolution in absolute positioning was put forward when the internal clock of the spacecraft can be considered stable enough to be a valid reference and a previous coarse knowledge of the spacecraft position is acquired. Taking four pulsars with larger period as the initial estimation set, additional pulsars are substituted in observation equations one by one. Using known variance of TOA or range estimate as the threshold, the technique can eliminate a great number of possible ambiguity points, and finally find the 3D location of the spacecraft by MLE. Simulation results of positioning for single point and satellite trajectory demonstrate its feasibility and effectiveness.