Pulsar Angular Position Measurement Method Oriented To Micro-arcsecond Accuracy

Pulsar angular position parameters are the important basis of many research fields,such as reference frame establishment,pulsar timing modeling,gravitational wave detection and pulsar navigation.The parameter with high precision is essential part of the process from the research work on pulsars to practical engineering.The accuracy of very long baseline interferometry ranges from milliarcsecond to sub-milliarcsecond.Because of the limitation of Earth radius,atmospheric disturbance and estimation error of baseline length and time delay,it is difficult to improve the measurement accuracy.Aiming at the problem of inadequate accuracy of angular position by existing methods,this paper studies a high precision method for measuring the angular position of pulsars.Pulsar angular position measurement is a process of calculating the right ascension and the declination by the radiation signal of the pulsar in the inertial space reference.In this paper,we study a method for measuring the angular position of pulsars.Based on photon coincidence principle,a new method is proposed which uses the observed picosecond data of two or more spacecraft to precisely retrieve the right ascension and the declination of pulsars by statistical method.This paper introduces pulsar signal model,high precision photon arrival time,time transfer analysis,spatial baseline error analysis,coincidence matrix fitting and simulation of photon time of arrival.Firstly,we propose a method for measuring the angular position of pulsars based on photon coincidence.The method is based on the phenomenon that the number of photon coincidence in photon bunching effect is positively related to the accuracy of angular position parameters,so the high-precision pulsar angle position can be obtained through coherence measurement.We also design the calculation method of second-order coherence function,and analyze the broadening effect of this function by using experimental data,and propose the coherent measurement scheme for X-ray pulsars.Observing the radiation field coherence of X-ray pulsar,which is consistent with the number of photon coincidence,requires high accuracy angular position parameters.Based on this,this paper introduces the proof and flow of the method.In order to get angular position parameters from coincidence photons,we construct a coincidence matrix,and design a fitting method for the location of the largest element of the matrix,introducing constraint equation and algorithm when the main image features of the coincidence matrix are ellipse or straight line.Considering the self-motion of pulsars,we deduce the formula of angular position change rate,and analyze the constraints of observation time,and introduce the fitting method for obtaining the angular position at any time.The theoretical comparison between the proposed method and the angle measurement by time-delay method shows that the proposed method is convergent.Then,the influence factors of the proposed method are analyzed by simulation,such as time transfer model,photon bunching ratio,photon coincidence accuracy,position error and spacecraft orbit angle.The sub-picosecond simulation accuracy can only be achieved by using all time transfer items from spacecraft to the center of mass of the solar system.In addition,time transfer formula from spacecraft to reference position can be realized in picosecond order merely using geometry,Sun and Earth Shapiro time delay items.And the proposed method demands that the position error is less than centimeter.In the case of high photon bunching ratio,increasing photon coincidence accuracy by one order of magnitude leads to an increase in angle measurement accuracy by one order of magnitude.Otherwise,in the case of low photon bunching ratio,the same measurement accuracy can be achieved by reducing the photon coincidence accuracy appropriately.The orbital angle of spacecraft will affect the shape of the main characteristic image of coincidence matrix,so it is best to use three spacecraft for observation.Finally,we put forward a high-precision numerical simulation method and design a verification software.The timing model is deduced at the center of mass of the solar system containing pulsar velocity information,and the phase accuracy of the traditional timing model is about 10^-8 orders of magnitude in 30 days.A method of simulating photon time of arrival at spacecraft is proposed,which has sub-picosecond accuracy and second-order coherence.So the software can be used for ground verification before on-orbit experiments.The simulation results show that the measurement error of Crab pulsar right ascension and declination is less than 5?s and 32?as respectively,in the case of ratio of photon bunching 0.0001,photon coincidence accuracy 0.1 ns,position error 1cm,three spacecraft's effective area 100 cm² and total observation time length 10,000 s.The method based on photon coincidence proposed in this paper achieves the target of micro-arcsecond accuracy of pulsar angular position.The influencing factors are analyzed and verified by simulation.The accuracy of this method is 1 to 2 orders of magnitude higher than that of very long baseline interferometry.