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Pulsars are neutron stars with high rotation speeds and have extraordinary long-term rotational stability. X-ray pulsar-based navigation (XNAV) is a navigation method that estimates the position and velocity of a spacecraft using the X-ray radiation from pulsars. Flight experiments on Insight-Hard X-ray Modulation Telescope (Insight-HXMT) and Neutron Star Interior Composition Explorer (NICER) have successfully verified the feasibility of using XNAV for a single spacecraft. For spacecraft in formation, a pulsar-based navigation method that uses the pulse phase delay between spacecraft is derived. Moreover, a direct estimation method for pulse phase delay, which is independent from the pulsar template, is proposed. The proposed method is verified with simulation data of the Crab pulsar and real data of the same pulsar obtained from Insight-HXMT and NICER. [ABSTRACT FROM AUTHOR]

• Capable of simulating X-ray signals received by a near-Earth spacecraft. • Capable of providing supporting data for near-Earth space applications of X-ray Pulsar-based Navigation. • It is possible to determine the capacity of the atmosphere at different altitudes to absorb X-ray photons. The near-Earth space holds significant strategic value, and X-ray pulsar-based navigation in this region can diversify navigation methods, enhancing the safety and autonomy of spacecraft. Due to the challenges and high costs associated with obtaining actual measurements of pulsars in near-Earth space, the simulation technology for X-ray pulsar signals in this region can provide input for demonstrating the feasibility of technical solutions and experiments related to the application of X-ray pulsar-based navigation in near-Earth space. Therefore, this paper proposes a method for simulating X-ray signals in near-Earth space. Firstly, a scale transforming method is employed to generate a photon arrival time sequence at the spacecraft that includes energy information. Subsequently, the atmospheric transmittance model is utilized for photon selection, obtaining a sequence of photons that have passed through the atmosphere after absorption. Finally, experimental validation of the proposed algorithm is conducted using Crab pulsar data measured by the Insight-HXMT. The similarity between the simulated data and the measured data is evaluated in terms of profiles, phases, and energy spectra. Simulation experiments demonstrate that the time delay estimation error caused by the simulation algorithm is less than 17.17 us. When the observation tangent point altitude is in the range of 160 km to 180 km, the Pearson correlation coefficient of the profiles between simulated and measured data is 73.74 %. The Pearson residuals of the energy spectra are evenly distributed between −0.2 and 0.2, indicating a good level of similarity between the two. [ABSTRACT FROM AUTHOR]

Pulsars are neutron stars with high rotation speeds and have extraordinary long-term rotational stability. X-ray pulsar-based navigation (XNAV) is a navigation method that estimates the position and velocity of a spacecraft using the X-ray radiation from pulsars. Flight experiments on Insight-Hard X-ray Modulation Telescope (Insight-HXMT) and Neutron Star Interior Composition Explorer (NICER) have successfully verified the feasibility of using XNAV for a single spacecraft. For spacecraft in formation, a pulsar-based navigation method that uses the pulse phase delay between spacecraft is derived. Moreover, a direct estimation method for pulse phase delay, which is independent from the pulsar template, is proposed. The proposed method is verified with simulation data of the Crab pulsar and real data of the same pulsar obtained from Insight-HXMT and NICER.

Distributed X-ray pulsar-based navigation (DXNAV) is an effective method to realize earth-orbit satellite positioning under weak pulsar signal conditions. In this paper, we propose a new DXNAV method based on multiple information fusion. The DXNAV system principle and the pulse phase estimate Cramér-Rao lower bound are deduced. To suppress the calculation complexity and the error source, the X-ray pulsar photon time-of-arrival detected by each satellite is equivalently converted to the leading satellite directly using the inter-satellite link ranging and starlight angular distance measurement. A high precision estimate model of the pulse phase is built using pulsar standard profile, observed profile, and star-geocentric angular distance from distributed satellites. The estimated pulse phase is real-time supplied to the navigation system, which is established in the form of a deviation equation. The two-stage Kalman filter is designed to estimate the pulse phase in profile histogram bin step and the leader position in real-time step. Compared separately with the maximum likelihood phase estimate method and the celestial navigation method using only the star-geocentric angular distance, the simulation analysis shows that the estimation precisions of position and velocity are improved by 29% and 25%. [ABSTRACT FROM AUTHOR]

In this paper, the inter-satellite link (ISL) aided X-ray pulsar-based navigation (XPNAV) system is studied to improve the survivability of space-borne gravitational wave detector. An unscented transform (UT) based distributed Kalman estimator is proposed for state estimation within less computational and communication costs. Three different navigation scenarios are designed based on a typical large-scale distributed heliocentric orbital space-borne gravitational wave detector, Laser Interferometer Space Antenna (LISA). Simulation results show that the positioning root-mean-square error (RMSE) reduces ̃28% after introducing the ISL to XPNAV. Moreover, the proposed distributed Kalman estimator and the classical Kalman estimator shows similar performance in XPNAV/ISL integrated navigation system with the positioning RMSE of ̃528 m and ̃520 m, respectively. Compared with the classical method, both analytical and simulating analyses demonstrate that the proposed algorithm efficiently reduces the computational costs to 1 / N 2 for a team with N agents and avoids additional communication needs simultaneously. The efficient distributed Kalman estimator-based XPNAV/ISL integrated navigation provides a high-performance autonomous navigation solution for interplanetary spacecraft formation flying missions. • Pulsar and inter-satellite link are used to aid space-borne gravitational wave detector. • We Introduce distributed estimator into autonomous navigation for formation flying. • Distributed estimator reduce computational costs within seldom loss of accuracy. [ABSTRACT FROM AUTHOR]

At present, studies on X-ray signal processing and the navigation filtering algorithm in X-ray pulsar navigation are largely independent; thus, navigation accuracy analysis must be based on the analysis of a sound and complete navigation system. In this study, a navigation system simulation initiated from the numerical generation of the observed signals to navigation filtering solutions was established on the basis of the requirements of the authenticity and integrity of a demonstration of Earth-orbit spacecraft navigation. The influences of the navigation observation time, time delay estimation algorithms, and different pulsar combinations imposed on navigation accuracy were therefore analyzed. The simulation results showed that an optimal observation time existed with the highest navigation accuracy in Earth-orbit applications when three pulsars were observed in parallel, thereby obtaining the optimal observation time and its corresponding navigation accuracy. Using the short time high-accuracy algorithm of time delay estimation, the navigation accuracy of low-orbit spacecraft was greatly improved by 1010 m when the observation time was 60 s. Among three combinations of pulsars analyzed in this study, the pulsar combination of PSR B0531+21, PSR B1821-24, and PSR B1937+21 achieved the highest navigation accuracy on a low orbit, whose result was 560 m. The corresponding simulation results were based on a complete and near-real navigation algorithm, thereby offering a theoretical foundation for determining the navigation accuracy and selecting the orbit and observation time parameters in Earth-orbit pulsar navigation applications. [ABSTRACT FROM AUTHOR]

X-ray pulsar-based navigation (XPNAV) is one of the perfect ways for autonomous deep-space navigation in the future. Due to spacecraft state model errors and strong cosmic background noises, low navigation accuracy is one of the main problems in XPNAV. This paper proposes a robust navigation filtering method to reduce the serious effect of spacecraft state model errors and strong noises on XPNAV. This method uses state model errors and pulsar observation errors to estimate and correct the state model. And then, to predict the spacecraft' state in the next moment with high precision, the gain matrix is adjusted in quasi real-time by using the fading factor to ensure a minimized state estimation error variance in the next moment and an orthogonal residual sequence at different times. Finally, experimental results of multi-group simulations show that the proposed method had significantly improved navigation accuracy. And the accuracy of the proposed method is better than that of H∞ robust filter and STUKF, especially when the state model errors and noise are great. Under the same conditions, compared with the other two methods, the proposed method has the minimum navigation filtering error and the strongest robustness.

In this paper, comprehensive pulsar-based Guidance, Navigation and Control (GNC) system is designed and applied to satellites formation flying. The complete autonomy of the X-ray pulsar navigation technology provides both absolute and relative positioning information for spacecraft in or even beyond the solar system, and provides an interesting alternative solution to classical navigation techniques such as Global Navigation Satellite System (GNSS). The navigation measurements are studied using a relative time of arrival (RTOA) estimating method, which takes advantage of the noise-filtered pulsar profiles in the cross-correlation estimator to achieve robustness. An adaptive Kalman filter is exploited to minimise the effect of processing noises caused by the primary satellite. A linear Quadratic Gaussian regulator is then applied to control the formation. Two different configurations are studied in high Earth orbits (HEOs). Simulation results show that the designed GNC algorithms can fulfill the required accuracy (10% of the baseline) of the Magnetospheric Multiscale Mission, with the position root-mean-square error of ~ 1.6 km.. The excellent robustness of the designed GNC system on the positioning errors of the primary satellite suggests a role for X-ray pulsar-based formation flying technique in HEOs and the solar system. • A comprehensive pulsar-based GNC system is first designed and applied to satellite formation flying (FF) missions. • The navigation measurement (RTOA) strategies are investigated and new RTOA estimation method is proposed. • The simulation studies the performance of the presented pulsar-based FF GNC system. • The FF GNC system shows good robustness on the positioning errors of the primary satellite. [ABSTRACT FROM AUTHOR]

X-ray pulsar-based navigation (XNAV) is a promising autonomous navigation method, and the pulse phase is the basic measurement of XNAV. However, the current methods for estimating the pulse phase for orbiting spacecraft have a high computational cost. This paper proposes a stellar angle measurement-aided pulse phase estimation method for high Earth orbit (HEO) spacecraft, with the aim of reducing the computational cost of pulse phase estimation in XNAV. In this pulse phase estimation method, the effect caused by the orbital motion of the spacecraft is roughly removed by stellar angle measurement. Furthermore, a deeply integrated navigation method using the X-ray pulsar and the stellar angle is proposed. The performances of the stellar angle measurement-aided pulse phase estimation method and the integrated navigation method were verified by simulation. The simulation results show that the proposed pulse phase estimation method can handle the signals of millisecond pulsars and achieve pulse phase estimation with lower computational cost than the current methods. In addition, for HEO spacecraft, the position error of the proposed integrated navigation method is lower than that of the stellar angle navigation method.

Pulse phase is the basic measurements of X-ray pulsar-based navigation, and thus how to estimate a pulse phase for an orbiting spacecraft is important. The current methods for on-orbit pulse phase estimation could provide an accurate estimation performance enhancing with the photon amount, but its central processing unit (CPU) time cost also increases sharply with the increase of photon amount. In this paper, an on-orbit pulse phase estimation method based on the cross-entropy adaptive moment estimation (CE-Adam) algorithm is proposed to reduce the CPU time cost while retaining decent estimation accuracy. This method combines the CE and Adam algorithms, and is able to obtain a global optimum with low CPU time cost. The performance of the proposed algorithm is verified by simulation data and real data from the Neutron Star Internal Composition Detector (NICER). The results show that the proposed algorithm could greatly reduce the CPU time cost, which is about 1.5% of the CE algorithm, and retain similar estimation accuracy of pulse phase with CE algorithm.

Abstract In this paper, a focused detection system for X-ray pulsar-based Navigation (XNAV) is designed based on Silicon Drift Detector (SDD). The detector electronics mainly adopts the digital trapezoidal shaping method to measure the Times-Of-Arrival (TOAs) and energy of photons. The time measurement accuracy is better than 500ns. The energy resolution is 191eV at 8.05keV, and the maximum count rate is 500kcps between 1 and 12keV. In the semi-physical simulation experiment, the filtering of noise photons by energy discrimination significantly improves the correlation degree between the cumulative pulse profile and the standard profile. [ABSTRACT FROM AUTHOR]

Recently, X-ray pulsar-based navigation (XPNAV) as a significant navigation method has been widely used in deep space exploration. However, the accuracy of XPNAV is limited to the existence of the pulsar direction error. To improve the performance of XPNAV, we have proposed a novel algorithm named “the modified augmented state extended Kalman filter” (MASEKF). The algorithm considers the high-order terms of direction error and then adds a more precise direction error into state equation and measurement equation. In the simulation, by comparing the performance of MASEKF, EKF, and ASEKF at the same time, it is found that MASEKF has better performance in the accuracy and stability, and the results also demonstrate that MASEKF algorithm has faster convergence speed. This paper provides a strong reference for other improvements of algorithms towards direction error. The purpose of this study is to establish MASEKF and add the direction error into the measurement equation and the state equation, so as to realize the coordination and symmetry of the algorithm.

The accuracy of X-ray pulsar-based navigation is greatly affected by the Doppler effect caused by the spacecraft orbital motion and the systematic biases introduced by the pulsar directional error, spacecraft-borne clock error, etc. In this paper, an innovative navigation method simultaneously employing the pulse phase (PP), the difference of two neighbor PPs (DPP) and the Doppler frequency (DF) of X-ray pulsars as measurements is proposed to solve this problem. With the aid of the spacecraft orbital dynamics, a single pair of PP and DF relative to the spacecraft’s state estimation error can be estimated by using the joint probability density function of the arrival photon timestamps as the likelihood function. The systematic biases involved to the PP is proved to be nearly invariant over two adjacent navigation periods and the major part of it is eliminated in the DPP; therefore, the DPP is also exploited as additional navigation measurement to weaken the impact of systematic biases on navigation accuracy. Results of photon-level simulations show that the navigation accuracy of the proposed method is remarkably better than that of the method only using PP, the method using both PP and DF and the method using both PP and DPP for Earth orbit.

A pulse template establishment method considering the directional error of the pulsar is proposed in this paper. This method folds the series of photon time of arrival (TOA) of symmetric time intervals to reduce the impact of directional error on pulse template. Firstly, the characteristic of this error is analyzed. And then, its analytical formula of the average value for a whole year is derived as well as that for arbitrary time interval. Finally, the simulated and real data are employed to investigate the performance of the proposed method. Results have shown that this method can establish a relative high-accuracy pulse template. [ABSTRACT FROM AUTHOR]

An X-ray pulsar/starlight Doppler deeply-integrated navigation method is proposed in this paper. A starlight Doppler measurement-aided phase propagation model, which can remove the orbital effect within the recorded photon Time Of Arrivals (TOAs), is derived, and guarantees that the pulse phase can be extracted from the converted photon TOAs using computationally efficient methods. Some simulations are performed by a hardware-in-loop system to verify the performance of the integrated pulse phase estimation method as well as of the integrated navigation method. The integrated pulse phase estimation method could achieve an estimation performance similar to the existing method for orbiting vehicles at the cost of much less computational complexity, is capable of handling the signals of millisecond pulsars, and is applicable to various vehicles. In addition, the proposed integrated navigation method could provide reliable positioning results for various vehicles. [ABSTRACT FROM AUTHOR]

Celestial navigation (CeleNav) has been successfully used for position determination in many Mars exploration missions. Traditional CeleNav usually uses star angle as measurement, which is a function of spacecraft's position. Its accuracy is affected by the distance between the spacecraft and the Mars. X-ray pulsar-based navigation (XNAV) is a feasible autonomous method which can provide highly accurate distance measurements. However, single pulsar navigation system is unobservable and its navigational performance is influenced by the corresponding systematic biases caused by the pulsar directional error and the spacecraft-borne clock error. For the complementary of the CeleNav and the XNAV, the differential X-ray pulsar aided CeleNav method is proposed, which adopts the time-differenced X-ray pulsar measurement to eliminate the major part of systematic biases and improve the navigation accuracy. Simulations demonstrate the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]

A pulsar profile denoising method using kernel regression based on maximum correntropy criterion is proposed. This method uses the kernel regression to reduce the human visual inspection inescapable in the current profile denoising methods and the reliance of the prior knowledge on the profile of interest. In order to cope with the non-Gaussian case that is common in a real application, the maximum correntropy criterion is introduced into the kernel regression to resist the impact of non-Gaussian noise. The performance of the prosed method is verified via simulation and real data. The results have shown that the proposed method outperforms the current signal denoising methods in a non-Gaussian environment and is readily to be applied. [ABSTRACT FROM AUTHOR]

The X-ray energy band, which has a direct impact on the detector configuration and the estimation accuracy of the pulse time of arrival (TOA), is an important physical parameter for X-ray pulsar based navigation (XPNAV). Despite nearly five decades of work, there is still no convincing quality analysis for the effect of the X-ray energy on the XPNAV. In this paper, the impacts of the X-ray energy on the XPNAV are quantified for the first time through the Cramér-Rao lower bound (CRLB) theory. A lower bound on the variance of the pulse TOA is derived, and the indicators of the geometric factor and signal to noise ratio (SNR) are presented as the basic selection criteria. The RXTE observations of the Crab pulsar about 11 years (2001–2011) are applied to subdivide the entire 2–60 keV into finer energy windows of 2–10 keV, 10–20 keV, 20–30 keV, 30–40 keV, 40–50 keV and 50–60 keV to obtain pulse profiles in different energy bands. Discrepancies of these pulse profiles are investigated, and their impacts on the navigation accuracy are evaluated. The results demonstrate that the estimation accuracy of the pulse TOA applying the energy band 2–30 keV is improved by 15.54% compared with 2–10 keV, while an improvement of about 15.95% can merely be achieved applying 2–60 keV than 2–10 keV for the Crab pulsar. [ABSTRACT FROM AUTHOR]

A pulse phase estimation of an X-ray pulsar with the aid of vehicle orbital dynamics is proposed. The original continue-time X-ray pulsar signal model is modified to be a term of vehicle position and velocity varying with time, and a modified definition of pulse time of arrival is given. The modified signal model is further linearized around the predicted position and velocity of the vehicle to the second order. The initial phase and the coefficients of the extended signal model can be estimated by maximum likelihood estimator. Some simulations are performed to verify the method and show the method has robustness to the initial error within initial state of the vehicle and is capable of handling the phase-estimation problem for pulsars with low fluxes. [ABSTRACT FROM AUTHOR]

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Abstract: In order to reduce the composite impacts of the systematic biases in the X-ray pulsar-based navigation system, an innovative navigation method is proposed. The proposed method employs the time-differenced measurement which is the difference between the measurements at the neighbor epochs. For Earth-orbiting satellite, the systematic biases vary slowly over the navigation period, and the time-differenced measurement can greatly reduce the major part of systematic biases. Through observability analysis, the corresponding navigation system is demonstrated to be completely observable. In order to solve the correlation between the process and measurement noises in the proposed method, a modified unscented Kalman filter is derived. In addition, the modified unscented Kalman filter propagates the selected sigma points to generate the time-differenced measurement model without involving linearization error. The results of simulations have shown that the proposed method can effectively reduce the composite impacts of systematic biases including the pulsar angular position error, pulsar distance error, Earth ephemeris error, and satellite-borne clock error. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to investigate and reduce the impact of the errors in the planetary ephemerides on X-ray pulsar-based navigation system for Earth-orbiting satellite. Expressions of the system biases caused by the errors in the planetary ephemerides are derived. The result of investigation has shown that the impact of the error in Earth’s ephemeris is must greater than the errors in the other ephemerides and would greatly degrade the performance of X-ray pulsar-based navigation system. Moreover, the system bias is modeled as a slowly time-varying process, and is handled by including it as a part of navigation state vector. It has been demonstrated that the proposed navigation system is completely observable, and some simulations are performed to verify its feasibility. [Copyright &y& Elsevier]

X-ray pulsar-based navigation (XNAV) is a promising autonomous navigation method, and the pulse phase is the basic measurement of XNAV. However, the current methods for estimating the pulse phase for orbiting spacecraft have a high computational cost. This paper proposes a stellar angle measurement-aided pulse phase estimation method for high Earth orbit (HEO) spacecraft, with the aim of reducing the computational cost of pulse phase estimation in XNAV. In this pulse phase estimation method, the effect caused by the orbital motion of the spacecraft is roughly removed by stellar angle measurement. Furthermore, a deeply integrated navigation method using the X-ray pulsar and the stellar angle is proposed. The performances of the stellar angle measurement-aided pulse phase estimation method and the integrated navigation method were verified by simulation. The simulation results show that the proposed pulse phase estimation method can handle the signals of millisecond pulsars and achieve pulse phase estimation with lower computational cost than the current methods. In addition, for HEO spacecraft, the position error of the proposed integrated navigation method is lower than that of the stellar angle navigation method. [ABSTRACT FROM AUTHOR]

Pulse phase is the basic measurements of X-ray pulsar-based navigation, and thus how to estimate a pulse phase for an orbiting spacecraft is important. The current methods for on-orbit pulse phase estimation could provide an accurate estimation performance enhancing with the photon amount, but its central processing unit (CPU) time cost also increases sharply with the increase of photon amount. In this paper, an on-orbit pulse phase estimation method based on the cross-entropy adaptive moment estimation (CE-Adam) algorithm is proposed to reduce the CPU time cost while retaining decent estimation accuracy. This method combines the CE and Adam algorithms, and is able to obtain a global optimum with low CPU time cost. The performance of the proposed algorithm is verified by simulation data and real data from the Neutron Star Internal Composition Detector (NICER). The results show that the proposed algorithm could greatly reduce the CPU time cost, which is about 1.5% of the CE algorithm, and retain similar estimation accuracy of pulse phase with CE algorithm. [ABSTRACT FROM AUTHOR]

In X-ray pulsar-based navigation (XPNAV), the appearance of Doppler effects caused by the dynamic motion of the spacecraft would severely degrade the navigation accuracy. In this paper, we develop a new XPNAV method based on a two-stage estimation method of Doppler frequency and phase delay to overcome the Doppler effects. Based on the pre-established phase model of the pulsar at the SSB and the predicted states of the spacecraft, the real-time phase model at the spacecraft is modeled with respect to the initial position and velocity errors of the spacecraft. It turns out that within an observation interval, a constant Doppler frequency can be estimated to overcome the effect of the initial velocity error, and then the phase delay caused by the initial position error can be estimated by using the computationally efficient methods based on epoch folding. Under this frame, the H-test for uniformity, which needs no prior knowledge of the light curve, is used to estimate the Doppler frequency and the fast maximum likelihood method is used to estimate the phase delay. The dynamic model and measurement model of the proposed navigation method are also given. Photon-level simulation results obtained by using the ground-based semi-physical simulation system for X-ray pulsar signals show a significant improvement over the traditional XPNAV method. [ABSTRACT FROM AUTHOR]

Recently, X-ray pulsar-based navigation (XPNAV) as a significant navigation method has been widely used in deep space exploration. However, the accuracy of XPNAV is limited to the existence of the pulsar direction error. To improve the performance of XPNAV, we have proposed a novel algorithm named "the modified augmented state extended Kalman filter" (MASEKF). The algorithm considers the high-order terms of direction error and then adds a more precise direction error into state equation and measurement equation. In the simulation, by comparing the performance of MASEKF, EKF, and ASEKF at the same time, it is found that MASEKF has better performance in the accuracy and stability, and the results also demonstrate that MASEKF algorithm has faster convergence speed. This paper provides a strong reference for other improvements of algorithms towards direction error. The purpose of this study is to establish MASEKF and add the direction error into the measurement equation and the state equation, so as to realize the coordination and symmetry of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we provided a Gaussian fitting method for fast periodic search to improve the accuracy of chi-square method. And this method can be used for the pulse periodic search of X-ray Pulsar. Firstly, we built the fast search model based on the epoch folding procedure by employing the basic principle of the chi-square evaluation. Secondly, we simulated the distribution of chi-square value by applying the pulsar profile to the fast search model, and it is fitting well with the Gaussian function. Finally, the designed experiments indicated that applying Gaussian fitting to chi - square method can significantly improve period search accuracy. [ABSTRACT FROM AUTHOR]

Celestial navigation system (CNS) and inertial navigation system (INS) are traditional autonomous integrated navigation methods. CNS is generally used to correct the cumulative error of the gyroscope in INS. The cumulative error of the accelerometer in INS cannot be corrected. As a new type of autonomous navigation method, the X-ray pulsar navigation system (XNAV) can correct the cumulative error of the accelerometer. This study proposes an integrated navigation method based on a combination of single x-ray pulsar navigation (SXPN), INS, and CNS. The method constructs a virtual accelerometer (VA) by coordinate system transformation, then compensates the error of the virtual accelerometer by using single X-ray pulsar navigation method, and then estimates the position, velocity, and angle errors by Kalman filtering method. The proposed method is an improvement of the SXPN navigation method of Q. Xu et al. in 2018. These improvements are twofold, that is, the positioning has high accuracy and is stable. A method was proposed to correct the error of the accelerometer and then analysis and simulation to support our guess is provided. This navigation method not only can correct the zero-order error of the accelerometer but also the first-order error that few scholars have studied. Simulations show that the proposed method reduces the total position error in three directions. In comparison with the method of adding the pulsar arrival time directly to the observation equation, our proposed method not only has higher precision, but it can also alleviate the jitter of the velocity position and attitude curve. [ABSTRACT FROM AUTHOR]

The accuracy of X-ray pulsar-based navigation is greatly affected by the Doppler effect caused by the spacecraft orbital motion and the systematic biases introduced by the pulsar directional error, spacecraft-borne clock error, etc. In this paper, an innovative navigation method simultaneously employing the pulse phase (PP), the difference of two neighbor PPs (DPP) and the Doppler frequency (DF) of X-ray pulsars as measurements is proposed to solve this problem. With the aid of the spacecraft orbital dynamics, a single pair of PP and DF relative to the spacecraft's state estimation error can be estimated by using the joint probability density function of the arrival photon timestamps as the likelihood function. The systematic biases involved to the PP is proved to be nearly invariant over two adjacent navigation periods and the major part of it is eliminated in the DPP; therefore, the DPP is also exploited as additional navigation measurement to weaken the impact of systematic biases on navigation accuracy. Results of photon-level simulations show that the navigation accuracy of the proposed method is remarkably better than that of the method only using PP, the method using both PP and DF and the method using both PP and DPP for Earth orbit. [ABSTRACT FROM AUTHOR]