X-ray Pulsar-based Navigation System Research Articles

Characterization of Candidate Solutions for X-Ray Pulsar Navigation

X-ray pulsar based navigation (XNAV) can be used to estimate spacecraft state information based on observation of distant pulsars. XNAV system concepts typically require an initial position estimate since there are many candidate positions which may produce the same measurement. If position ambiguity can be resolved, XNAV may enable full state estimation without prior information. This study seeks to efficiently find candidate spacecraft positions and determine how to select pulsars to minimize the number of candidate solutions within a given domain. A numeric scheme for determining candidate positions is developed for an arbitrary number of observed pulsars. Pulsar selection criteria are developed in terms of relative direction, period, and phase accuracy. Results indicate that it is more time efficient to observe additional pulsars rather than improve the accuracy of pulsar measurements. A smaller angular separation and increased period of the observed pulsars reduces the number of candidate solutions within a given domain. Phase measurement accuracy should be improved simultaneously for all pulsars rather than prioritizing a single pulsar. These selection criteria are verified by evaluating the number of candidate solutions for permutations of 34 real pulsars.

Decentralized X-ray pulsar-based navigation system for space-borne gravitational wave detector

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 ̃528m and ̃520m, respectively. Compared with the classical method, both analytical and simulating analyses demonstrate that the proposed algorithm efficiently reduces the computational costs to 1/N2 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.

Improving Pulse Phase Estimation Accuracy with Sampling and Weighted Averaging

The accuracy in an X-ray pulsar-based navigation system depends mainly on the accuracy of the pulse phase estimation. In this paper, a novel method is proposed which combines an epoch folding process and a cross-correlation method with the idea of “averaging multiple measurements”. In this method, pulse phase is estimated multiple times on the sampled subsets of arriving photons' time tags, and a final estimation is obtained as the weighted average of these estimations. Two explanations as to how the proposed method can improve accuracy are provided: a Signal to Noise Ratio (SNR)-based explanation and an “error-difference trade-off” explanation. Numerical simulations show that the accuracy in pulse phase estimation can be improved with the proposed algorithm.

An initial orbit determination method from relative position increment measurements

Both Global Navigation Satellite Systems and X-ray pulsar-based navigation system use relative position information to provide accurate spacecraft navigation. To supplement that navigation information, an absolute reference position from other types of measurements should be provided; however, that may increase the complexity or decrease the autonomy of the navigation system. To overcome those drawbacks, this paper proposes an initial orbit determination method using only relative position increment measurements and their corresponding epoch. The proposed method can be summarised as three steps: first, determining the orbital plane from a set of relative position vectors; next, determining the shape of the orbit by solving an ellipse fitting problem in two dimensions; finally, estimating the absolute position and all six orbital elements according to Kepler's equation and geometric relations. Monte Carlo simulations were done to analyse the feasibility and features of the proposed method. The results show that the algorithm we used does not need an initial guess and is robust. It can obtain an acceptable result from a 20% portion of an orbit when the signal-to-noise ratio is set at 15 dB with determining the inclination and right ascension of the ascending node quickly and accurately.

Modified unscented Kalman filter for X-ray pulsar-based navigation system in the presence of measurement outliers

In order to eliminate the influence of outlier in measurement to X-ray pulsar based navigation system, a modified unscented Kalman filter-based filtering algorithm is proposed. First, the outlier detection function is established based on the statistical information of measurement residuals to detect whether the fault occurs in the measurements. Then, the filter gain in regular unscented Kalman filter algorithm is modified so that the dramatic changes of measurement residual are avoided. The modified unscented Kalman filter filtering algorithm is tested on the existing high earth orbit to verify the validity in the presence of the measurement with outliers. Simulation results show that the proposed modified unscented Kalman filter can effectively reduce the impact of the outliers on X-ray pulsar-based navigation system and has higher accuracy than the unscented Kalman filter method.

Autonomous navigation for lunar satellite using X‐ray pulsars with measurement faults

X-ray pulsar-based navigation (XNAV) is a navigation method using celestial X-ray source observations for spacecraft orbit determination. However, if the measurements are not reliable due to any kind of malfunction, the performance of XNAV may result in considerable errors and even divergence. In this study, a new algorithm called robust extended Kalman filter (REKF) is proposed for the lunar satellite autonomous navigation system, which is robust against measurement malfunctions. First, the satellite dynamic model applied perturbations is derived under the J2 perturbation of the Moon. The pulse time-of-arrival (TOA) is used to build the observation model. Second, the performance of XNAV system is discussed by analysing the transformation error of TOA, system observability and controllability. Then, an adaptive measurement noise scale factor (AMNSF) is designed by using the innovation sequence in REKF. Meanwhile, the gain matrix is modified by adding the AMNSF to reduce the influence of malfunction and enhance the robustness of XNAV system. Finally, the simulation results show the proposed navigation scheme is valid and feasible, and it is appropriate for lunar satellite autonomous navigation.

A sparse representation-based optimization algorithm for measuring the time delay of pulsar integrated pulse profile

The time delay of the pulsar integrated pulse profile relative to standard pulse profile is one of the important observations in X-ray pulsar-based navigation system, which accuracy directly affects the accuracy of the pulsar-based navigation system. In order to improve the measuring accuracy of the time delay of the pulsar integrated pulse profile and reduce computation complexity, a novel optimization algorithm based on sparse representation is proposed in this paper. This method firstly constructs a waveform-matched dictionary in accordance with standard pulse profile. On the basis of the dictionary, first order sparse coefficient vector that contains the phase information of time delay is used to represent measurement pulse profile. Then, the time delay for integrated pulse profile is calculated with the sparse coefficient by the matching pursuit algorithm. The proposed algorithm is validated with the real data observed by Rossi X-ray Timing Explorer. Comparing with the state-of-the-art fast Fourier transform algorithm, experiments show that the proposed algorithm can significantly reduce the impact of signal-to-noise ratio of the observed pulse profile on the measuring accuracy of the time delay. Even in a short observation time, the proposed algorithm can still maintain the high measuring accuracy. In addition, the measuring accuracy of the proposed algorithm can be further improved when the redundant dictionary is constructed with more sampling phase bins of the standard pulse profile.

X-ray pulsar-based navigation system/Sun measurement integrated navigation method for deep space explorer

In order to enhance the autonomy and survivability of deep space explorers, an X-ray pulsar-based navigation system (XNAV)/Sun measurement integrated navigation system is proposed. In this method, the directional measurement of the line-of-sight of Sun, the Doppler radical velocity measurement, and the measurement from an X-ray pulsar are fused for navigation. A square-root unscented kinematic and static filter (SUKSF) is derived to optimally fuse the three types of measurements. SUKSF utilizes the unscented formation to reduce the impact of linearization error, and uses the square-root technique to enhance the computational stability. Compared with the federated filter, SUKSF can provide a globally optimal estimation result with less computation cost. Some simulations are performed to verify the proposed integrated navigation system, and the results have illustrated that the proposed method outperforms the navigation method employing only Sun measurement as well as XNAV.

X-ray pulsar-based navigation using time-differenced measurement

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.

X-ray pulsar-based navigation system with the errors in the planetary ephemerides for Earth-orbiting satellite

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.

Augmentation of XNAV System to an Ultraviolet Sensor-Based Satellite Navigation System

X-ray pulsar-based navigation (XNAV) using one X-ray detector is investigated as an augmentation to the capability of an ultraviolet (UV) sensor-based satellite autonomous navigation system. The satellite state dynamics are analyzed to establish the dynamical equations of the satellite autonomous navigation system. A time transformation equation that accounts for relativistic effects is presented and the measurement model of the XNAV system is derived using pulse phase information from only one pulsar. The measurement model of the UV sensor-based satellite navigation system is presented using the Earth image information from the UV sensor. In order to integrate the measurements from the X-ray sensor and the UV sensor, a federated filter is developed to provide the optimal simultaneous estimation of position and velocity of the satellite. The concept is demonstrated on a GPS orbit and a geosynchronous orbit and it is found that the performance of the integrated satellite navigation system is improved with respect to that of the UV sensor-based satellite navigation system.