Enhanced X-ray pulsar navigation based on ranging information of a satellite

We use radio millisecond pulsars (MSPs) to determine the position of the Parkes telescope to explore the feasibility of pulsar navigation for terrestrial application, as well to investigate the relations between pulsar observations and the positional errors for potential X-ray pulsar navigation (XNAV). Different from the analytical algorithm (Han et al. Astrophys. Space Sci. 364, 3, 2018) which derives the relations between observatory coordinates and pulsar timing residuals, a grid search method is used in our work. The method divides the space adjacent to the radio telescope into small grids, from which we form the rms timing residuals and fit pulsar parameters to find the position with minimal χ2 value. Six pulsars from the Parkes Pulsar Timing Array (PPTA) are selected to perform position determinations. The positional errors are analyzed together with the pulsar reference phase, timing residuals, and observation numbers. Using a hybrid database of pulsar timing and cartographic data, we obtained best positional accuracy of around 10 m by PSR J0437 − 4715. To investigate the feasibility of pulsar terrestrial navigation, only few observations from PSR J0437 − 4715 are used for position determinations. The results show that the precision of about 100 m is achievable with only 3 or 4 observations. In this paper, we introduce our method in detail and discuss the positioning performance in different scenarios.

The increasing number of private and public actors interested in space-based missions has driven need for greater flexibility and reliability in regards to navigation. Autonomous navigation in space will reduce reliance on ground-based systems and high operational costs due to crowded communication networks. Further, there is a clear need for autonomous navigation solutions in GPS-denied environments, as well as deep-space regions in which traditional GPS methods are infeasible. One promising approach for achieving autonomous navigation in the dynamic landscape of space is X-ray pulsar-based navigation (XNAV). XNAV capitalizes on the periodicity of pulsar-emitted X-rays for positioning, navigation, as well as determining and responding to timing error (PNT). In this paper, a novel, flexible pulsar simulation framework for the testing, and validation of XNAV systems is presented. Pulsar-Leveraged Autonomous Navigation Testbed System (PLANTS) is a low-cost software-hardware hybrid testbed for XNAV PNT solutions. PLANTS simulates high-fidelity pulsar X-ray events along desired flight trajectories over a user-defined mission timeline, which can be used to optimize XNAV hardware and mission planning components (such as spacecraft attitude and X-ray detector orientation planning, based on output pulsar viewing schedules and angles over time). Ultimately, this testbed provides a flexible platform for a wide array of future XNAV research and development efforts aimed at the goal of mission-readiness and sustained space operations. The goal of the PLANTS framework is to develop a system for XNAV project teams which is cost-efficient, algorithm-agnostic (i.e. supports interoperability with current and emerging software toolkits), and incorporates hardware-in-the-loop (HWIL). This paper describes the first iteration of PLANTS, which leverages software-defined radios (SDRs), coupled with a number of software utilities including the Python-based PINT pulsar timing software package. Initial results exhibit successful outputs of pulsar data extraction, transformation, and loading (ETL), flight plans, timing models, and light curves portraying photon arrival events. The future of XNAV will require the development of effective, intelligent navigation algorithms and accessible testing facilities with HWIL. The PLANTS framework meets these needs and empowers advancement of the state-of-the-art in autonomous space navigation.

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 $\text{H}\infty $ 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.

Effect of X-ray energy band on the X-ray pulsar based navigation

The further development of X-ray pulsar-based NAVigation (XNAV) is hindered by its lack of accuracy, so accuracy improvement has become a critical issue for XNAV. In this paper, an XNAV augmentation method which utilizes both pulsar observation and X-ray ranging observation for navigation filtering is proposed to deal with this issue. As a newly emerged concept, X-ray communication (XCOM) shows great potential in space exploration. X-ray ranging, derived from XCOM, could achieve high accuracy in range measurement, which could provide accurate information for XNAV. For the proposed method, the measurement models of pulsar observation and range measurement observation are established, and a Kalman filtering algorithm based on the observations and orbit dynamics is proposed to estimate the position and velocity of a spacecraft. A performance comparison of the proposed method with the traditional pulsar observation method is conducted by numerical experiments. Besides, the parameters that influence the performance of the proposed method, such as the pulsar observation time, the SNR of the ranging signal, etc., are analyzed and evaluated by numerical experiments.

Libration point orbit is playing more and more significant role in deep space exploration. X-ray pulsar-based navigation (XNAV) is a novel and promising autonomous navigation method. However, there are only a few research papers concerning how to employ XNAV in libration orbit, especially the application of integrated navigation based on XNAV. The libration orbit is unstable. It is a new research topic for us to delve deeper. To improve the autonomous navigation performance in halo orbit, an integrated navigation method was proposed. The dynamic model of halo orbit was presented. Two-level differential correction method was introduced. The measurement models of the XNAV and the ultraviolet sensor were analyzed. The federated unscented kalman filter based on UD factorization was adopted to estimate the state of the system. The clock error correction was included in the filter. The simulation results show that the proposed integrated navigation is feasible in halo orbit of Earth-Moon system, and can provide better performance in comparison with XNAV or ultraviolet sensor-based navigation. Not only can the integrated navigation obtain a highly accurate spacecraft position, but also it can restrain clock drift.

Star angle/ double-differenced pulse time of arrival integrated navigation method for Jupiter exploration

Augmentation method of XPNAV in Mars orbit based on Phobos and Deimos observations

Pulsar navigation has gradually attracted increased attention because of its unique advantages in the study of high‐attitude missions and deep space exploration. Low navigation accuracy, due to the long integration period, is one of the main problems with X‐ray pulsar navigation. In this study, a new observation strategy for pulsar navigation that could greatly increase observations compared with the traditional synchronous observation model has been proposed. Due to the uncertainty of the measured angles of the pulsar navigation model, a robust Kalman filter was designed based on the new observation model, and mathematical simulation results showed that the proposed method had improved navigation accuracy.

PurposeThe authors proposed a new method of fast time delay measurement for integrated pulsar pulse profiles in X-ray pulsar-based navigation (XNAV). As a basic observation of exact orientation in XNAV, time of arrival (TOA) can be obtained by time delay measurement of integrated pulsar pulse profiles. Therefore, the main purpose of the paper is to establish a method with fast time delay measurement on the condition of limited spacecraft’s computing resources.Design/methodology/approachGiven that the third-order cumulants can suppress the Gaussian noise and reduce calculation to achieve precise and fast positioning in XNAV, the proposed method sets the third-order auto-cumulants of standard pulse profile, the third-order cross-cumulants of the standard and the observed pulse profile as basic variables and uses the cross-correlation function of these two variables to estimate the time delay of integrated pulsar pulse profiles.FindingsThe proposed method is simple, fast and has high accuracy in time delay measurement for integrated pulsar pulse profiles. The result shows that compared to the bispectrum algorithm, the method improves the precision of the time delay measurement and reduced the computation time significantly as well.Practical implicationsTo improve the performance of time delay estimation in XNAV systems, the authors proposed a novel method for XNAV to achieve precise and fast positioning.Originality/valueCompared to the bispectrum algorithm, the proposed method can improve the speed and precision of the TOA’s calculation effectively by using the cross-correlation function of integrated pulsar pulse profile’s third-order cumulants instead of Fourier transform in bispectrum algorithm.

Pulsar navigation using time of arrival (TOA) and time differential TOA (TDTOA)

Research progress of autonomous navigation technology for multi-agricultural scenes

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.

Celestial navigation system (CNS) and X-ray pulsar-based navigation (XNAV) are two kinds of autonomous navigation methods for spacecraft. Because these two methods are complementary, CNS/XNAV integrated navigation is a feasible solution to improve the navigation accuracy and reliability. However, the pulsar's direction has a great impact on the navigation accuracy of CNS/XNAV integrated navigation because of the existence of measurement errors. In this paper, the analytic expression of the estimation errors of CNS/XNAV integrated navigation is deduced, based on which the impact of the pulsar's direction on the estimation errors is analyzed. A modified observability analysis method on the basis of the unscented Kalman filter is presented and applied to give the quantitative index of the pulsar's direction, whose observability matrix is constructed by the equivalent state transition matrix and measurement matrix. The equivalent state transition matrix is obtained through sigma points, and the equivalent measurement matrix is acquired with the help of the cross-covariance matrix and the predicted covariance matrix. Simulations demonstrate that the position and velocity estimation errors of CNS/XNAV integrated navigation increase exponentially with the angle between the pulsar's direction and the target body's direction. Both the error analysis method and the observability analysis method have been verified as suitable and effective for the analysis of the best choice for a pulsar in the CNS/XNAV integrated navigation system.

X-ray pulsar navigation is a promising technology for autonomous spacecraft navigation. The key measurement of pulsar navigation is the time delay (phase delay). There are various methods to estimate phase delay, but most of them have high computational complexities. In this paper, a new method for phase delay estimation is proposed, which is based on the time-shift property of Discrete Fourier Transformation (DFT). With this method, the time complexity can be greatly reduced. Also, a delta-function approximation can be used to further decrease the computational cost. Numerical simulation shows that the proposed method is effective for phase delay estimation, and the reduced complexity makes our method more suitable for on board implementation.