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The Solar System Boundary Exploration (SSBE) mission is the focal point for future far-reaching space exploration. Due to the SSBE having many scientific difficulties that need to be studied, such as a super long space exploratory distance, a super long flight time in orbit, and a significant communication data delay between the ground and the probe, the probe must have sufficient intelligence to realize intelligent autonomous navigation. Traditional navigation schemes have been unable to provide high-accuracy autonomous intelligent navigation for the probe independent of the ground. Therefore, high-accuracy intelligent astronomical integrated navigation would provide new methods and technologies for the navigation of the SSBE probe. The probe of the SSBE is disturbed by multiple sources of solar light pressure and a complex, unknown environment during its long cruise operation while in orbit. In order to ensure the high-accuracy position state and velocity state error estimation for the probe in the cruise phase, an autonomous intelligent integrated navigation scheme based on the X-ray pulsar/solar and target planetary Doppler velocity measurements is proposed. The reinforcement Q-learning method is introduced, and the reward mechanism is designed for trial-and-error tuning of state and observation noise error covariance parameters. The federated extended Kalman filter (FEKF) based on the Q-learning (QLFEKF) navigation algorithm is proposed to achieve high-accuracy state estimations of the autonomous intelligence navigation system for the SSBE probe cruise phase. The main advantage of the QLFEKF is that Q-learning combined with the conventional federated filtering method could optimize the state parameters in real-time and obtain high position and velocity state estimation (PVSE) accuracy. Compared with the conventional FEKF integrated navigation algorithm, the PVSE navigation accuracy of the federated filter integrated based the Q-learning navigation algorithm is improved by 55.84% and 37.04%, respectively, demonstrating the higher accuracy and greater capability of the raised autonomous intelligent integrated navigation algorithm. The simulation results show that the intelligent integrated navigation algorithm based on QLFEKF has higher navigation accuracy and is able to satisfy the demands of autonomous high accuracy for the SSBE cruise phase. [ABSTRACT FROM AUTHOR]

An algorithm is presented for solving the lost-in-space problem using simultaneous observations of X-ray pulsars. Using a norm-minimization-based approach, the algorithm extends a previous banded-error intersection model to 3-dimensional space. Higher-fidelity X-ray pulsar signal models are considered, including the parallax effect, Shapiro delay, time dilation, and higher-order pulsar frequency models. The feasibility of solving the lost-in-space problem using X-ray pulsar navigation is revisited with the improved models and prior knowledge requirements are discussed. Monte Carlo simulation techniques are used to establish upper bounds on uncertainty and determine the accuracy of the algorithm. Results indicate that it is necessary to account for the parallax effect, time dilation, and higher-order pulsar frequency models in order to successfully determine the position of the spacecraft in a lost-in-space scenario. In a heliocentric case study, the algorithm uniquely identified a candidate spacecraft position within a spheroid search domain up to 10 × 10 × 0.01 AU 3 in size by simultaneously observing eight to nine pulsars. The maximum search domain size can be increased by observing additional pulsars, which may allow the lost-in-space problem to be solved anywhere within the Solar System. The median position error of the algorithm is on the order of 15 km. Results further indicate that choosing lower-frequency pulsars increases the maximum search domain size at the expense of increased position error. [ABSTRACT FROM AUTHOR]

• A Fourier-series based frequency estimation method of X-ray pulsars is proposed. • The truncation point in the Fourier series is derived theoretically. • The algorithm shows strong robustness and reliability. • The effectiveness of this method is verified by real data from NICER mission. The spin frequency estimation algorithm is the foundation to recover the profile from the observation data of X-ray pulsar. In this work, a frequency-domain method based on the Fourier series is proposed to estimate the spin frequency and recover the profile of X-ray pulsar. The quality of evaluation indexes of recovered profile and the truncation point in the Fourier series are derived. The performance of the algorithm is first analyzed by simulation. The results show that the algorithm is little affected by the noise within the recovered profile and is reliable to estimate the spin frequency. Finally, the proposed algorithm is further verified by the real pulsar data from the Neutron star Interior Composition Explorer (NICER). [ABSTRACT FROM AUTHOR]

The traditional pulsar period estimation method using a single distorted profile averts multiple epoch folding processes, but still has space for accuracy to improve. To give consideration to both accuracy and computational load, we combine the fast butterfly epoch folding (FBEF) with the single distorted profile (SDP)-based pulsar period estimation, and propose the FBEF-based pulsar period estimation with a few distorted profiles (FBEF-FDP), which merely uses a few epoch folding processes to enhance accuracy sharply. Firstly, the fast butterfly epoch folding is used to produce a few distorted pulsar profiles with different periods. And then the single distorted profile-based pulsar period estimation explores each distorted prolife to provide a corresponding distortion degree. Finally, using these distortion degree values, the nonlinear search method for multiple minimums can get an optimal distortion degree estimation. Besides, we prove that distortion degree estimation errors of different accumulative distorted profiles from the same pulsar photon sequence are incompletely correlated. This is the theorical basis that the distortion degree estimation values from the same pulsar photon sequence can be fitted to obtain more highly accurate distortion degree estimation. The computational complexity demonstrates that the computational load increases with the number of groups. Thus, to ensure the real-time of the FBEF-FDP, the number of groups should not be too large. Simulation results demonstrate that the accuracy of the fast butterfly epoch folding-based pulsar period estimation using a few distorted profiles enhances at the cost of a small computational load.

Pulsars, especially X-ray pulsars detectable for small-size detectors, are highly accurate natural clocks suggesting potential applications such as interplanetary navigation control. Due to various complex cosmic background noise, the original pulsar signals, namely photon sequences, observed by detectors have low signal-to-noise ratios (SNRs) that obstruct the practical uses. This paper presents the pulsar denoising strategy developed based on the variational mode decomposition (VMD) approach. It is actually the initial work of our interplanetary navigation control research. The original pulsar signals are decomposed into intrinsic mode functions (IMFs) via VMD, by which the Gaussian noise contaminating the pulsar signals can be attenuated because of the filtering effect during signal decomposition and reconstruction. Comparison experiments based on both simulation and HEASARC-archived X-ray pulsar signals are carried out to validate the effectiveness of the proposed pulsar denoising strategy.

Existing methods for simulating pulsar signals at a spacecraft are inapplicable for large flux or high frequency because of their low efficiency, hindering research on X-ray pulsar-based navigation. To solve the problem, we propose a fast method based on the relation derivation between the photon arrival time and corresponding photon phase at the spacecraft. The absolute differences of searched frequencies between simulated data and observational data for the Crab pulsar are less than10−4, which sufficiently validates the method. Furthermore, the proposed method is up to 3 orders of magnitude faster than other methods, which shows that it is more efficient and better satisfies the needs of real-time navigation verification. • A fast simulation method of X-ray pulsar signals at a spacecraft is proposed. • The proposed method is appropriate for simulating the signals of any pulsar. • The simulated data agrees with the observational data. • The proposed method is up to 3 orders of magnitude faster than other methods. [ABSTRACT FROM AUTHOR]

The traditional pulsar period estimation methods have high computational loads as a result of the tentative epoch folding. The tentative epoch folding means that the massive pulsar signals are folded multiple times with different periods. However, due to the low computing power of on-board computer, the tentative epoch folding with high computational load must be avoided. To achieve this objective, we propose a fast compressive sensing-based pulsar period estimation method, which directly estimates the pulsar period according to the distortion degree of the accumulated profile. The compressive sensing (CS) includes three aspects: the dictionary, the measurement matrix and the sparse recovery algorithm. In the proposed method, the pulsar profiles with different distortion degrees comprise the distorted profile dictionary; the low-frequency Fourier transform matrix is developed as the measurement matrix; the super-resolution sparse recovery using the maximal elements is proposed to estimate the pulsar period. Besides, the pulsar period estimation performance against the Cramér-Rao lower bound (CRLB) is studied. And the computational complexity analysis is also provided. The simulation results demonstrate that the fast CS-based pulsar period estimation method approaches the CRLB and its computational time is only 37 ms. • The proposed pulsar period estimation does not require tentative epoch folding. • The proposed method directly estimates the period according to the distortion degree. • The compressive sensing is used to optimize the pulsar period estimation. • The period estimation performance against the Cramér-Rao lower bound is studied. • The proposed method has high accuracy and low computational load. [ABSTRACT FROM AUTHOR]

The process of a resonant production of an ultrarelativistic electron–positron pair in the process of gamma-quantum scattering in the X-ray field of a pulsar is theoretically studied. This process has two reaction channels. Under resonant conditions, an intermediate electron (for a channel A) or a positron (for a channel B) enters the mass shell. As a result, the initial second-order process of the fine-structure constant in the X-ray field effectively splits into two first-order processes: the X-ray field-stimulated Breit–Wheeler process and the the X-ray field-stimulated Compton effect on an intermediate electron or a positron. The resonant kinematics of the process is studied in detail. It is shown that for the initial gamma quantum there is a threshold energy, which for the X-ray photon energy (1–102) keV has the order of magnitude (103–10) MeV. In this case, all the final particles (electron, positron, and final gamma quantum) fly in a narrow cone along the direction of the initial gamma quantum momentum. It is important to note that the energies of the electron–positron pair and the final gamma quantum depend significantly on their outgoing angles. The obtained resonant probability significantly exceeds the non-resonant one. The obtained results can be used to explain the spectrum of positrons near pulsars.

The resonant photoproduction of the electron-positron pairs on a nucleus near a surface of the X-ray pulsar was studied theoretically. The main feature of the processes, which are responsible for the formation of the electron-positron fluxes, is a capability to occur in a resonant way in the electromagnetic field of the X-ray pulsar. One of the properties of the resonant case is that the initial process of second order in the fine structure constant in an external field effectively reduces into two successive processes of the first order due to the fact that in the resonant conditions intermediate virtual electron (positron) becomes a real particle. It is shown that the resonances are possible only when the initial gamma quantum energy is more than the threshold energy, which significantly depends on the number of absorbed photons of an external electromagnetic field. Additionally, in the resonant conditions, the energies of the particles depend on the outgoing angle of a positron (channel A) or an electron (channel B). It is shown that the resonant differential cross section has an extremely large magnitude in units αZ2re2. A mechanism to explain the presence of anomalous fluxes of ultrarelativistic positrons near the surface of an X-ray pulsar was proposed.

Abstract Autonomous navigation of the Mars probe is a key step for the survivability of the space mission and the success of the scientific experiments. However, Mars probe positioning has large uncertainty due to imprecise techniques and limited observations. In this paper, several key factors of X-ray Pulsar, Optical Celestial, and Gravity-aided navigational system are investigated by the simulation in term of Nonlinear Kalman Filters. The navigational performances are evaluated to investigate the autonomy, accuracy, and stability of the systems. The numbers and the kinds of X-ray Pulsars detected by the antenna system have significant influence on the accuracy and stability of the X-ray Pulsars Navigation (XNAV) system. The XNAV achieves several hundreds of meters orbit accuracy by scanning PSR B1937 + 21, B1821–24 and B0531 + 21 in Earth-Mars cruise orbit. The improvement of pointing-accuracy of the celestial sensor has less effect on increasing accuracy of the Optical Celestial Navigation (OCN) system. The OCN has relatively lower navigation accuracy with a few hundred kilometers but higher stability. For surface rover positioning, we introduce the Gravity-aided Odometry (GAO) and design two algorithms to verify its navigation ability. The accuracy of GAO approximately equals to the performance of the ground-based Radio Tracking (RT). The potential scientific perspectives of above methods are discussed, which could improve the astrophysical and planetary geodetic study. Highlights • X-ray Pulsars Navigation (XNAV) achieves 350 m accuracy by appropriate combinations with current detectors. • More precise cameras cannot improve the navigation accuracy of OCN significantly. • Gravity-aided Odometry (GAO) navigation approximately equals to the performance of Radio Tracking (RT). [ABSTRACT FROM AUTHOR]

Currently, very long baseline interferometry technology is widely used in the astronomical measurement areas, providing about 1 μ as pulsar positioning accuracy. However, these conventional methods cannot meet the higher position accuracy requirements of X-ray pulsar navigation. In this paper, we provide a novel method to measure the angular position based on X-ray intensity correlation. First, we show the relationship between the pulsar angular position and the X-ray intensity correlation. Second, we simulate the measurement error within the constraint on the photon energy fluctuations and compensation time. Finally, we propose a way to achieve such measurement. These theoretical analyses will improve the measurement accuracy of the pulsar angular position to a large extent. [ABSTRACT FROM AUTHOR]

Spacecraft navigation in space requires high real-time. Towards this end, when using pulsar navigation, it is necessary to reduce the pulse profile construction time. In this paper, the method of constructing a pulse profile based on compressed sensing (CS) is improved from two aspects: Double Redundant Dictionary (DRD) search method and Same-Scale L1-Norm (SSLN) cost function. The method of calculating the optimal dimension of the DRD is given. A random observation matrix is designed. We provide both analytical and experimental evidence that supports our method. The proposed method is compared with the traditional methods of Amplitude Search (AS) and Hadamard Observation Matrix (HOM) in terms of computational complexity. Simulation using NASA data is consistent with the quantitative analysis. It is illustrated that DRD and SSLN can serve as an effective method with the resulting running time considerably less than that in AS or HOM. The proposed method gets a considerable reduction in pulse profile construction time. [ABSTRACT FROM AUTHOR]

The positioning accuracy of the X-ray pulsar navigation depends on the angular position accuracy of the pulsars. Currently, long baseline interferometer technology provides 0.1 mas pulsar positioning accuracy, which is far away from the requirement of X-ray pulsar navigation. Using classical statistical optics, we studied the relationship between direct observation of the pulsar angular position and second-order correlation. As an application, we give a proposal to realize angular position measurement of pulsars based on X-ray intensity correlation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To achieve a precise Mars landing, the autonomous navigation performance of Mars final approach phase need to be further improved. In this paper, an absolute navigation scheme for Mars finial approach phase using relative measurements of X-ray pulsars and Mars orbiter is proposed. By introducing the difference of time of arrival (DTOA) measurement, the states of approach spacecraft and orbiter are estimated at the same time. Compared to the navigation scheme based on the absolute measurements of pulsars, the error sources such as planetary ephemeris error, pulsar parameter uncertainties, and radio beacon position deviations, are correspondingly reduced or eliminated. Through observability analysis, the method of absolute navigation using relative information is proved observable under the condition of reasonable pulsars selection. The design optimization of beacon configuration based on the Fisher Information Matrix (FIM) is also carried out for achieving a better observability. Two navigation schemes respectively based on the absolute/relative measurements of X-ray pulsars are compared by numerical simulations, and the navigation performance is assessed and the feasibility of the proposed scheme is verified. [ABSTRACT FROM AUTHOR]

In order to solve the impact of the impulse noise in the universe on the long time epoch folding of X-ray pulsar profile, an innovative denoising method using the wavelet packet transformation is proposed. First, the system model containing noisy signal for X-ray pulsar is established. The time series of X-ray pulsar are sampled as certain time interval and folded as its rotational period. Secondly, the signal transformed by wavelet packet is computed according to the given entropy, aiming to obtain the optimum basis. Finally, the impulse noise is filtered with the proper threshold. The experimental results show that the impulse noise can be filtered by the proposed method, and the algorithm improves the signal-to-noise ratio (SNR) by about 40% compared with other methods under low SNR conditions. [ABSTRACT FROM AUTHOR]

In order to achieve high accuracy of autonomous navigation for Mars probes, an integrated navigation method using X-ray pulsar measurement and optical data of viewing Martian moons is proposed. For single X-ray pulsar measurement on board a Mars probe, navigation accuracy is low due to its poor observability. On the other hand, Phobos and Deimos, two natural moons of Mars, are important optical navigation information sources available for Mars missions. However, the Martian moons ephemeris bias and the differences between barycentre and centre of brightness of Martian moons will result in low navigation accuracy. The method of integrated navigation using X-ray pulsar measurement and optical data of viewing Martian moons can overcome the defect and achieve accurate navigation. Two sequential orbit determination algorithms, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), are compared. The simulation results show this method can obtain high autonomous navigation accuracy during the phase of a probe orbiting Mars. [ABSTRACT FROM PUBLISHER]

Autonomous navigation for Mars probe spacecraft is required to reduce the operation costs and enhance the navigation performance in the future. X-ray pulsar-based navigation (XPNAV) is a potential candidate to meet this requirement. This paper addresses the use of the Mars’ natural satellites to improve XPNAV for Mars probe spacecraft. Two observation variables of the field angle and natural satellites’ direction vectors of Mars are added into the XPNAV positioning system. The measurement model of field angle and direction vectors is formulated by processing satellite image of Mars obtained from optical camera. This measurement model is integrated into the spacecraft orbit dynamics to build the filter model. In order to estimate position and velocity error of the spacecraft and reduce the impact of the system noise on navigation precision, an adaptive divided difference filter (ADDF) is applied. Numerical simulation results demonstrate that the performance of ADDF is better than Unscented Kalman Filter (UKF) DDF and EKF. In view of the invisibility of Mars’ natural satellites in some cases, a visibility condition analysis is given and the augmented XPNAV in a different visibility condition is numerically simulated. The simulation results show that the navigation precision is evidently improved by using the augmented XPNAV based on the field angle and natural satellites’ direction vectors of Mars in a comparison with the conventional XPNAV. [ABSTRACT FROM AUTHOR]

This paper develops an integrated navigation method based on the X-ray pulsar navigation (XNAV) system and an autonomous optical navigation system for spacecrafts. The X-ray pulsar navigation is implemented by using the difference between the measured and predicated pulse arrival time, which is calculated by comparing an observed pulse profile with a standard pulse profile. A problem arises from the X-ray signal processing in that the spacecraft’s orbit information, which may be unknown, is required to construct the observed pulse profile. The effect of the spacecraft orbit error on the accuracy of the pulse TOA (time of arrival) difference determination is analyzed. It is specified that the performance of the XNAV system may be degraded in the presence of large orbit error. In order to improve the navigation accuracy, an integrated navigation scheme is presented by fusing the measurement information of a X-ray detector and an ultraviolet optical sensor. The XNAV/optical integrated navigation system is effective to mitigate the effect of the spacecraft orbit error. The superiority of the presented scheme is illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

X-ray pulse profile is an important physical quantity for X-ray pulsar based navigation (XPNAV). In order to improve the Signal-to-Noise-Ratio (SNR) of pulse profile and reduce computation complexity, this paper proposed an efficient pulse profile construction method based on Compressed Sensing (CS). This method first builds models for standard and integrated pulse profiles. Then, a sensing matrix based on Hadamard matrix is proposed for enhancing the percentage of successful construction. Finally, based on the sparse coefficient vector calculated by the proposed CS method, a pulse profile with high SNR will be obtained. The proposed method is validated using the real data of Crab pulsar observed by Rossi X-ray Timing Explorer (RXTE). Compared with the random 0–1 matrix and random Gaussian matrix, the pulse profile can be completely constructed by using the proposed matrix when the sampling ratio is 0.6, and compared with Epoch Folding method, the proposed CS method can improve the SNR of the pulse profile at least 15.859 dB when the observation time is 1 s and at least 20.33 dB when the observation time is 700 s. The results demonstrate the high performance of the proposed method in constructing pulse profile of high SNR with short-time observation data, which can significantly facilitate the real-time and high precision time-of-arrival (TOA) estimation and the position and velocity measurement in XPNAV. [ABSTRACT FROM AUTHOR]

The starlight Doppler navigation must be integrated with other navigation methods to operate normally since it is not completely observable. The star selection for the Doppler navigation system influences the whole integrated navigation performance greatly. The star magnitude-based star selection method is commonly used to select the star for the Doppler navigation. However, it can be found that the direction of star is more important than the measurement accuracy. To select the optimal navigation star, the star selection strategy for the starlight Doppler-based integrated navigation system, where both the direction and magnitude of star are considered, is proposed in this paper. Considering the impact of the star direction and measurement noise, the measurement coupling matrix is constructed to give the relationship between the star direction and the integrated navigation accuracy, and utilize this matrix as the star selection criterion. According to the perturbation matrix theory, the measurement coupling matrix is analyzed to obtain the theoretical maximum and minimum of its trace by formula derivation. Finally, the proposed star selection criterion is utilized to select the optimal navigation star from the first-magnitude stars. In this paper, the XNAV (X-ray pulsar navigation)/starlight Doppler integrated navigation system is taken as an instance to analyze and simulate. The simulation results demonstrate that using the star selected by our method as the navigation star, the XNAV/starlight Doppler integrated navigation has good performance. Compared with the X-ray sensor area and the spectrometer measurement accuracy, the direction of star is more important for the improvement of the integrated navigation performance. [ABSTRACT FROM AUTHOR]

During maneuvering flight, a spacecraft is subject to the engine thrust besides the gravitational force fields of celestial bodies. Moreover, the engine thrust model can hardly be built accurately due to its imbalance. Accordingly, the traditional orbit dynamic mode cannot predict the state accurately, which results in a great decline of navigation filter performance. In order to solve this problem, a state prediction model based on starlight Doppler is proposed for orbital maneuver. In this model, the velocity of the spacecraft is obtained from the starlight Doppler measurement instead of the orbit dynamic model. According to the measured velocities and the constant acceleration model, the state in the navigation filter can be predicted precisely. By this means, the state prediction is not influenced by engine thrust. The proposed state prediction model is applied in the XNAV (X-ray pulsar navigation) system for orbital maneuver. In this navigation system, the starlight Doppler velocity and the pulse time-of-arrival from the X-ray pulsar are utilized to predict and update the state, respectively. The simulation results demonstrate that the state provided by the starlight Doppler-based state prediction model is immune to the engine thrust. The starlight Doppler prediction-based XNAV can provide highly-accurate navigation information for spacecraft orbital maneuvers. [ABSTRACT FROM AUTHOR]