Autonomous Orbit Determination Research Articles

Автономное определение орбиты на борту космического аппарата

Автономное определение орбиты на борту космического аппарата

A new approach of orbit determination for LEO satellites based on optical tracking of GEO satellites

Ability of autonomous orbit determination (OD) for a satellite is receiving increasing interests due to its considerable value in engineering application. A new OD approach for low earth orbit (LEO) satellites based on tracking geosynchronous orbit (GEO) satellites using space-based optical tracking approach is proposed which can improve the autonomy of LEO satellites and reduce their dependence on ground facilities. Based on the information support of Space Surveillance Network (SSN), several GEO satellites are selected as guidance and calibration functions like beacons for LEO satellites equipped with space-based optical (SBO) sensors, as they are called beacon GEO satellites in this paper. LEO satellites can determine their own orbits by tracking these GEO objects without measures of ground facilities, which only need to provide necessary information of beacon objects for them. Unlike traditional space-based observation, long arcs and high-frequency measurements, which are more beneficial to determine orbit precisely, are possibly obtained. This paper focuses on demonstrating the feasibility and performance of proposed approach. To determine orbits, batch least-squares (LS) estimator with Tschauner–Hempel (T–H) equation state-transition matrix to estimate the propagation of initial errors is used. Different scenarios are simulated and results show that tracklet length, measurement frequency, and measurement errors are the main factors that influence the accuracy of OD.

Autonomous orbit and attitude determination for Earth satellites using images of regular-shaped ground objects

Orbit and attitude determination (OAD) is a crucial problem in spacecraft missions. For Earth satellites, especially Earth-observing satellites, images of ground landmarks are feasible to be used for autonomous OAD. Previous studies have demonstrated the possibility of image-based OAD using the light-of-sight (LOS) vector to ground point feature as measurement. However, valid ground point features might not always be available, for example, when the ground landmarks have smooth edges. Besides, when ground landmarks are regular-shaped, this method would discard useful shape information of the objects and affect OAD precision. Aimed at the problem, we present a new OAD scheme using onboard images of regular-shaped ground objects. In the scheme, the LOS vector to the center of the ground objects is used as measurement and is obtained based on the widely-used 3D reconstruction algorithms in machine vision. With the help of an extended Kalman filter (EKF), orbit and attitude parameters can be estimated. The OAD performance of the scheme is assessed using Monte-Carlo simulations. Results demonstrate the feasibility of the scheme and the substantial influence from both lighting constraints and image sampling frequency on the OAD performance. The scheme is also compared with a deterministic scheme, which directly derives position and attitude parameters purely based on the 3D reconstruction algorithm. For the current sensor precision, the proposed scheme is found to have a better performance.

Conservative Term Constrained Kalman Filter for Autonomous Orbit Determination

This paper presents a novel constrained Kalman filter framework for autonomous orbit determination. By using Lagrangian multiplier techniques, the conserved terms of orbit motion are incorporated into the estimation routines to reconstruct the Kalman filter, and then the orthogonal and multipartial-norm-constrained Kalman filters are developed for the satellite in circular orbit and eccentric ones, respectively. Finally, scenarios of both circular and eccentric orbits with unknown measurement bias are simulated by using the proposed constrained Kalman filter; the simulation results show that the estimation accuracy is significantly improved after introducing the conservative terms as constraint.

Precision analysis of autonomous orbit determination using star sensor for Beidou MEO satellite

This paper focuses on the autonomous orbit determination accuracy of Beidou MEO satellite using the onboard observations of the star sensors and infrared horizon sensor. A polynomial fitting method is proposed to calibrate the periodic error in the observation of the infrared horizon sensor, which will greatly influence the accuracy of autonomous orbit determination. Test results show that the periodic error can be eliminated using the polynomial fitting method. The User Range Error (URE) of Beidou MEO satellite is less than 2 km using the observations of the star sensors and infrared horizon sensor for autonomous orbit determination. The error of the Right Ascension of Ascending Node (RAAN) is less than 60 μrad and the observations of star sensors can be used as a spatial basis for Beidou MEO navigation constellation.

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements. This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time. The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure. The ranging error of the ISL measurements is less than 0.25 ns. This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy. The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination. The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 0.5 ns. The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study. Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination. Therefore, the hardware delays are estimated simultaneously with the satellite orbits. To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination. The root-mean-square values of orbit determination residuals are within 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits. The results indicate that the radial overlap differences between the autonomous orbits are less than 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.

The Effectiveness of Solution Technique on the Autonomous Orbit Determination Accuracy of Lagrangian Navigation Constellation

The Effectiveness of Solution Technique on the Autonomous Orbit Determination Accuracy of Lagrangian Navigation Constellation

Orbit determination of the Next-Generation Beidou satellites with Intersatellite link measurements and a priori orbit constraints

Intersatellite Link (ISL) technology helps to realize the auto update of broadcast ephemeris and clock error parameters for Global Navigation Satellite System (GNSS). ISL constitutes an important approach with which to both improve the observation geometry and extend the tracking coverage of China’s Beidou Navigation Satellite System (BDS). However, ISL-only orbit determination might lead to the constellation drift, rotation, and even lead to the divergence in orbit determination. Fortunately, predicted orbits with good precision can be used as a priori information with which to constrain the estimated satellite orbit parameters. Therefore, the precision of satellite autonomous orbit determination can be improved by consideration of a priori orbit information, and vice versa. However, the errors of rotation and translation in a priori orbit will remain in the ultimate result. This paper proposes a constrained precise orbit determination (POD) method for a sub-constellation of the new Beidou satellite constellation with only a few ISLs. The observation model of dual one-way measurements eliminating satellite clock errors is presented, and the orbit determination precision is analyzed with different data processing backgrounds. The conclusions are as follows. (1) With ISLs, the estimated parameters are strongly correlated, especially the positions and velocities of satellites. (2) The performance of determined BDS orbits will be improved by the constraints with more precise priori orbits. The POD precision is better than 45m with a priori orbit constrain of 100m precision (e.g., predicted orbits by telemetry tracking and control system), and is better than 6m with precise priori orbit constraints of 10m precision (e.g., predicted orbits by international GNSS monitoring & Assessment System (iGMAS)). (3) The POD precision is improved by additional ISLs. Constrained by a priori iGMAS orbits, the POD precision with two, three, and four ISLs is better than 6, 3, and 2m, respectively. (4) The in-plane link and out-of-plane link have different contributions to observation configuration and system observability. The POD with weak observation configuration (e.g., one in-plane link and one out-of-plane link) should be tightly constrained with a priori orbits.

Autonomous orbit determination using epoch-differenced gravity gradients and starlight refraction

Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPS-denied environments. Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates. The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency. The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation. An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination. Truth-model simulations are used to test the performance of the algorithm, and the effects of differencing intervals and orbital heights are analyzed. A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) combined with simulated starlight refraction measurements is further conducted, and a three-dimensional position accuracy of better than 100m is achieved.

The research on system error of Inter-Satellite-Link (ISL) measurements for autonomous navigation of Beidou system

In this paper, the system error of inter-satellite-link measurements for autonomous navigation is studied, which is an important parameter for autonomous navigation technology based on inter-satellite-link of Beidou system. The physical meaning of system error of inter-satellite-link measurements and the influence of its error on autonomous navigation are clarified. On this basis, to solve the problem that it is difficult to calibrate the system error of inter-satellite-link measurements precisely on the ground before the satellite launches, a calibration method based on onboard measurement data for this parameter is put forward. Onboard test results show that the mean of the user range error of autonomous orbit determination is less than 6m in 9days using the system error of inter-satellite-link measurements calibrated according to the proposed method. Specially, the user range error is less than 3m when the system error calibrated based on the latest measurement data is used. And in post-process, using the latest system error, the mean of user range error is less than 2.5m and the error of autonomous time synchronization is within ±10ns. All the results above prove the effectiveness of the calibration method for the system error of inter-satellite-link measurements and the effectiveness of the autonomous navigation algorithm.

Orbit determination for remote-sensing satellites using only optical imagery

ABSTRACTThe development of high-resolution remote-sensing satellites is paving a promising path towards autonomous orbit determination using optical imagery. In this article, an image-based orbit determination strategy is investigated with a focus on the effects of lighting constraints, image resolution, and pointing accuracy on orbit determination performance. The measurement model is established based on the perspective projection and its observability is demonstrated. To investigate the influence of lighting constraints, four cases of simulations (considering no lighting constraints, either cloud-coverage constraint or night-time constraint, or both constraints) are conducted for the WorldView-3 satellite. The obtained root- mean square (RMS) errors of position and velocity in the four cases remain below 10.83 m and 1.42 cm , respectively, at an image resolution of 0.3 m and a pointing accuracy of 0.0005. By varying the values of image resolution and pointing accuracy, the effects of these two factors and their relative importance are further investigated. The final results indicate that pointing accuracy plays a dominant role in image-based orbit determination for high-resolution remote-sensing satellites.

Autonomous Orbit Determination for Lagrangian Navigation Satellite Based on Neural Network Based State Observer

In order to improve the accuracy of the dynamical model used in the orbit determination of the Lagrangian navigation satellites, the nonlinear perturbations acting on Lagrangian navigation satellites are estimated by a neural network. A neural network based state observer is applied to autonomously determine the orbits of Lagrangian navigation satellites using only satellite-to-satellite range. This autonomous orbit determination method does not require linearizing the dynamical mode. There is no need to calculate the transition matrix. It is proved that three satellite-to-satellite ranges are needed using this method; therefore, the navigation constellation should include four Lagrangian navigation satellites at least. Four satellites orbiting on the collinear libration orbits are chosen to construct a constellation which is used to demonstrate the utility of this method. Simulation results illustrate that the stable error of autonomous orbit determination is about 10 m. The perturbation can be estimated by the neural network.

Centralized autonomous orbit determination of Beidou navigation satellites with inter-satellite link measurements: preliminary results

Autonomous orbit determination is the process by which the orbit parameters of navigation satellites are estimated onboard using Inter-Satellite Link (ISL) measurements. In this contribution, autonomous orbit determination experiments using ISL measurements in a centralized mode of the new-generation Beidou navigation satellites are conducted. The mathematical formulation and the processing method of the dual one-way measurements are addressed as well as the main feathers of the ISL measurements are introduced. It is concluded that the ISL ranging data are high-precision measurements. The centralized autonomous orbit determination is processed in a batch mode. The average value of ISL measurements residuals is within 1.0 cm, standard deviation of ISL measurements residuals is within 10.0 cm and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The orbital accuracy is assessed by overlap comparison, User Equivalent Ranging Error and Satellite Laser Ranging (SLR) residuals. The radial overlap differences of the autonomous orbits are less than 6.0 cm and 24 h predicted orbital radial overlap differences less than 10.0 cm. The User Equivalent Ranging Error of 24 h predicted autonomous orbits is about 0.43 m and is better than the 24 h predicted L-band orbits at the 0.76 m level. The SLR residuals for the autonomous orbits are less than 10.0 cm. The ground anchor station which observes the constellation with ISL is important to maintain the Earth-Fixed-Frame and avoid the uncertainties of the entire constellation orientation. The influence of the ground station observation time span on autonomous orbit accuracy is also discussed. Even if the cutoff elevation of the ground anchor station is less than 60°, the radial accuracy of the autonomous orbits and 24 h predicted orbits is still better than 10.0 cm and three-dimensional orbit accuracy better than 1.5 m.

Autonomous orbit determination via kalman filtering of gravity gradients

Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the observations with a precise gravity model. The extended Kalman filter is investigated as the principal estimator. The stochastic model of orbital motion, the measurement equation and the model configuration are discussed for the filter design. An augmented state filter is also developed to deal with unknown significant measurement biases. Simulations are conducted to analyze the effects of initial errors, data-sampling periods, orbital heights, attitude and gradiometer noise levels, and measurement biases. Results show that the filter performs well with additive white noise observation errors. Degraded observability for the along-track position is found for the augmented state filter. Real flight data from the GOCE satellite are used to test the algorithm. Radial and cross-track position errors of less than 100 m have been achieved.

Research on the Effectiveness of Different Estimation Algorithm on the Autonomous Orbit Determination of Lagrangian Navigation Constellation

The accuracy of autonomous orbit determination of Lagrangian navigation constellation will affect the navigation accuracy for the deep space probes. Because of the special dynamical characteristics of Lagrangian navigation satellite, the error caused by different estimation algorithm will cause totally different autonomous orbit determination accuracy. We apply the extended Kalman filter and the fading–memory filter to determinate the orbits of Lagrangian navigation satellites. The autonomous orbit determination errors are compared. The accuracy of autonomous orbit determination using fading-memory filter can improve 50% compared to the autonomous orbit determination accuracy using extended Kalman filter. We proposed an integrated Kalman fading filter to smooth the process of autonomous orbit determination and improve the accuracy of autonomous orbit determination. The square root extended Kalman filter is introduced to deal with the case of inaccurate initial error variance matrix. The simulations proved that the estimation method can affect the accuracy of autonomous orbit determination greatly.

A new autonomous orbit determination algorithm based on inter-satellite ranging measurements

Due to the limitation of onboard computers relatively low storage and processing ability, current autonomous orbit determination (OD) algorithms mostly adopt sequential and distributed method for navigation satellite. Such algorithms can save computing resources, however have met the problem of filter divergence and rapid accuracy decline especially under the condition of less inter-satellite links (ISLs). This paper proposes a new rapid and stable centralized algorithm based on powerful high frequency inter-satellite measurement capability under the space/time-division multiple access (STDMA) system. This approach describes the difference between the real and long term forecasting orbit as the simple higher order polynomials, which needs no complex dynamic modeling, trajectory integration and the state transition matrix calculation, thus greatly saves computing resources. Meanwhile, this paper advances to make full use of the longitude of the ascending node information of forecast orbit so as to reduce the dependence on ground support system. Finally, we simulate the Beidou global constellation structure and ISL measurements, demonstrate the impact of the number of ISL, the noise of ISL on the performance of autonomous OD, and analyze the total amount of computation theoretically. The simulation results show that the algorithm with high stability has no error accumulation, and can run normally even with 3 ISLs, and under the condition of no less than 5 ISLs, the orbit user orbit error (URE) is about 0.9 m after 60 days autonomous operation. The total amount of calculation of the new method is theoretically one-seventh of the distributed extended Kalman filter algorithm.

Method and Analysis of Medium and Long Term Satellite Orbit Prediction Based on Satellite Broadcast Ephemeris Parameters

Given the lag of IGS precise ephemeris and complexity of dynamic models, in order to solve the problem of long-term satellite orbit prediction in autonomous orbit determination, a new medium and long term orbit prediction method that based on satellite broadcast ephemeris parameters has been put forward. This method is that forecasting the orbit parameters firstly according to broadcast ephemeris history data, and then calculating satellite position according to the forecast ephemeris parameters. In order to verify the feasibility of this method, using 40 days of broadcast ephemeris data, adopting ARMA model combined with sliding window model to predict broadcast ephemeris orbit parameters value in 25 days. Analyzed the parameters prediction error and the influence of parameters prediction error to satellite orbit accuracy, 25 days of orbit prediction error can be controlled in 150 meters. The results show that the predictability of orbit parameters has certain application value for satellite orbit prediction, the medium and long term orbit prediction that based on the satellite broadcast ephemeris parameters is a new and feasible method of orbit prediction.

The Method of Satellite Autonomous Orbit Determination Based on Star and Sun Sensor Wireless System

The method of satellite orbit determination on real time was proposed based on star sensor and sun sensor. According to the wireless net composed by star sensor and sun sensor, the kinematics orbit data of satellite will be generated. With the restriction of kinematics model, the parameters in dynamic model such as atmosphere index and sunlight radiation index could be estimated accurately with appropriate algorithm. For the non-linear characteristic of the dynamic model, the UKF estimator was put forward to restrain the interceptive error. The simulation experiment results shown that the method of satellite orbit determination based on UKF method and wireless net data system based on star sensor and sun sensor was excellent to adapt the complex space circumstance, and can generate high precise orbit.

Nonlinear Filter Designed Suitable for Orbit Estimation

Satellite autonomous orbit determination is a necessary condition for satellite autonomous survival. Spacecraft borne sensors are used for observing common natural celestial to get a linear observation equation after appropriately conversion. It can signiflcantly reduce the calculation and has a more intuitive physical meaning; taking advantage of the special position of starlight vector when refraction occurs to calculate geocentric distance, increase the observation equation information; system model error introduced by flrst-order recursive approximation of two-body orbital kinetic model is one of the key factors that afiect the performance of fllter, a linear combination of the flrst-order derivative function value take place of higher derivatives function can greatly reduce the linearization error of difierential equations. In the design process of fllter, the method is applied to process the state equation, greatly improves the recursive accuracy of the fllter state equation. Simulation results show that, under the same conditions performance of this fllter based on higher order nonlinear orbit estimator is far superior to the flrst order orbit estimator based on extended Kalman flltering technique.

Feasibility study of autonomous orbit determination using only the crosslink range measurement for a combined navigation constellation

In order to expand the coverage area of satellite navigation systems, a combined navigation constellation which is formed by a global navigation constellation and a Lagrangian navigation constellation was studied. Only the crosslink range measurement was used to achieve long-term precise autonomous orbit determination for the combined navigation constellation, and the measurement model was derived. Simulations of 180days based on the international global navigation satellite system (GNSS) service (IGS) ephemeris showed that the mentioned autonomous orbit determination method worked well in the Earth–Moon system. Statistical results were used to analyze the accuracy of autonomous orbit determination under the influences of different Lagrangian satellite constellations.