Autonomous Orbit Research Articles

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.

Rotating Machinery Diagnostics Using Deep Learning on Orbit Plot Images

Although the orbit analysis (orbit shape and size) is commonly used to diagnose rotating machinery, the diagnosis heavily depends on the expert knowledge or experience due to the difficulties of extracting mathematical features for data-driven approaches. Therefore, in this paper, we propose an autonomous orbit pattern recognition algorithm using the deep learning method on shaft orbit shape images. In details, the convolutional neural network is implemented to construct weights between neurons and to generate the entire structure of the neural network. Then, the created network enables us to classify fault modes of rotating machinery via orbit images. Furthermore, we demonstrate the proposed framework through a rotating testbed.

GPS/Galileo navigation in GTO/GEO orbit

The development of electrically propelled geostationary platforms, together with alternative strategies to reach geostationary orbit, increase the interest for autonomous satellite localization and particularly GNSS navigation for high altitude orbits. It is known that GNSS navigation in GTO/GEO is much more difficult than in LEO since the GNSS receiver is often or permanently at an altitude greater than the altitude of the GNSS constellations, making the GNSS signals drastically less available and weaker. This work is about GPS and Galileo navigation on GEO and GTO orbits, with revised hypotheses compared to studies sometimes more than 15 years old. Moreover, the study goes beyond GNSS geometrical visibility by dealing with operating thresholds and showing the sensitivity to key GNSS receiver thresholds and simulation hypotheses. Comprehensive simulation results and analyses come along with a discussion of the operational benefits of using GPS and Galileo navigation. These data eventually set the ground for a discussion of the key technical options (number and antenna types, GNSS function architecture, signal processing algorithms, orbital filter…). It is shown that using GNSS for GTOGEO orbits is feasible, even considering current spaceborne receivers state-of-the-art, and provides most of the acclaimed benefits of GNSS in LEO, among them more accurate spacecraft localization, precise onboard absolute time and increased autonomy.

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.

Application of two special orbits in the orbit determination of lunar satellites

Using inter-satellite range data, the combined autonomous orbit determination problem of a lunar satellite and a probe on some special orbits is studied in this paper. The problem is firstly studied in the circular restricted three-body problem, and then generalized to the real force model of the Earth-Moon system. Two kinds of special orbits are discussed: collinear libration point orbits and distant retrograde orbits. Studies show that the orbit determination accuracy in both cases can reach that of the observations. Some important properties of the system are carefully studied. These findings should be useful in the future engineering implementation of this conceptual study.

How to Get the Solar Direction from Skylight Polarization for Satellite Autonomous Navigation

The solar direction is an important clue for satellite autonomous navigation. A new method for obtaining the solar direction from skylight polarization for satellite navigation is discussed. The new method is using two E-vector polarization sensors to get solar direction, and the view field of the polarization sensor is discussed.

Simplified Orbit Determination Algorithm for Low Earth Orbit Satellites Using Spaceborne GPS Navigation Sensor

ABSTRACT In this paper, the main work is focused on designing and simplifying the orbit determination algorithm which will be used for Low Earth Orbit (LEO) navigation. The various data processing algorithms, state estimation algorithms and modeling forces were studied in detail, and simplified algorithm is selected to reduce hardware burden and computational cost. This is done by using raw navigation solution provided by GPS Navigation sensor. A fixed step-size Runge-Kutta 4th order numerical integration method is selected for orbit propagation. Both, the least square and Extended Kalman Filter (EKF) orbit estimation algorithms are developed and the results of the same are compared with each other. EKF algorithm converges faster than least square algorithm. EKF algorithm satisfies the criterions of low computation burden which is required for autonomous orbit determination. Simple static force models also feasible to reduce the hardware burden and computational cost.

A Universe Light House — Candidate Architectures of the Libration Point Satellite Navigation System

In view of the shortcomings of existing satellite navigation systems in deep-space performance, candidate architectures which utilise libration point orbits in the Earth-Moon system are proposed to create an autonomous satellite navigation system for lunar missions. Three candidate constellations are systematically studied in order to achieve continuous global coverage for lunar orbits: the Earth-Moon L1,2 two-satellite constellation, the Earth-Moon L2,4,5 three-satellite constellation and the Earth-Moon L1,2,4,5 four-satellite constellation. After a thorough search for possible configurations, the latter two constellations are found to be the simplest feasible architectures for lunar navigation. Finally, an autonomous orbit determination simulation is performed to verify the autonomy of the system and two optimal configurations are obtained in a comprehensive consideration of coverage and autonomous orbit determination performance.

GNSS Vulnerability Analysis and Assessment

A Global Navigation Satellite System (GNSS) vulnerability assessment approach based on separately detecting possible factors is developed in this paper. The consistency judgment of visible satellites and navigation message, carrier-to-noise ratio (C/No), Satellite Autonomous Integrity Monitoring (SAIM), Receiver Autonomous Integrity Monitoring (RAIM), Ionosphere delay and Receiver’s Position error are chosen as key features to detect whether the GNSS vulnerability is serious. By monitoring those key features, potential vulnerability factor can be excluded in steps. This approach is established in clearly elaborating the concept of GNSS vulnerability and fully analyzing the potential vulnerability factors in system segment, environment segment and user segment. A GNSS vulnerability physical simulation, verification and mitigation platform is also designed; the establishment of this platform is a future work to realize this approach and to mitigate the vulnerability while it happens.

Virtual Formation Method for Precise Autonomous Absolute Orbit Control

This paper analyzes the problem of precise autonomous orbit control of a spacecraft in a low Earth orbit. Autonomous onboard orbit control means that the spacecraft maintains its ground track close to a reference trajectory, without operator intervention. The problem is formulated as a specific case of two spacecraft in formation in which one, the reference, is virtual and affected only by the Earth’s gravitational field. A new parametrization, the relative Earth-fixed elements, is introduced to describe the relative motion of the two spacecraft’s subsatellite points on the Earth surface. These relative elements enable the translation of absolute-into-relative orbit-control requirements and the straightforward use of modern control-theory techniques for orbit control. As a demonstration, linear and quadratic optimum regulators are designed and compared, by means of numerical simulations, with an analytical autonomous orbit-control algorithm that has been validated in flight. The differences of the numerical and analytical control methods are identified and discussed.

利用恒星与地磁场确定卫星自主轨道

An autonomous navigation method suitable for low orbit satellites is proposed.Different from traditional method that takes a start light angle as the observed variable,the method determines the real time orbital parameters by a start sensor and a geomagnetism sensor,and converses the unit vector observation equation of satellite position into linear equations by converting the observation data from the start sensor appropriately.With fitting the relationship of magnetic field strength and orbit height,it obtains the geocentric distance by using a magnetometer.Moreover,it determines the satellite initial orbit by Lagrange difference algorithm to provide initial value for the filter.As the performance of the filter is effected by the system model error caused from the first-order linear approximation of two body dynamic orbit model,and the high order derivative function values can be replaced by a linear combination of one order derivative function values,this paper processes the state equation by a higher order linearity in design of the KALMAN filter to reduce the calculation.By proposed method,the discretized accuracy of state equation for the filter is improved greatly.Finally,a simulation experiment is performed,which verifies that the method is effective and feasible.

Autonomous orbit determination and its error analysis for deep space using X-ray pulsar

Autonomous orbit determination (OD) is a complex process using filtering method to integrate observation and orbit dynamic model effectively and estimate the position and velocity of a spacecraft. As a novel technology for autonomous interplanetary OD, X-ray pulsar holds great promise for deep space exploration. The position and velocity of spacecraft should be estimated accurately during the OD process. However, under the same condition, the accuracy of OD can be greatly reduced by the error of the initial orbit value and the orbit mutation. To resolve this problem, we propose a novel OD method, which is based on the X-ray pulsar measurement and Adaptive Unscented Kalman Filter (AUKF). The accuracy of OD can be improved obviously because the AUKF estimates the orbit of spacecraft using measurement residual. During the simulation, the orbit of Phoenix Mars Lander, Deep Impact Probe, and Voyager 1 are selected. Compared with Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF), the simulation results demonstrate that the proposed OD method based on AUKF can accurately determinate the velocity and position and effectively decrease the orbit estimated errors which is caused by the orbit mutation and orbit initial errors.

Distributed Control of Networked Dynamical Systems: Static Feedback, Integral Action and Consensus

This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.

Model predictive orbit control of a Low Earth Orbit satellite using Gauss’s variational equations

In this paper, an autonomous orbit control of a satellite in Low Earth Orbit is investigated using model predictive control. The absolute orbit control problem is transformed to a relative orbit control problem in which the desired states of the reference orbit are the orbital elements of a virtual satellite which is not affected by undesirable perturbations. The relative motion is modeled by Gauss’s variational equations including J2 and drag perturbations which are the dominant perturbations in Low Earth Orbit. The advantage of using Gauss’s variational equations over the Cartesian formulations is that not only the linearization errors are much smaller, but also each orbital element can be controlled independently. Model predictive control finds the finite horizon optimal firing times of the satellite thrusters. The problem of orbit control has been cast as a linear programming which is a subset of convex optimization problems. As a result, model predictive control can maintain and control orbits of Low Earth Orbit satellites in optimal way, and this modern control technique can be an alternative for traditional analytical-based orbit control methods. Also, a comparison between model predictive control and linear quadratic regulator orbit control showed the superiority of MPC in fuel consumption.

A starlight refraction scheme with single star sensor used in autonomous satellite navigation system

For autonomous satellite navigation, the method based on stellar refraction is studied in this paper. In the previous studies, two star sensors have been used for navigation. Actually, only one star sensor is sufficient for navigation. The additional sensor will result in an extra burden for the initial alignment process and design cost. In this paper, an autonomous satellite navigation scheme based on stellar refraction with a single star sensor is presented. The installed angle of star sensor is closely related with the navigation precision of satellite, and the refraction star identification is crucial in stellar refraction method. Hence the determination of installed angle and refraction star identification are also considered. Finally, to verify the feasibility of the proposed scheme, a simulation for low-Earth-orbit (LEO) satellite is carried out and its result indicates that the proposed method is practical with high-precision.

Inter-satellite Ranging Augmented GPS Relative Navigation for Satellite Formation Flying

An Augmented Relative Navigation System (ARNS) is proposed for autonomous satellite formation flying in low-Earth-orbit (LEO). Inter-satellite ranging systems such as those based on radio frequency transmissions can provide additional observation information, e.g. inter-satellite distance measurement, which can be used to increase the Global Positioning System (GPS) stand-alone observation dimension, or treated as a non-linear equality constraint within a smoothly-constrained Kalman filter. Both approaches are implemented in the proposed ARNS described in this paper. An innovative phase integer ambiguity fixing and feedback scheme is implemented to increase the ambiguity fix rate of the GPS carrier phase measurements. A set of Gravity Recovery and Climate Experiment (GRACE) flight data is used to test and validate the relative navigation performance of the proposed methods. Results indicate that the augmented system can improve relative positioning accuracy by an order of magnitude.