Relative Attitude Determination Research Articles

Gyro Observability Research of a Relative Attitude Determination System Based on Stereo Vision

The analysis of the observability of system states is very important in the design of an optimal filter estimation algorithm. A relative attitude estimation algorithm is developed based on a stereo vision system and a gyroscope, and the observability of this algorithm is studied. First, we build the error model of the relative attitude determination system. Second, the observability of every state of the filter is studied. Third, by choosing different variables as the states of the error model, the unobservable subspace of the system is confirmed. Furthermore, the system structural decomposition reveals that this type of relative attitude determination system can only determine the relative attitude between the deputy and the chief and that their gyro drift errors are unobservable. In addition, the structural decomposition also tells us that when the feature points measured by the stereo vision system are greater than two, increasing the number of feature points provides little benefit for improving the observability of the gyro drift errors. Considering the incomplete observability of the original system, the star sensor is added into the system to enable it to be completely observable. The final simulation result indicates that after adding the star sensor, the system, which becomes completely observable, can estimate the body attitude, the relative attitude and the gyro error while providing improved accuracy.

An algorithm and observability research of autonomous navigation and joint attitude determination in asteroid exploration descent stage

In this paper, an autonomous relative navigation and joint attitude determination algorithm in asteroid exploration descent stage is researched based on feature point information of perpendicular asteroid surface image observed by optical navigation camera, distance vectors from spacecraft to asteroid measured by three angled installed lidars and relative velocity increment measured by accelerometer when the relative distance vector to the centroid of asteroid can not be obtained. The inertial attitude of spacecraft is determined by sun vector, star vectors and inertial angular velocity respectively measured by sun sensor, star trackers and inertial reference unit. Also, in order to obtain measurement error model transferred from sensor noise, a covariance matrix solver considering error correlation is presented via the error model of normalized vector to first order. Numerical simulation and improved observability evaluation of filtering are undertaken to discuss the results of complete sensor observation and weak observation of lidars, and verify the effectiveness of the presented relative navigation and attitude determination algorithm.

Satellite relative motion determination during separation using image processing

Satellite relative position and attitude determination algorithm by video processing is developed. The algorithm is numerically simulated and studied. Relative state determination accuracy depending on a distance and pre-defined points image size is investigated. Microsatellite ‘Chibis-M’ and spaceship ‘Progress-13M’ relative motion after separation is determined by the algorithm.

Relative Status Determination for Spacecraft Relative Motion Based on Dual Quaternion

For the two-satellite formation, the relative motion and attitude determination algorithm is a key component that affects the flight quality and mission efficiency. The relative status determination algorithm is proposed based on the Extended Kalman Filter (EKF) and the system state optimal estimate linearization. Aiming at the relative motion of the spacecraft formation navigation problem, the spacecraft relative kinematics and dynamics model are derived from the dual quaternion in the algorithm. Then taking advantage of EKF technique, combining with the dual quaternion integrated dynamic models, considering the navigation algorithm using the fusion measurement by the gyroscope and star sensors, the relative status determination algorithm is designed. At last the simulation is done to verify the feasibility of the algorithm. The simulation results show that the EKF algorithm has faster convergence speed and higher accuracy.

Relative Attitude Determination of Formation Spacecraft Based on Flight Mechanics

According to " leader missiles - attack missiles " formation model, the measurement model of missile in formation flight VisNav is derived. The observability analysis of missile VisNav is shown for cases involving three vector observations, the conclusion is that at least three characteristic points are visible to insure visual navigation systems to work properly. The least square algorithm is applied to process the data of VisNav to estimate the relative attitude and position. The results of simulation show that the accuracy of least square algorithm would be influenced by the relative position of missile in formation flight mechanics.

Determination of inter-satellite relative position using X-ray pulsars

Pulsars are rapidly rotating neutron stars that generate pulsed electromagnetic radiation. A new method for inter-satellite relative position determination between a global navigation satellite system (GNSS) and spacecraft using X-ray pulsars is proposed in this paper. The geometric model of this method is formulated, and two different resolution algorithms are introduced and analyzed. The phase cycle ambiguity resolution is investigated, and a new strategy is proposed and formulated. Using the direct vector parameters of the pulsar, geometric dilution of precision (GDOP) is studied. It is shown that this method has advantages of simplicity and efficiency, and is able to eliminate the clock errors. The analytical results are verified numerically via computer simulations.

PROBA-3 mission

PROBA-3 is the ESA mission devoted to the demonstration of precise formation flying technology. Precise formation flying will allow small spacecraft, flying with a fixed relative geometry, to synthesise giant structure-less instruments. PROBA-3 consists of two satellites keeping a formation from 25 to 250 metres controlling relative position with about one millimetre accuracy. The spacecraft will autonomously manage the formation and take mission critical decision with no ground supervision. The metrology sensors chain will allow formation acquisition and relative position determination maintenance with micrometric precision. Periodic in flight automatic calibration will compensate the systematic deformation induced by the space environment. This paper details the mission objectives and the challenging requirements. It describes the overall mission design and in particular the formation flying technology demonstration plan. The main mission novelties are highlighted and the mission autonomy, formation flying sensors and algorithms and verification approaches are introduced. The preliminary performance results are presented. Eventually, the potential exploitation of the PROBA-3 demonstration for future missions is presented in the conclusions.

Real-Time Determination of Relative Position Between Satellites Using Laser Ranging

We made a study on real-time determination method for relative position using the laser-measured distance data between satellites. We numerically performed the determination of relative position in accordance with extended Kalman filter algorithm using the vectors obtained through nonlinear equation of relative motion, laser simulator for distance measurement, and attitude determination of chief satellite. Because the spherical parameters of relative distance and direction are used, there occur some changes in precision depending on changes in relative distance when determining the relative position. As a result of simulation, it was possible to determine the relative position with several millimeter-level errors at a distance of 10 km, and sub-millimeter level errors at a distance of 1 km. In addition, we performed the determination of relative position assuming the case that global positioning system data was not received for long hours to see the impact of determination of chief satellite orbit on the determination of relative position. The determination of precise relative position at a long distance carried out in this study can be used for scientific mission using the satellite formation flying.

Stepwise gradient elution in RP HPTLC with a new horizontal developing chamber

A general equation for determination of relative position, Rpg , of solutes chromatographed under conditions of stepwise gradient elution with one void volume of mobile phase in reverse-phase thinlayer chromatography has been applied to separation of ten component dye mixture. A satisfactory agreement between calculated (by computer program) and experimental values of Rpg has been demonstrated. A device with the new horizontal developing chamber has been applied to the investigations. This device showed practical advantages in comparison to other chambers especially in respect of its application to stepwise gradient elution.

Relative position determination of a lunar rover using the biased differential phase delay of same-beam VLBI

When only data transmission signals with a bandwidth of 1 MHz exist in the rover, the position can be obtained using the differential group delay data of the same-beam very long baseline interferometry (VLBI). The relative position between a lunar rover and a lander can be determined with an error of several hundreds of meters. When the guidance information of the rover is used to determine relative position, the rover’s wheel skid behavior and integral movement may influence the accuracy of the determined position. This paper proposes a new method for accurately determining relative position. The differential group delay and biased differential phase delay are obtained from the same-beam VLBI observation, while the modified biased differential phase delay is obtained using the statistic mean value of the differential group delay and the biased phase delay as basis. The small bias in the modified biased phase delay is estimated together with other parameters when the relative position of the rover is calculated. The effectiveness of the proposed method is confirmed using the same-beam VLBI observation data of SELENE. The radio sources onboard the rover and the lander are designed for same-beam VLBI observations. The results of the simulations of the differential delay of the same-beam VLBI observation between the rover and the lander show that the differential delay is sensitive to relative position. An approach to solving the relative position and a strategy for tracking are also introduced. When the lunar topography data near the rover are used and the observations are scheduled properly, the determined relative position of the rover may be nearly as accurate as that solved using differential phase delay data.

Relative Position and Attitude Determination for Robotic Mars Soft Landing Using Multi-Point Laser Rangefinder

Several international deep space exploration plans aimed at Mars landing and surface sample returning. Because of the communication delay between Earth and Mars and the lack of information on the Mars complicated surface, autonomous landing at selected location is required. Based on multi-point laser rangefinder and optical navigation camera, the relative position and attitude rapid determination algorithm is present in order to ensure precise and safe landing. To get the normal direction of the landing plane and the target point position, the geometry relation of laser measure vectors and target point are used. Finally, performance of the autonomous relative position and attitude determination system is verified using the numerical simulation. The results show that the proposed methods can achieve accurate position and attitude determination.

GPS/VISNAV integrated relative navigation and attitude determination system for ultra-close spacecraft formation flying

For the improvement of accuracy and better fault- tolerant performance, a global position system (GPS)/vision navi- gation (VISNAV) integrated relative navigation and attitude deter- mination approach is presented for ultra-close spacecraft forma- tion flying. Onboard GPS and VISNAV system are adopted and a federal Kalman filter architecture is used for the total naviga- tion system design. Simulation results indicate that the integrated system can provide a total improvement of relative navigation and attitude estimation performance in accuracy and fault-tolerance.

Constrained Relative Attitude Determination for Two-Vehicle Formations

This paper studies constrained relative attitude determination of a formation of two vehicles. A deterministic solution for the relative attitude between the two vehicles with line-of-sight measurements between them and a common object observed by both vehicles is presented. The solution represents the minimum number of measurements required to determine the relative attitudes and no ambiguities are present. To quantify the performance of the algorithm the covariance of the attitude error is derived using a linearized error model from a least-squares point of view. Simulation results are also provided to assess the performance of the proposed new approach.

Intersatellite Links and Relative Navigation: Pre-conditions for Formation Flights with Pico- and Nanosatellites

AbstractA group of satellites can be classified as a constellation, formation or cluster. Multiple coordinated satellites are described as a formation, if a closed-loop control is adjusted, thus providing a coordinated motion control on basis of their relative positions to preserve the topology (Schilling [2009]). This technology enables various application scenarios, for example, interferometry or in-orbit servicing and it is subject to multiple technological requirements related to formation flying, limited resources or scientific payloads. In the framework of the feasibility study NaKoFo, this paper discusses the potential benefits, drawbacks and problems associated with intersatellite links and relative navigation with pico- and nanosatellites. The requirements of an intersatellite link are analyzed based on frequency, modulation, antenna, power and network protocol. A short overview of adequate communication systems for pico- and nanosatellites is also presented. Technologies for relative position determination are presented and discussed regarding their applicability in small satellite systems as well as their requirements on an intersatellite link.

A vectorial bootstrapping approach for integrated GNSS-based relative positioning and attitude determination of spacecraft

Traditionally in multi-spacecraft missions (e.g. formation flying, rendezvous) the GNSS-based relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibility to use multi-antenna data from each spacecraft, not only for attitude determination, but also to improve the relative positioning between spacecraft. Both for ambiguity resolution and accuracy of the baseline solution, we will show the theoretical improvement achievable as a function of the number of antennas on each platform. We concentrate on ambiguity resolution as the key to precise relative positioning and attitude determination and will show the theoretical limit of this kind of approach. We will use mission parameters of the European Proba-3 satellites in a software-based algorithm verification and a hardware-in-the-loop simulation. The software simulations indicated that this approach can improve single epoch ambiguity resolution up to 50% for relative positioning applying the typical antenna configurations for attitude determination. The hardware-in-the-loop simulations show that for the same antenna configurations, the accuracy of the relative positioning solution can improve up to 40%.

Determinating relative motion trajectory and orientation angles by GNSS phase measurements and micromechanical gyroscope data

A short review of the existing methods for resolving phase measurement ambiguity is given. The general structure of the developed algorithms for solving relative navigation and attitude determination problems by means of GNSS phase measurements is presented. Two GNSS receivers and the azimuthal angular velocity data generated by a strapdown inertial module are used in the attitude determination problem. The original techniques for phase measurement cycles integer search are revealed for both problems. These make it possible to reduce computational costs of ambiguity resolution as compared to existing methods. The results from processing phase single-frequency measurements and micromechanical gyroscope data recorded on board a car and a vessel are presented.

Deterministic Relative Attitude Determination of Three-Vehicle Formations

DOI: 10.2514/1.42849 This paper proves that deterministic relative attitude determination is possible for a formation of three vehicles. The results provide an assessment of the accuracy of the deterministic attitude solutions, given statistical properties oftheassumednoisymeasurements.Eachvehicleisassumedtobeequippedwithsensorstoprovideline-of-sight,and possibly range, measurements between them. Three vehicles are chosen because this is the minimum number required to determine all attitudes given minimal measurement information. Three cases are studied. The first determines the absolute (inertial) attitude of a vehicle knowing the absolute positions of the other two. The second assumes parallel beams between each vehicle to determine relative attitudes, and the third assumes nonparallel beams for relative attitude determination, which requires range information to find deterministic solutions. Covariance analyses are provided to gain insight on the stochastic properties of the attitude errors and the observability for all three cases.

New means of cybernetics, informatics, computer engineering, and systems analysis

The class of combinatorial problems equivalent to the problem of determination of relative positions of n interval sequences is formulated. It is shown that an adequate mathematical model of solving a stated problem is a finite dynamic memoryless automaton and that the adequate mathematical apparatus is continuous logic. Algorithms that solve the problem are constructed.

Multiplatform Instantaneous GNSS Ambiguity Resolution for Triple‐ and Quadruple‐Antenna Configurations with Constraints

Traditionally the relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibilities of using multiantenna (i.e., triple and quadruple) data, not only for attitude determination but also for relative positioning. The methods developed are rigorous and have the additional advantage that they improve ambiguity resolution on the unconstrained baseline(s) and the overall success rate of ambiguity resolution between a number of antennas.

CDGPS Relative Position Determination of Distributed SAR Satellite Formation Based on Dynamic Orbit Model

针对分布式SAR卫星编队星间基线的高精度确定问题, 提出了基于轨道动力学模型的分布式SAR卫星编队CDGPS相对定位方法. 根据CDGPS原理及基于轨道动力学模型的星间相对定位原理,在CDGPS测量的基础上, 引入轨道动力学模型提供的先验约束信息, 对长弧段的观测数据进行解算, 克服了运动学逐点解算方法在观测几何较差或观测数据不足情况下无法应用的缺点. 此方法能够有效抑制测量中的随机误差, 提高相对定位精度, 提供了一种可实现mm量级星间基线确定的技术途径. 通过仿真计算验证了动力学方法的有效性. 计算结果表明, 动力学方法可以显著提高相对定位精度. 相对于运动学方法, 前者L1固定解的精度提高了68%, 而消电离层固定解的精度提高了95%.