State interpolation for on-board navigation systems

Common concepts for autonomous on-board navigation systems rely on the numerical integration of a spacecraft trajectory between subsequent measurements of a navigation sensor such as GPS. In combination with a Kalman filter, a predicted state vector becomes available at discrete, but not necessarily equidistant time steps. When used for real-time attitude control or geo-coding of image data, the on-board navigation system has to provide continuous dense output at equidistant time steps, which usually conflicts with the natural stepsize of the relevant integration methods and the non-equidistant measurement times. To cope with this problem, the integrator has to be supplemented by an interpolation scheme of compatible order and accuracy.After presenting a representative formulation of an on-board navigation system and deriving related timing and accuracy requirements, suitable Runge–Kutta methods and associated interpolants are selected and evaluated. Promising results are obtained for the classical RK4 method in combination with Richardson extrapolation and 5th-order Hermite interpolation. The 5th-order Fehlberg method with interpolation due to Enright and, for drag-free scenarios, the 5th-order Runge–Kutta–Nystrom method with 5th-order Hermite interpolation provide a good performance in terms of position interpolation. However, as both methods exhibit significant errors for the velocity interpolation, they are not recommended for use with the outlined navigation filter.     

Spacecraft orbit determination using GPS navigation solutions

The orbit determination using the GPS navigation solutions for the KOMPSAT-1 spacecraft has been studied. The Cowell method of special perturbation theories was employed to develop a precision orbit propagation, and the perturbations due to geopotential, the gravity of the Sun and the Moon, solid Earth tides, ocean tides, the Earth's dynamic polar motion, solar radiation pressure, and atmospheric drag were modeled. Specifically, the satellite box-wing macro model was applied to minimize the drag errors at low altitude. The estimation scheme consisted of an extended Kalman filter and Bayesian least square method. To investigate the applicability of the method to the KOMPSAT-1 spacecraft, the orbit determination was accomplished using the GPS navigation solutions for the TOPEX/POSEIDON and TAOS satellites. The orbit determination results were compared with NASA POE generated by global laser tracking. The position and velocity accuracy was estimated about 16∼7 m and 0.0157∼0.0074 m·s⁻¹ RMS, respectively, for the two satellites in the presence of SA. These results verify that an orbit determination scheme using GPS navigation solutions can provide the static orbit information and reduce conspicuously the position and velocity errors of navigation solutions. It can be suggested that the sequential and batch orbit determination using the GPS navigation solutions be the most appropriate method in the KOMPSAT-1 type mission.     

Highly accurate, noncoherent technique for spacecraft Dopplertracking

A two-way, noncoherent spacecraft navigation technique has been developed to provide velocity accuracy comparable to that available from a deep space coherent transponder (0.1 mm/s). The technique is compatible with the normal tracking procedures of the Deep Space Network (DSN) ground stations and does not require the use of a highly stable oscillator on-board the spacecraft. The measurement technique, potential error sources, and test results obtained with prototype hardware are described     

Geostationary orbit determination for time synchronization using analytical dynamic models

A real time analytical orbit determination method has been developed for precision national time synchronization. The one-way time transfer technique via a geostationary TV satellite standard time and frequency signal (STFS) dissemination system was considered. The differential method was also applied for mitigating errors in geostationary satellite STFS dissemination system. Analytical dynamic orbit determination with extended Kalman filter (EKF) was implemented to improve differential mode STFS (DSTFS) service accuracy by acquiring better accuracy of a geostationary satellite position. The perturbation force models applied for satellite dynamics include the geopotential perturbation up to fifth degree and order harmonics, luni-solar perturbations, and solar radiation pressure. All of the perturbation effects were analyzed by secular, short, and long period variations for equinoctial orbit elements such as semimajor axis, eccentricity vector, inclination vector, and mean right ascension of the geostationary satellite. The reference stations for orbit determination were composed of four calibrated stations. Simulations were performed to evaluate the performance of real time analytical orbit determination in Korea. The simulation results demonstrated that it is possible to determine real time position of geostationary satellite with the accuracy of 300 m rms. This performance implies that the time accuracy is better than 25 ns all over the Korean peninsula. The real time analytical orbit determination method developed in this research can provide a reliable, extremely high accurate time synchronization service through setting up domestic-only benchmarks.     

航天器DOR信号本地相关处理的建模与仿真

详述了DOR（差分单向测距）信号的本地相关处理方法。首先根据轨道预报确定先验时延模型值,利用高精度频率估算方法估计航天器DOR信号的星上发射频率,然后通过时延模型值与频率估计值构造DOR本地模型信号,再将此模型信号分别与测站接收的DOR实测信号进行互相关运算,提取相关相位,解算高精度时延观测量。推导了DOR信号本地相关处理的数学模型,通过信号仿真验证了该方法的有效性,在仅考虑系统噪声影响与轨道预报误差的条件下,仿真时延测量精度达到0.1 ns,为深空航天器精密轨道测量提供了一种可借鉴的技术方法。     

空间平台机动变轨自主导航研究

针对空间平台在高轨道机动变轨过程中自主导航的需求,采用了基于Kalman滤波器的捷联惯导与星敏感器的组合导航方案。结合Kalman滤波中协方差更新的误差分配分析方法,分析了影响空间平台状态估计误差的主要因素。采用适用于高轨道的球谐重力模型,运用STK工具包设计了变轨机动轨迹,将该轨迹应用于组合导航方案的仿真验证。仿真结果表明,量测噪声是影响空间平台姿态精度的主要因素,加速度计零偏对变轨过程速度精度有决定性影响,改善两者的精度可以实现空间平台机动变轨的高精度自主导航。     

一种基于轨道要素形式终端约束的航天器空间变轨迭代制导算法

针对航天器空间变轨任务的制导问题,研究了一种适用的迭代制导算法。在传统迭代制导方法的基础上,直接在地心惯性系中建立最优控制模型,以推力方向矢量为控制量来适应大姿态角变化情形;推导直接以目标轨道要素为终端约束的边界条件,给出终端约束方程求解精度和入轨精度的关系;得到一种简单有效的基于轨道要素形式终端约束的航天器空间变轨迭代制导算法。通过仿真验证了所给制导算法的有效性,相比传统迭代制导方法其具有更强的适应性。     

Accurate and autonomous navigation for the ATV

The Automated Transfer Vehicle (ATV) is a European spacecraft intended to service the International Space Station (ISS). It is designed to perform automated phasing, approach, rendezvous and docking to the ISS, then departure and deorbitation manoeuvres. Such an automated rendezvous mission towards a manned facility raises severe performance and safety constraints for the vehicle, which are declined towards the on-board Navigation in terms of availability, accuracy and failure tolerance: the ATV shall be operational after any first failure and safe conditions shall be reached after a second failure. The whole ATV navigation system has been designed to fulfil these very stringent requirements. Based on fully redundant hardware, the navigation algorithms present optimal estimators and multi-layers Failure, Detection, Isolation and Recovery (FDIR) capabilities to ensure the continuity of the state vector in case of failure. Several functions provide state vectors estimations and health reports, according to the flight phase: the attitude and drift estimation function provides the vehicle absolute attitude and angular rate during the whole flight; for the far rendezvous, position and velocity relative to the ISS are estimated by the relative GPS navigation and a dedicated relative navigation with Videometer applies in close rendezvous, in the final approach. All these autonomous navigation functions offer nevertheless a high level of monitoring and control to the ATV Control Centre operators. Thus the ATV innovative navigation chain provides the high level of performance, robustness and autonomy required by modern spacecrafts involved in human programs, today in Earth orbit but also for future space exploration missions.     

Application of GPS to space vehicles: analysis of space environmentand errors

GPS based systems become extremely competitive for space applications because of their all-weather capabilities and continual information on position, velocity, precise time and even attitude to increase mission effectiveness, reduce mission cost, minimize requirements of on-board devices. In this paper, space application environment and error sources have been systematically analyzed, including geometric location of user with GPS satellites, dynamic state, physical environment and the effects on positioning accuracy. Several special differential GPS technologies to space use are proposed     

基于自适应SRCKF的空间非合作目标实时轨道确定

针对天基测角对非合作目标跟踪定轨的动力学模型简化误差问题,提出一种基于非线性预测滤波和SRCKF(Square Root Cubature Kalman Filter,平方根容积Kalman滤波)的自适应滤波方法.采用考虑地球J2摄动影响的轨道动力学模型作为状态方程,在跟踪滤波过程中,用NPF(Nonlinear Predictive Filter,非线性预测滤波)对动力学模型进行实时修正,利用SRCKF对修正后的动力学模型进行状态估计.将该方法应用于高轨航天器对非合作低轨目标的实时测角定轨任务中,进行数字仿真,仿真结果证明,该方法相比传统的滤波方法具有更高的精度、更强的鲁棒性和稳定性.     

无线电掩星技术在大气探测的应用

通过介绍GPS在大气探测中的应用,引入了一种新的研究大气模型的方法——无线电掩星技术。阐明了无线电掩星技术的发展历程、反演原理及应用前景,并结合我国航天实际,提出了一种利用北斗导航系统进行大气参数反演,修正航天器轨道测量数据,从而提高定轨精度的新思路。     

绕月探测器的自主光学导航研究

提出了一种利用高斯-马尔科夫过程和Unscented卡尔曼滤波的绕月探测器自主光学导航算法。针对很难事先确定精确地绕月探测器轨道动力学模型问题,提出利用高斯-马尔科夫过程来近似轨道动力学中的无模型加速度,进而提高了轨道动力学模型的精度;考虑到基于扩展卡尔曼滤波的轨道确定存在的问题,提出利用基于Unscented卡尔曼滤波来估计探测器的位置、速度及无模型加速度,提高了轨道估计精度和保证了算法的稳定性。最后,通过数学仿真验证了自主光学导航算法的有效性。     

天基低轨空间监视雷达密集短弧观测数据的定轨应用研究

当天基雷达采用多波束扫描时,每次与空间目标交会可获取类似跟踪的观测数据。本文讨论了这些密集短弧观测数据在目标轨道改进中的应用。在没有测量时,采用矩阵Ricatti方程计算状态误差;引入观测数据时,比较了EKF和UKF两种滤波算法的轨道改进效果。仿真表明,UKF的收敛速度优于EKF;天基短弧观测数据可以很好地抑制误差发散,满足监视任务需求。     

双星定位系统及其备份星在近地卫星联合定轨建模中的应用

建立了基于双星定位系统距离和观测数据的近地卫星联合定轨模型,设计了相应的数值融合联合定轨算法;为进一步提高近地卫星定轨精度,考虑融合双星及备份星距离和观测数据,建立了基于双星和备份星的近地卫星联合定轨模型及实现算法,并针对不同仿真条件进行了联合定轨仿真实验。仿真计算结果表明,联合定轨方式较传统近地卫星精密定轨方式可以更好地抑制双星星历误差对近地卫星定轨精度的影响,近地卫星和双星的定轨精度均得到了一定程度的提高;同时,融合备份星观测数据的近地卫星联合定轨精度得到进一步改善,达到5.17m。     

Spacecraft attitude/rate estimation using vector-aided GPSobservations

A sequential filtering algorithm is presented for spacecraft attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the state of the filter, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the robustness and accuracy of the method. Numerical examples are used to demonstrate the performance of the method     

Simultaneous spacecraft attitude and orbit estimation using magnetic field vector measurements

Based on magnetometer measurements only, three-axis attitude, rate, and orbit estimation are successfully achieved. A single Augmented Dynamics Extended Kalman Filter (ADEKF) is configured by combining the spacecraft nonlinear attitude dynamics and quaternion kinematics with orbital mechanics. The filter design is adopted for three-axis stabilized spacecraft in low Earth orbits where the aerodynamic drag is the dominant source of disturbances in addition to the spacecraft magnetic residuals. To reduce the computational burden, another Interlaced Extended Kalman Filter (IEKF) is developed to uncouple the attitude/rate from the orbit dynamics. Both filters are implemented using the magnetometer measurements and their corresponding time derivatives. As a part of EgyptSat-1 flight scenario, detumbling and standby modes are used for performance testing of the ADEKF. The concept of local observability is applied to the basic filter and the stability is investigated by incorporating extensive Monte Carlo simulations with uniformly distributed initial conditions. The filter shows the capability of estimating the attitude better than 5 deg and rate of order 0.03 deg/s in each axis. In orbit estimation, the filter is capable of estimating the position with accuracy less than 8 km and velocity upto 5 m/s in each axis.     

A reduced-order model for integrated GPS/INS

The dominant factor in determining the computation time of the Kalman filter is the dimension n of the model state vector. The number of computations per iteration is on the order of n³. Any reduction in the number of states will benefit directly in terms of increased computation time. In this paper, a high order model in integrated GPS/INS is described first, then a reduced-order model based on the high-order model, is developed. Finally, a faster tracking approach for Kalman filters is discussed. A typical aircraft trajectory is designed for a complex high-dynamic aircraft flight experiment. A Monte Carlo analysis shows that the reduced order model presented in this paper provides satisfactory accuracy for aircraft navigation     

基于改进混合卡尔曼滤波器的航空发动机机载自适应模型

提出了基于改进混合卡尔曼滤波器的航空发动机机载自适应模型方法,即以机载非线性模型的输出作为分段线性卡尔曼滤波器的稳态基准值,将性能蜕化因子作为该滤波器的增广状态量进行在线估计,并反馈给机载非线性模型使其完成在线更新.同时,根据工作模式切换机制使该模型获得有效输出.通过将该方法应用于某型涡扇发动机进行一系列仿真表明,在全飞行包线内、不同工作状态以及性能蜕化严重的情况下,该模型能够始终与实际发动机相匹配,满足实际应用需求.      

绕飞慢自旋小天体的航天器运动分析

针对可以用三轴椭球体近似建模的小天体,给出了非球形引力势函数,建立了航天器绕飞小天体的轨道动力学方程。利用Jacobi积分常数绘制了探测器在小天体周围的零速度曲线,并分析了探测器的可能运动区域,给出了航天器不碰撞小天体的边界条件。针对绕飞慢自旋小天体的情况,基于平均轨道根数的近似解分析了小天体扁率和椭率的摄动影响,并给出了几条冻结轨道及其稳定条件。