Monocular Vision-based Two-stage Iterative Algorithm for Relative Position and Attitude Estimation of Docking Spacecraft

Relative position and attitude estimation for satellite formation with coupled translational and rotational dynamics

The relative position and attitude estimation of non-cooperative spacecraft is essential to high-precision guidance, navigation, and control systems. This paper mainly proposes a method to measure the relative position, velocity and attitude of non-cooperative spacecrafts using stereo camera and dynamics. First, using stereo camera observe the spacecraft, and extract the feature points of images. Then, calculate the 3D position of the feature points, and match the relationship between the feature points to obtain geometric constraint information between frames. Based on this, the relative position, velocity, attitude and angular velocity of the target spacecraft are calculated. According to relative orbit dynamics and relative attitude dynamics model, design extended Kalman filter to update the measurement results. The simulation results show that the estimation accuracy is better than 0.01m, the relative velocity accuracy is better than 0.001m/s, and the relative attitude accuracy is better than 0.01°. This method can provide technical support for the relative navigation of non-cooperative spacecraft.

This paper presents a novel adaptive iterated extended Kalman filter (AIEKF) for relative position and attitude estimation, taking into account the influence of model uncertainty. Considering a nonlinear stochastic discrete‐time system with unknown disturbance, the AIEKF algorithm adopts the Gauss‐Newton iterative optimization steps to implement a maximum a posteriori (MAP) estimation, and the switch‐mode combination technique is used to achieve the adaptive capability. The mean‐square estimation error (MSE) of the state estimate is derived. It is proved that the AIEKF can yield a smaller MSE than that of the traditional extended Kalman filter (EKF) or iterated extended Kalman filter (IEKF). The performance advantage of the AIEKF is illustrated via Monte Carlo simulations on a typical relative position and attitude estimation application. Through comparisons in different scenarios, the presented algorithm is shown to improve adaptability and ensure estimation accuracy.

Cubature Kalman filtering for relative spacecraft attitude and position estimation

Study of Relative Position and Attitude Estimation and Control Scheme for the Final Phase of an Autonomous Docking Mission

A comparative study of spacecraft attitude determination and estimation algorithms (a cost–benefit approach)

In this paper a novel approach is developed for relative state estimation of spacecraft flying in formation. The approach uses information from an optical sensor to provide multiple line-of-sight vectors from one spacecraft to another. The line-of-sight measurements are coupled with gyro measurements and dynamical models in an extended Kalman filter to determine relative attitude, position, and gyro biases. The quaternion is used to describe the relative kinematics, whereas general relative orbital equations are used to describe the positional dynamics. Three different attitude formulations are presented. The first estimates the relative attitude and individual gyro biases for the chief and deputy spacecraft. The second estimates the relative attitude, and the relative velocity bias and the deputy gyro bias. The third estimates the relative attitude, and the relative velocity bias and the chief gyro bias. Simulation results indicate that the combined sensor/estimator approach provides accurate relative attitude and position estimates.

An algorithm is developed for estimating the motion (relative attitude and relative position) of large pieces of space debris, such as failed satellites. The algorithm is designed to be used by a debris removal system which would perform various operations on space debris such as observation, investigation, capture, repair, refuel and de-orbit. During these operations, the debris removal system must control its position and attitude simultaneously. Such six degree-of-freedom control becomes more difficult if the failed satellite is changing attitude, such as by nutation. The information required as feedback signals for such a controller is relative - position, velocity, attitude and angular velocity - and these are expected to be measured or estimated from image data. The algorithm uses a combination of stereo vision and 3D model matching, applying the ICP (iterative closest point) algorithm, and uses time series of images to increase the reliability of the relative attitude and position estimates. To evaluate the algorithm, a visual simulator is prepared to simulate the on-orbit optical environment in terrestrial experiments, and the motion of a miniature satellite model is estimated using images obtained from the simulator

The first ground test results of the UCLA formation flight control computer (FFCC) are presented. The FFCC are designed to calculate real time, relative states of multiple aircraft accurately enough to fly two F-18 A/C autonomously in formation flight for a drag reduction experiment. This paper compares three schemes of differing complexity for the estimation of relative position, velocity, and attitude of two FFCC. Each scheme processes measurements from a GPS receiver and an INS on each vehicle. In the first scheme, each FFCC estimates its own absolute state using an extended Kalman filter (EKF) and the relative state is found by differencing the absolute state estimates from each filter. In the second scheme, one vehicle processes the single vehicle EKF while the second processes the differential range and Doppler measurements to estimate the relative state. In the third scheme, differential carrier phase measurements are added to the relative state estimation filter. The third scheme meets the target values for flying two NASA F-18 A/C in flight formation. Relative position is estimated within 10 cm, and relative attitude within 0.5 deg.

This article proposes the use of a feedforward neural network (FNN) to select the starting point for the first iteration in well-known iterative location estimation algorithms, with the research objective of finding the minimum size of a neural network that allows iterative position estimation algorithms to converge in an example positioning network. The selected algorithms for iterative position estimation, the structure of the neural network and how the FNN is used in 2D and 3D position estimation process are presented. The most important results of the work are the parameters of various FNN network structures that resulted in a 100% probability of convergence of iterative position estimation algorithms in the exemplary TDoA positioning network, as well as the average and maximum number of iterations, which can give a general idea about the effectiveness of using neural networks to support the position estimation process. In all simulated scenarios, simple networks with a single hidden layer containing a dozen non-linear neurons turned out to be sufficient to solve the convergence problem.

To determine the relative pose between an object and a single camera using 2D-to-3D point correspondences, a kind of iterative methods based on inverse projection ray approach is proposed. An iterative algorithm which is divided into depth recovery stage and absolute orientation stage is also proposed. In the first stage, the optimal translation vector is first computed in terms of rotation matrix via least square method, then the depths of the observed points are estimated by projecting the estimated point orthogonally to the inverse projection ray defined by the image point, and finally 3D points are reconstructed using the estimated depths from previous step. In the second stage, the optimal rotation matrix is estimated by applying Umeyama algorithm to fitting of the 3D model points and 3D estimated points. The above two stages are repeated until the result converges. The global convergence of the two-stage iterative algorithm is proven based on the global convergence theorem. Finally, a spacecraft docking application is implemented to test the effectiveness and convergence of the proposed algorithm by mathematical simulation and physical simulation.

A pose (relative attitude and position) estimation approach to support proximity operations such as autonomous landing of unmanned air vehicles or spacecraft on-orbit servicing is investigated in this paper. An algorithm is developed based on a feature detection capability using the point cloud data that a flash lidar (light detection and ranging) produces. The feature refers to an edge, a corner, or a distinct geometrical shape of an object. Once features are detected, orthogonal triads that are attached to the object are constructed using them. Pose estimation is then performed based on the orientation of the triads with respect to the lidar sensor frame. Since the algorithm employs detected features, it allows pose estimation of an object from a single set of point cloud data. In contrast, the conventional iterative closest point based algorithms typically require two sets of point cloud data. The estimated pose thus represents the changes in pose between the two data sets, leaving the pose of the object with respect to the sensor still to be determined. This featurebased pose estimation capability performs directly an initial pose acquisition with respect to the sensor. The algorithm may also help reduce the number of data points required for pose estimation since a small, selected feature of an object within the sensor field of view can be employed to estimate the pose. Employing the algorithm developed, pose estimation tests were conducted and their preliminary results are presented, which were obtained using a flash lidar in a laboratory testing environment.

This study proposes a complete method for estimating the relative motion parameters of noncooperative targets in space and analyzes the system observability for the optically autonomous relative navigation problem of noncooperative targets in space. First, using the installation offset of the onboard monocular camera, a relative navigation system model is established herein by observing the three feature points of the target using the line-of-sight direction of the feature points as the measurement information and combining the target's relative orbital dynamics, attitude kinematics, and dynamics. Second, the system observability is analyzed based on the system observability matrix and combined with the null-space theory. The conditions under which the system does not satisfy the observability are analyzed through the definition of observability. An iterative extended Kalman filter based on this system model is then derived to realize the complete estimation of the target relative position, relative velocity, target attitude, angular velocity, inertia ratio, and position of the feature points under the target body frame. Finally, the effect of the camera offset on the system observability is analyzed through a numerical simulation. The results verify that an appropriate camera offset can make the monocular relative navigation system fully observable. The only existing unobservable state variable is found at 0 camera offset.

Currently, monocular localization as a category of vision-based indoor localization methods has attracted more attention because of its application to indoor navigation and augmented reality. In a typical monocular localization system, the absolute position estimation is utilized to acquire the initial position of the query camera, and then the relative position estimation is employed to achieve subsequent camera positions. However, accumulative errors, i.e., localization drifts, caused by the relative position estimation seriously affect the localization performance. Therefore, a line model that contains a fitted line segment and some visual features is introduced, and the line model is used to seek inliers of the estimated features for the drift estimation. Based on the pre-constructed dense 3D map, a line model-based drift estimation method is presented to monitor accumulative errors. As a switching mechanism, the proposed method determines when the relative position estimation should switch to the absolute position estimation to correct user positions. Compared with the existing monocular localization methods, the proposed drift estimation method significantly reduces the accumulative errors, and the average errors are limited within a desirable range by giving a proper drift threshold. Experimental results demonstrate that the average localization errors of the proposed method are limited within 30 centimeters in various scenes by a 50-centimeters drift threshold.

IRASSI is an interferometry-based mission concept, composed of five free-flying telescopes orbiting the Sun-Earth/Moon second Lagrange point, L2. IRASSI aims to observe particular regions of the sky, where Earth-like planets are likely to form, such as stellar disks and cold dust clouds. In these regions, important chemical and physical phenomena observable in the far-infrared frequencies (1 to 6 THz) can be recorded, enabling scientists to study star formation and evolution processes, as well as early planetary origins. Such phenomena must be resolved finely by the telescopes, with the angular resolution goal set to 0.1 arcsec or lower. To achieve such granular resolution magnitudes, the interferometer relies on dynamically changing baselines (i.e., physical separation) during the scientific observations. This is coupled with heterodyne detection, which collects and correlates detected signals of a celestial object from all telescopes simultaneously. With such a setup, the telescopes can combine their detected signals at different locations, improving the obtained angular resolution of the observations. In order to precisely correlate the detected far-infrared signals, the baseline vectors between the telescope reference points must be determined with an accuracy of 5 μm. This requirement poses a challenge to existing navigation technology. To overcome this challenge, a ranging system is employed to provide the distance measurements at micrometer-level accuracy between ranging sensors located at each satellite. A further important task is the determination of the lever arms (between the ranging sensor and the telescope reference point) and its orientation in space. Since the position estimation at L2 cannot be provided in absolute coordinates with such high accuracy, the navigation concept consists of two interacting components: (I) the absolute position estimation, with respect to Earth; and (II) the relative position estimation, determining satellite's positions, with respect to each other. For relative positioning, a geometric approach is currently under development, because it is capable of real-time processing. In future work, a semi-kinematic approach is aimed for, i.e., process dynamics is included, in order to increase robustness in case of measurement outliers or missing measurements. For absolute positioning, the Earth-based navigation method has been selected due to its potential to satisfy high accuracy expectations for the initialization of the relative position algorithms. The paper begins with a brief description of the IRASSI mission, where the issue of baseline accuracy determination is introduced. The Nominal Operations phase of the mission is presented in detail, with a focus on formation dynamics. A description of the navigation concepts, including the absolute and relative position estimation, is thereafter provided. The absolute and relative position estimation is analyzed in terms of their dynamic models, observation models and estimation methods. Furthermore, their performance relative to the requirements and overcoming challenges are discussed and compared in terms of their response time and accuracy. The key challenges in the frame of baseline measurement accuracy is then highlighted. Finally, the content of the paper is summarized and the scope of future work concludes the manuscript.