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

The FORMOSAT-5 (FS-5), the fifth space program initiated in 2008, is currently developed by National Space Organization (NSPO) of the National Applied Research Laboratories (NARL) in Taiwan, Republic of China (ROC). The satellite will be deployed into a sun-synchronous orbit with 720-km altitude and 98.28o inclination angle. It is a threeaxis attitude stabilized spacecraft providing high precision attitude determination and control for a high resolution Remote Sensing Instrument (RSI). To meet the 0.012 deg, 3sigma, per axis, absolute bus attitude knowledge requirement flown-down from RSI for meeting its geo-location accuracy, the micro-Advanced Stellar Compass (ASC) consisting of three Camera Head Units (CHUs) along with four single-axis fiber-optics gyros is mounted on a stable optical bench common to the RSI structure. The ASC is a highly advanced and fully autonomous star tracker produced by the Measurement & Instrument System (MIS) Section of the Orsted Department of the Technical University of Denmark (DTU). The gyroscopes considered in this mission are the fiber-optics rate sensors, -FORS6U, manufactured by Litef, a Northrop Grumman branch in Germany. The -FORS6U was originally designed to meet the requirements of a wide range of air, land, and sea applications, and was later certified by NSPO for space applications after a series of environmental tests. The primary spacecraft attitude and rate determination for the spacecraft Attitude and Orbit Control System (AOCS) will be provided by a gyro-stellar attitude determination system, which utilizes attitude data provided by three CHUs and rate data provided by the four single-axis fiber-optics gyros. To account for the possibility of more than one gyro failures due to lack of space-flight heritage, a gyro-less attitude and rate determination algorithm is developed as a back-up for the AOCS design. This paper describes the detailed development of a gyro-less attitude and rate determination algorithm which uses the computed gyro data (numerical gyro data) instead of physical gyro data as in a typical gyro-stellar attitude determination system. The numerical gyro data are computed using the assumed spacecraft dynamics (or Euler equations of motion). By perturbing the spacecraft kinematic equations, the linearized attitude error equations are obtained. Similarly, by perturbing the spacecraft dynamic equations, the linearized rate error equations are obtained. With the obtained linearized attitude error equations and the linearized rate error equations, a reduced-order (6-state) Extended Kalman Filter (EKF) providing spacecraft attitude and rate estimates is then implemented in the algorithm. The developed gyro-less attitude and rate determination algorithm was incorporated and tested in a 6-DoF nonlinear, high-fidelity simulation model developed for the FS-5 program to assess its performance. Its performance estimates and sensitivities to spacecraft inertia tensor uncertainties, reaction wheel momentum uncertainties, and torque uncertainties produced by torque-rods during normal operations will be presented in the paper.

Current emphasis on low-budget missions involving small spacecraft leads to a need for an efficient and effective algorithm for attitude and rate estimation. This paper investigates the performance of a Pseudo-Linear Kalman Filter (plkf) with continuous-time dynamics for attitude and rate estimation. The plkf differs from the traditional Extended Kalman Filter (ekf) with its continuous-time dynamics performing estimation using a pseudo-linear state-dependent dynamic model. Both quaternion-based and vector-based measurements have been considered and the dynamic model of the spacecraft accounts for external environmental disturbances. Using computer simulations, the designed filter is shown to overcome large initial errors and yields accurate estimates. The performance indices used for evaluation are based on robustness against plant, measurement and initial estimate errors. While the ekf remains more robust for some cases of angular velocity estimation, the plkf, in general, outperforms the ekf in attitude estimation.

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

We consider the attitude and gyro-bias estimation as well as the attitude stabilization problem of a rigid body in space using low-cost sensors. We assume that a biased measurement of the angular velocity of the rigid body is provided by a low-cost gyroscope, and the attitude measurements are obtained using low-cost (low-pass) sensors such as accelerometers and magnetometers. We provide an attitude and gyro-bias estimation algorithm using the biased gyro measurement and the attitude measurements - which represent the true attitude only at low frequencies - provided by the low-cost attitude sensors. Finally, the proposed estimation algorithm is coupled with a quaternion-based attitude stabilization scheme, and simulation results are provided to show the effectiveness of the proposed algorithm.

Accurate estimation of the attitude of unmanned aerial vehicles (UAVs) is crucial for their control and displacement. Errors in the attitude estimate may misuse the limited battery energy of UAVs or even cause an accident. For attitude estimation, proprioceptive sensors such as inertial measurement units (IMUs) are widely applied, but they are susceptible to inertial guidance error. With antenna arrays currently being installed in UAVs for communication with ground base stations, we can take advantage of the array structure in order to improve the estimates of IMUs. In the state-of-the-art attitude estimation algorithm, the first crucial step is phase delay estimation, which directly affects the attitude estimation performance. In this paper, by exploiting the parallelogram shape of the crossshaped antenna array, a 2-D unitary ESPRIT is used for phase delay estimation to achieve high attitude accuracy as well as computational efficiency. Moreover, we relax the known yaw to unknown case by adding an additional pair of antennas along the normal direction of the body-wing plane. The extension from one frequency bin to the case of multiple frequency bins is also included. Simulations show the feasibility of our proposed solution for different SNR levels as well as multipath scenarios.

Attitude determination & control system design for gravity recovery missions like GRACE

Aiming at the attitude estimation errors existed in the attitude measurement system using the magnetic, angular rate and gravity (MARG) sensors, a novel attitude compensation algorithm based on the neural network using data from sensor networks is proposed in this paper. It provides a more accurate measurement with simple implementation. A simple Kalman filter (KF) is designed to achieve prior attitude estimation. A back-propagation neural network is designed to compensate the attitude errors for the KF. The neural network is trained by the data from MARG sensor networks and errors of attitude estimation algorithm. Taking the data from triaxial MARG sensors as inputs, the trained network could predict the estimated attitude errors in Euler-angles form. Moreover, to validate the effectiveness of the proposed algorithm, two different experiments are accomplished. In the first experiment, the designed neural network is utilized to compensate the attitude estimation errors of a micro quadrotor helicopter using the publicly available datasets. In the second experiment, the KF is combined with the neural network to estimate the attitude of a self-designed single axis platform. Results show that the estimated attitude is closer to actual attitude after compensation which indicates that it is effective to utilize the neural network to compensate for estimation errors in attitude detection field even the attitude estimation algorithm is a simple Kalman filter.

The attitude determination system of the RAX satellite

Due to the advancement of nano-satellite technology, CubeSats and fleets of CubeSats can form an alternative to high-cost large-size satellite missions with the advantage of extended spatial coverage. One of these initiatives is the Cubesats Applied for MEasuring and LOcalising Transients (CAMELOT) mission concept, aimed at detecting and localizing gamma-ray bursts with an efficiency and accuracy comparable to large gamma-ray space observatories. While precise attitude control is not necessary for such a mission, attitude determination is an important issue in the interpretation of gamma-scintillator detector data as well as for telemetry. The employment of star trackers is not always a viable option for such small satellites, hence another alternative is necessary. In this correspondence we present a new method, utilizing thermal imaging sensors to provide simultaneous measurement of the attitude of the Sun and the horizon by employing a homogeneous array of such detectors and show that with the proposed setup the location of an infrared point source can be determined with an accuracy of 400. We also introduce our ongoing work on a simulation model aimed at testing the applicability of our attitude determination algorithm. The first part of the simulation determines the orbit and rotation of a satellite with arbitrary initial conditions while its second part will do the attitude determination based on a multiplicative extended Kalman filter..

Flying vehicle’s navigation, direction, and control in real‐time results in the design of a strap‐down inertial navigation system (INS). The strategy results in low accuracy, performance with correctness. Aiming at the attitude estimation problem, many data fusion or filtering methods had been applied, which fail in many cases, which attains the nonlinear measurement model, process dynamics, and high navigation range. The main problem in unmanned aerial vehicles (UAVs) and flying vehicles is the determination of attitude angles. A novel attitude estimation algorithm is proposed in this study for the unmanned aerial vehicle (UAV). This research article designs two filtering algorithms for fixed‐wing UAVs which are nonlinear for the attitude estimation. The filters are based on Kalman filters. The unscented Kalman filter (UKF) and cubature Kalman filter (CKF) were designed with different parameterizations of attitude, i.e., Euler angle (EA) and INS/unit quaternion (UQ) simultaneously. These filters, EA‐UKF and INS‐CKF, use the nonlinear process and measurement model. The computational results show that among both filters, the CKF attains a high accuracy, robustness, and estimation for the attitude estimation of the fixed‐wing UAV.

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.

This paper introduces the three-axis attitude control of the ESAT platform. ESAT is a modular nanosatellite that implements the popular 10x10x10 cm CubeSat standard, designed for hands-on learning at different educational levels as well as professional training. ESAT features the full set of characteristic spacecraft subsystems (power, on-board data handling, attitude control, communications, and payload). The satellite can be disassembled to focus on each subsystem, one at a time, or used all together, and features a flexible ground segment. Courses using the ESAT platform are imparted in our university, as part of the last year of the master’s degree in Aerospace engineering, and in other institutions like the ESA Academy. They cover aspects ranging from subsystems design to testing and spacecraft operations. In addition, the platform is used in master’s thesis and research activities. Although the version that is currently being used in the courses allows only one-axis attitude control, the ESAT is in continuous development and two prototypes of the satellite have already been developed that allow three-axis control based on reaction wheels and/or magnetorquers, which is essential for the testing and verification of attitude determination and control algorithms. For this purpose, the ground support equipment has also been updated to be able to carry out the turns in three axes, with the development of new testbeds and a complete magnetic field simulator. The present work aims to show the new three-axis platform designs and its main functionalities

Are External Magnetic Disturbances Suppressed by Magnetometer Noise when Estimating a Nanosatellite’s Rotational Motion?

During subsea lifting operations in harsh sea conditions, the involved crane system is subjected to extensive dynamic forces due to vertical vessel motion. Thus, active heave compensation systems can be used to compensate for vertical vessel motion and to reduce forces acting on the crane structure. Furthermore, such systems allow an exact positioning of the load on the seabed. However, active heave compensation systems always require knowledge about the vertical position of the crane depending on the ship's heave, roll, and pitch motion. Hence, an attitude estimation method for ships during subsea lifting operations is proposed. To estimate the roll and pitch motion of a vessel with high accuracy, rotation rate sensors are fused with accelerometers using an Extended Kalman Filter. Since an exact knowledge of the yaw motion is not required to determine the crane's vertical motion, the yaw angle is stabilized around zero with an additional virtual sensor signal. The attitude estimation algorithm is evaluated with simulation and measurement results from an experimental setup.

Accurate three-step algorithm for joint source position and propagation speed estimation