On-orbit Gyroscope Bias Compensation to Improve Satellite Attitude Control Performance

Fault detection and isolation algorithms for LEO satellite attitude determination and control system using an approach for checking the statistical characteristics of EKF innovation sequence are proposed. The fault detection algorithm is based on statistic for the mathematical expectation of the spectral norm of the normalized innovation matrix of the EKF. This approach permits simultaneous real-time checking of the mathematical expectation and the variance of the innovation sequence and does not require a priori information about the faults and statistical characteristics of the system in fault cases. In this study an attitude estimation and control system for LEO satellite is proposed. To determine the attitude of the satellite, this system use algebraic method (two-vector algorithm). As a reference direction, the unit vectors toward the Sun, the Earth’s center, and the Earth magnetic field are used. Thus, it includes three different two-vector algorithms based on using the Earth’s magnetic field – the Sun vector, the Earth’s magnetic field – nadir vector, and nadir vector – the Sun vector couples. In order to increase the attitude determination accuracy, the redundant data processing algorithm, based on the Maximum Likelihood Method, is used. An extended Kalman filter has been developed for nonlinear rotational dynamics estimation of LEO satellite. Failures in the sensors affect the characteristics of the innovation sequence of the EKF. The failures that affect the mean and variance of the innovation sequence have been considered. The application of the proposed fault detection algorithm to the LEO satellite attitude determination and control system has shown that, sensor fault detection by the presented algorithm is possible in real time. Assuming that the effect of the faulty sensor on its channel is more significant than on the other channels, a sensor isolation method is presented by transforming n-dimensional innovation process to n one-dimensional processes. The simulations, carried out on a nonlinear dynamic model of the rotational motion of LEO satellite, confirm the theoretical results. The future work is to investigate the faults affecting the attitude dynamics e.g., actuator faults and to perform the integrated sensor/actuator FDI via innovation approach.

In order to enhance the accuracy and the robustness of the attitude determination and control system in observation satellites, a new way to fuse gyro and star tracker measurement with image registration is described. In this method, a novel and complete framework is proposed to estimate the on-orbit attitude variations from multi-spectrum remote sensing images. An extended Kalman filter is derived to calibrate the gyro bias drift and the star tracker error. The new framework is tested with realistically simulated data and remote sensing images based on JL-1 satellite. Simulation and experiment results indicate that based on the image registration, the satellite attitude variations could be detected in real time and applied for the accurate gyro and star tracker bias calibration.

When satellite is running, it may be influenced by external factors, and the measurement models of gyro and star sensor are changing with time uncertainly. This situation may lead extended Kalman filter(EKF) divergent. So new adaptive filter can be used in this situation, and it can estimate process noise and measuring noise on-time. This paper has applied Sage-Husa adaptive filter in satellite attitude determination. This adaptive filter algorithm can estimate satellite attitude parameters and gyro drift on-time with high accuracy reaching 10-3 level, and stability of the algorithm is also very good.

A highly accurate, gyroless, attitude determination and control system for advanced environmental satellites is developed and validated by analysis and simulation. The features of this approach include an algorithm to determine satellite rates directly from the apparent motion of the stars on the focal plane and an extended square root Kalman filter algorithm to estimate attitude. This system is appropriate for satellites with slowly varying attitude dynamics and high priority accuracy. Missions of this variety are meteorology, Earth resources, communication and surveillance. Appropriate attitude control techniques are reaction wheel and bias momentum system providing three-axis pointing control. The simulation results of the attitude estimation with various noise statistics on the star data are shown. The results of this approach are also compared with the gyro-aided system in accuracy of the attitude estimation process. The results show that the concept presented in the paper does work and that the accuracy would meet a large variety of satellite mission requirements. The major result of this research is the realization of a space-capable stellar attitude determination system which does not require a rate gyro package.

This paper presents a new scheme for fault detection and diagnosis in spacecraft Attitude Determination (AD) sensors. An integrated attitude determination system, which includes measurements of rate and angular position using rate gyros and vector sensors, is developed. Measurement data from all sensors are fused by a linearized Kalman filter, which is designed based on the system kinematics, to provide attitude estimation and the values of the gyro bias. Using this information the erroneous sensor measurements are corrected, and unbounded sensor measurement errors are avoided. The resulting bias-free data are used in the Fault Detection and Diagnosis (FDD) scheme. The FDD algorithm uses model-based state estimation, combining the information from the rotational dynamics and kinematics of a spacecraft with the sensor measurements to predict the future sensor outputs. Fault isolation is performed through Extended Kalman Filters (EKFs). The innovation sequences of EKFs are monitored by several statistical tests to detect the presence of a failure and to localize the failures in all AD sensors. The isolation procedure is developed in two phases. In the first phase, two EKFs are designed, which use subsets of measurements to provide state estimates and form residuals, which are used to verify the source of the fault. In the second phase of isolation, testing of multiple hypotheses is performed. The generalized likelihood ratio test is utilized to identify the faulty components. In the scheme developed in this paper a relatively small number of hypotheses is used, which results in faster isolation and highly distinguishable fault signatures. An important feature of the developed FDD scheme is that it can provide attitude estimations in presence of fault in one type of sensors.

We present the discrete algorithms for filtering measurements, in-flight calibration and alignment of an astroinertial system for attitude and angular rate determination of a maneuvering land-survey satellite.

In this paper, Rauch-Tung-Striebel(RTS) optimal smoothing algorithm is applied to improving off-line satellite attitude determination accuracy. The measurements are first processed by the forward filter, and then, a separate backward smoothing pass is used for obtaining the smoothing solution. The performances between RTS and extended Kalman filter(EKF) in gyro/star-sensor integrated system are compared. RTS smoother exhibits better accuracy and robustness than EKF under the situation of lower sensors precision, different length of data and larger initial attitude error. The results verify the effectiveness and practicability of RTS smoothing algorithm in satellite attitude determination.

This paper discusses the attitude determination of the CNUSAIL-1 cube-satellite. The primary mission of the CNUSAIL-1 is sail deployment and operation in low Earth orbit, and the secondary mission is to look into influence of the sail deployment on satellite attitude and orbit. The attitude determination strategy is proposed depending on three mission phases, and its performance and applicability are verified through numerical simulations. This study considers the following sensors: Sun sensors and a three-axis magnetometer as attitude reference sensors, and a three-axis MEMS gyroscope as an inertial attitude sensor. Because sensors used for cube satellites have relatively low performances and worse noise characteristics, an Extended Kalman filter (EKF) is applied to attitude determination. Additionally, it has the merits to deal with the Gaussian noises and to predict the attitude even with no measurements from reference attitude sensors, especially in the eclipse of the cube satellite. The performance of the EKF is compared to a deterministic attitude determination technique, QUEST(QUaternion ESTimation).

The redundancy allocation problem is to find an optimal allocation of redundant components by considering the set of resources and cost constraints. In this research, the satellite attitude determination and control system is studied and its components is introduced, then the reliability of this system is modeled and optimized based on a mathematical approach based on the redundancy allocation. The model studied in this paper is about the structure of a series-parallel system that is in the exact mode of a satellite attitude determination and control system. In this paper, a new approach for modeling and optimization is presented. The mathematical model presented in this paper is into the class of mixed integer non-linear programming (MINLP). Solving these problems is very important for various researchers due to the high mathematical complexity. In this research, a heuristic method is used to the problem exact solution, the results of which have been reported.

This paper presents a new scheme for fault detection in satellite Attitude Determination (AD) sensors. The proposed method is based on derivation of all possible relations which result in Euler angles and comparison of these angles provided by them. Accordingly, significant changes in the distribution of Euler angles set, is used as a benchmark for fault detection. The features which have been achieved by this philosophy make it possible to provide an analytical approach for fault detection without imposing any additional sensors, mass, power consumption and costs. Also, the outlined method is a free-model based approach which allows combination of this algorithm with the model-based algorithms utilized in the attitude control subsystem. So it provides the detection of sensor faults independent of the actuators situations. The numerical simulations presented in this paper demonstrate the accuracy and robustness of the designed algorithms.

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

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.

In a waist-worn Pedestrian Navigation System (PNS) based on Dead-Reckoning (DR), heading drift caused by Micro-Electro-Mechanical System (MEMS) gyro bias is an essential factor affecting DR accuracy. Considering the characteristics of pedestrian navigation and the poor bias repeatability of MEMS gyros, this paper presents a standing calibration method for MEMS gyro bias. The current gyro biases for each boot can be calibrated accurately in the initial stage before walking. Since the attitude angles calculated by the output data from magnetic sensor and accelerometers do not drift, this paper applies the reverse algorithm of attitude updating to calculate the angular velocities of human motion. Then the gyro biases at each moment can be acquired by subtraction operation between the measured angular velocities from gyros and the calculated angular velocities of human motion. Finally, in order to restrain the random error caused by sensor noise, the calculated biases in the initial stage are smoothed, and consequently the optimal estimate of current gyro biases after each boot can be obtained. Still and dynamic turntable experiments and a walking experiment are performed to compare and analyse the proposed method and the Zero Angular Rate Update (ZARU) method. Experimental results show that the proposed method can also calibrate the gyro bias accurately in the case of body swaying.

The attitude determination system of the RAX satellite

Automatic dependent surveillance-broadcast (ADS-B) is a very important communication and surveillance technology in air traffic control (ATC). In the future, more and more satellites will carry out ADS-B technology to perform a global coverage. In order to make full use of the resources in the satellite, this paper proposes a solution for satellite three-axis attitude determination using the ADS-B receiver. The principle of ADS-B-based attitude determination is presented first. On this basis, ADS-B-based methods are employed to solve the problem. To achieve a higher attitude determination precision, gyro is combined with the ADS-B receiver using a multiplicative extended Kalman filter (MEKF). Finally, a simulation is carried out and the result is presented.