Three-Axis Attitude Estimation Using Rate-Integrating Gyroscopes

In this paper, a method for estimating aircraft att itude is proposed using an accelerometer based device combined with a gyro based sensors for estimating rotational rates. The device incorporates a series of low-cost accelerometers mounted in a circular arc to determine the local gravitational field vector. Once the local gravitational field vector is determined the orientation of the device can be est imated. However, the attitude estimate occurs at discrete time values and therefore is not a continuous estimate. Rate gyros measurements can be integrated producing continuous attitude estimates. However, the attitude estimates produced by rate gyro integratio n tend to drift over time due to drift and bias inherent to the rate gyro sensor. In this pape r, a method for re-initializing the initial condition of the rate gyro integration estimate is proposed using the discrete attitude estimate found from determining the local gravitati onal field vector. In an addition, the rate gyro biases and drift may be computed with knowledge of attitude at discrete intervals and subtracted from the rate gyro measurements producing a more accurate continuous attitude estimate. For this study, pitch angle estimates are only considered to analyze the feasibility of the proposed method but may be easily extended i ncluding the remaining degrees-offreedom. Simulation results of the proposed device are presented including real-world sensor noise and bias/drift effects analyzing the f easibility of the proposed system. A prototype device has been constructed and is currently being tested in a laboratory environment. Results of the simulation study indica te that accurate attitude estimates can be developed in the presence of large rate gyro drift and bias effects.

Attitude and angular velocity estimation is essential for various applications of the user equipment (UE). In gyroscope-free scenarios, how to perform attitude and angular velocity estimation is a critical issue. In this letter, we propose a UE attitude and angular velocity estimation framework with the assistance of channel state information (CSI) variation. We first present a detailed proof of the existence of the mapping from CSI variation to angular velocity. Furthermore, we employ a neural network to learn this mapping, leveraging its capacity to model complex relationships. Then the estimated angular velocity is incorporated into the kinematic model of the gyroscope to derive the current attitude estimate of the UE. Simulation results further substantiate the significant potential of our method as a viable alternative to gyroscopes. Moreover, results also show that more propagation paths leads to better angular velocity and attitude estimation.

NASA and other space agencies have shown interest in sending humans on missions beyond low Earth orbit. Proposed is an algorithm that estimates the attitude of a manned spacecraft using measured line-of-sight (LOS) vectors to stars and gyroscope measurements. The Manual Optical Attitude Reinitialization (MOAR) algorithm and corresponding device draw inspiration from existing technology from the Gemini, Apollo and Space Shuttle programs. The improvement over these devices is the capability of estimating gyro bias completely independent from re-initializing attitude. It may be applied to the lost-in-space problem, where the spacecraft's attitude is unknown.;In this work, a model was constructed that simulated gyro data using the Farrenkopf gyro model, and LOS measurements from a spotting scope were then computed from it. Using these simulated measurements, gyro bias was estimated by comparing measured interior star angles to those derived from a star catalog and then minimizing the difference using an optimization technique. Several optimization techniques were analyzed, and it was determined that the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm performed the best when combined with a grid search technique. Once estimated, the gyro bias was removed and attitude was determined by solving the Wahba Problem via the Singular Value Decomposition (SVD) approach. Several Monte Carlo simulations were performed that looked at different operating conditions for the MOAR algorithm. These included the effects of bias instability, using different constellations for data collection, sampling star measurements in different orders, and varying the time between measurements. A common method of estimating gyro bias and attitude in a Multiplicative Extended Kalman Filter (MEKF) was also explored and disproven for use in the MOAR algorithm.;A prototype was also constructed to validate the proposed concepts. It was built using a simple spotting scope, MEMS grade IMU, and a Raspberry Pi computer. It was mounted on a tripod, used to target stars with the scope and measure the rotation between them using the IMU. The raw measurements were then post-processed using the MOAR algorithm, and attitude estimates were determined. Two different constellations---the Big Dipper and Orion---were used for experimental data collection. The results suggest that the novel method of estimating gyro bias independently from attitude in this document is credible for use onboard a spacecraft.

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.

A method of attitude estimation with a low-cost, strap-on MEMS sensor was proposed in the article. The method relies on dynamic gyroscope bias change estimation and updates during detected stops of the robot. The algorithm has been tested in laboratory with iRobot Roomba robot and should be improved to be useful in an industrial environment. The measurement of attitude of a mobile platform is necessary for correct navigation, especially in autonomous vehicles, which use dead reckoning between position updates from external sources. Since the system is intended to operate indoors, in industrial halls and shops, it cannot avail of GPS and Earth magnetic field sensors because of anomalies, which are common inside the steel constructions. Therefore, the accuracy of the gyroscope-based attitude estimation is significant. The proposed method aims to address the common problem of gyroscope bias drift, by dynamic update of sensor bias and simultaneous use of all gyroscope axes, to improve the quality of the measurements. A popular 3-axial gyroscope and 3-axial accelerometer sensors were used during the test runs. Obtained results suggest that it is possible to improve short-term accuracy of inertial dead reckoning, to get a system that could be of practical use in industrial AGV systems or intelligent vehicles.

This paper proposes using TRIAD and Unscented Kalman Filter (UKF)algorithms in a sequential architecture as a part of the small satellite attitude estimation algorithm. This TRIAD+UKF approach can provide accurate attitude estimates for the satellite by calibrating the magnetometers in real-time. A complete calibration model for the magnetometers, considering bias, scale factor, soft iron and nonorthogonality errors, is assumed. In algorithm's first stage, the TRIAD uses the available vector measurements (e.g. from Sun sensor and magnetometers)to estimate a coarse attitude. In the second stage, these estimated values are used as quaternion measurements in the UKF algorithm, together with angular rate measurements provided by a triad of gyros. The state vector for the UKF is composed of the attitude, gyro biases and the magnetometer error terms. In result, we get fine attitude estimate for the satellite by calibrating the magnetometers against scaling, soft iron, nonorthogonality and bias errors in real-time. We evaluate the algorithm for a hypothetical nanosatellite by numerical simulations. The results show that the attitude of the satellite can be estimated with accuracy better than 1deg and the magnetometers can be fully calibrated.

Pico- and nano-satellites, due to their form factor and size, are limited in accommodating multiple or redundant attitude sensors. For such satellites, Murrell’s implementation of the extended Kalman filter (EKF) can be exploited to accommodate multiple sensor configurations from a set of non redundant attitude sensors. The paper describes such an implementation involving a sun sensor suite and a magnetometer as attitude sensors. The implementation exploits Murrell’s EKF to enable three sensor configurations, which can be operationally commanded, for satellite attitude estimation. Among the three attitude estimation schemes, (i) sun sensor suite and magnetometer, (ii) magnetic field vector and its time derivative and (iii) magnetic field vector, it is shown that the third configuration is better suited for attitude estimation in terms of precision and accuracy, but can consume more time to converge than the other two.

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.

This paper details a method to improve accuracy of the land vehicle attitude estimation. It employs the vehicle model constraints to enhance the integration of GPS and a low-cost MEMS inertial measurement unit (MIMU) (GPS/MIMU). To improve the yaw angle estimation, we propose a lateral velocity constraint (LVC) aided method based on the observability analysis for the integrated fusion system. The theoretical analysis indicates that the yaw angle will be directly observed if LVC is augmented into the GPS/MIMU fusion algorithm. Furthermore, for LVC/MIMU system without GPS, the roll angle is always well estimated regardless of whether the vehicle is moving or stationary, and, surprisingly, the pitch angle can also be relatively accurately estimated if the vehicle is moving. Thus, when GPS is unavailable, the LVC/MIMU fusion is proposed by replacing the GPS measurement with the virtual measurement LVC. It is an encouraging improvement since the accumulating errors induced by gyro bias can be suppressed using MIMU alone. Moreover, to overcome the shortage that the pitch angle is not observed if the vehicle is stationary, we propose to fuse the gyros with gravity-based angles by Kalman filtering if the vehicle is detected motionless based on a switching rule. The experimental results compare favorably to theoretical analysis, showing that the proposed method can effectively improve the accuracy for land vehicle attitude estimation.

Measurement of the geomagnetic field provides a reliable and economical basis for determining the attitude of low-Earth orbiting three-axis stabilized spacecraft. Magnetometers are often part of the momentum management system, working in parallel with the onboard attitude control system (ACS). They may also be used as primary ACS sensors for missions with relatively coarse pointing requirements or for acquisition or contingency control modes on fine-pointing star tracker-based missions. When used in combination with strap-down gyroscopes for rate determination, magnetometer data can be filtered to obtain surprisingly accurate attitude estimates. The attainable accuracy depends on the specifics of the gyroscope quality, prior magnetometer calibration, the length of the data set, and to a lesser extent, the orbital details. It has been found, though, that even with very clean sensor data the magnetometer residuals still show systematic variations arising from small errors in the reference Earth magnetic field model. Two filters have been developed to estimate and compensate for the reference field errors along with the attitude and gyroscope biases. The field errors are modeled as sequentially correlated random variables. In the first filter, the autocorrelation of the error is assumed to decay exponentially in time. In the second, the autocorrelation is a decaying sinusoid. The resulting attitude estimates are improved by 40 percent (to 126 arcsec) and the bias estimates by a factor of two. With these improvements, autonomous onboard attitude control using magnetometers and gyroscopes becomes practical for a much broader class of missions.

Requirements of highly precise pointing performance have been imposed on recently developed spacecrafts for a variety of missions. The stringent requirements have called on on-orbit estimation of spacecraft dynamics parameters and calibration of on-board sensors as indispensible practices. Consequently, on-orbit estimation of the mass moment of inertia of spacecraft has been a major issue mostly due to the changes by solar panel deployment and a large portion of fuel consumption (Creamer et al., 1996; Ahmed et al., 1998; Bordany et al., 2000; VanDyke et al., 2004; Myung et al., 2007; Myung & Bang, 2008; Sekhavat et al., 2009). As for measurement sensors, on-board calibration of alignment and bias errors of attitude and rate sensors is one of the main concerns of attitude sensor calibration researches (Pittelkau, 2001 & 2002, Lai et al., 2003). Pittelkau (2002) proposed an attitude estimator based on the Kalman filter (Kalman, 1960), in which spacecraft attitude quaternion, rate sensor misalignment and bias, and star tracker misalignments are taken into consideration as states, whereas the body rate is dealt as a synthesized signal by the estimates. Lai at al. (2003) derived a method for alignment estimation of attitude and rate sensors based on the unscented Kalman filter (UKF) (Julier and Uhlmann, 1997). Ma and Jiang (2005) presented spacecraft attitude estimation and calibration based only magnetometer measurements using an UKF. An interesting point is that we need predesigned 3-axis excitation manoeuvres of spacecraft for both dynamics parameter estimation and sensor calibration. Therefore, this study is motivated to merge above estimation and calibration processes into a single filtering problem. It is noteworthy that poor information of moments of inertia is to be treated as a system uncertainty while the rate sensor model errors are to be incorporated into the measurement process. As a filtering algorithm, this study employs a UKF. Extended Kalman filters (EKFs) have been successfully applied to the nonlinear attitude estimation problem (Crassidis et al., 2007). Hybrid estimation using the EKF has been reported by Myung at al. (2007). However, the EKF estimates using the first order linearization, which may lead to instability of the filter (ValDyke et al., 2004). The UKF approximates the nonlinear model to the second order by spreading points 1 sigma apart from the a priori mean. Performing nonlinear

Attitude control system plays the important role for to maintain the satellite to desired orientation. To control the satellite it is necessary to do the attitude stabilization. Attitude stabilization achieved by Star sensor, sun sensor, Earth sensors. Attitude control is mainly use for antenna pointing accuracy, camera focus to earth surface and solar panel pointing toward sun. Due to tumbling effects, satellite will rotate all the direction in the space. To maintain the orientation of the satellite it is necessary to design the attitude determination and control. Satellite consider as the rigid body. Inertia matrix describes the rigid body dynamics. The orientation of the satellite determine by Euler angle and Quaternion. The Low earth orbiting satellite will have enormous amount of aerodynamic drag stinking the satellite body and gravitational attraction another problem. Because of that satellite dwell, time is reduced. It means satellite more time spending particular part of the earth. The attitude estimation is measures by the orientation of vectors. Attitude estimation means to find the position and orientation of flying object with respect to the fixed reference of reference. Vector remains considered in the frame of reference to compute for find the orientation of the body of the satellite in the inertial reference system. The Earth is an inertial reference frame, and Satellite is a body frame. Attitude sensor used to measure the satellite orientation in the reference frame. This will help in accurately predicting the orbit deviation and a control system to correct if any by providing the satellite momentum means ‘mass in motion’ changes in a body rapidly in Low earth orbit due to centripetal force acting on a satellite. Attitude control system (ACS) need the numerical simulation to find the required torque demand by the help of difference between reference input (Attitude) signal and feedback signal measure by attitude sensor to trim the control surface maintain the actuator required orientation . The results will consist of two parts the first part consisting of the attitude estimation using Euler angle and Quaternion method, second part consist of estimate the control torque from magnetic torquer and error estimation using non-linear filter (Unscented Kalman Filter) with MATLAB simulation. Â

In navigation and motion control of an autonomous vehicle, estimation of attitude and heading is an important issue, especially when the localization sensors such as global positioning system (GPS) are not available and the vehicle is navigated by the dead reckoning (DR) strategies. In this paper, based on a new modeling framework, an extended Kalman filter (EKF) is utilized for estimation of attitude, heading, and gyroscope sensor bias using a low-cost microelectromechanical system (MEMS) inertial sensor. The algorithm is developed for accurate estimation of attitude and heading in the presence of external disturbances including external body accelerations and magnetic disturbances. In this study, using the proposed attitude and heading reference system (AHRS) and an identified surge dynamic model of an autonomous underwater vehicle, a low-cost model-aided DR navigation system has been designed for an AUV. The proposed algorithm application is evaluated by experimental tests in different acceleration bound and existence of external magnetic disturbances for an AUV. The results indicate that the roll, pitch, and heading are estimated by mean value errors about 0.35°, 0.29°, and 1.27°, respectively. Moreover, they indicate that a relative navigation error about 8% of the traveling distance can be achieved using the developed approach in during GPS outages.

We address the problem of attitude and rate gyro bias estimation based on inertial and range data. Range measurements are obtained from beacons installed in an inertial frame and acoustic sensors fixed in the moving body reference frame. A nonlinear observer is proposed and its stability and performance properties are studied using Lyapunov techniques. In the presence of constant bias on the rate gyro measurements, the attitude and bias estimates are shown to converge exponentially to the desired values inside an almost global region of attraction. For time-varying bias with bounded derivative, a local result of ultimate boundedness is provided. The performance of the proposed nonlinear observer is validated experimentally using a high-accuracy calibration table, which provides ground-truth signals for comparison with the resulting estimates.

Attitude and gyro bias estimation for a VTOL UAV