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This paper presents a real-time relative three-axis attitude estimation using a camera and two gyros under momentum changes during close-proximity operations. The camera sensor provides quaternion measurements that relate the body frame of the deputy spacecraft with respect to the body frame of the chief spacecraft. The quaternion measurements are coupled with gyro measurements and attitude dynamics model in a multiplicative extended Kalman filter to determine relative attitude and gyro biases under momentum changes. The relative quaternion kinematics is augmented with spacecraft relative motion dynamics to represent the filter process dynamics. The quaternion measurements from a camera sensor and inertial measurement units (IMU) are utilized to the filter measurement model. The fault-tolerant attitude controller actuated by four reaction wheels, which has no unwinding problem is used for attitude tracking maneuvers during close-proximity operations in the presence of external disturbances, uncertain inertia parameter and actuator faults. This controller is combined with the extended Kalman filter to filter noisy measurements and to estimate gyro biases, which leads to a full-state feedback control system. Numerical simulations are performed to verify the effectiveness of the attitude estimation and control systems of the spacecraft with four reaction wheels during close-proximity operations of spacecraft in low-Earth orbit. [ABSTRACT FROM AUTHOR]

In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group-affine and its error state model should be trajectory-independent. Moreover, with such a trajectory-independent error state model, the linear Kalman filter is still effective for large initialisation errors. However, the measurement model of the traditional MEKF is dependent on the attitude prediction, which is therefore trajectory-dependent. This is also the main reason why the performance of traditional MEKF is degraded for large initialisation errors. Through substitution of the attitude prediction related term with vector observations in the body frame, a trajectory-independent measurement model is derived for MEKF. Meanwhile, MEKFs with reference attitude error definition and with global state formulating on special Euclidean group have also been studied, with the main focus on derivation of the trajectory-independent measurement models. Extensive Monte Carlo simulations of spacecraft attitude estimation implementations demonstrate that the performance of MEKFs can be much improved with trajectory-independent measurement models. [ABSTRACT FROM AUTHOR]

This study investigates the application of a spaceborne gravity gradiometer to spacecraft attitude determination. Considering that the gradiometer raw measurements are influenced by angular rotation, a gyroscope is integrated to provide angular velocity information. To deal with unknown biases in both gradiometer and gyroscope measurements, a multiplicative extended Kalman filter (MEKF) is developed to estimate the attitude states and the instrument biases simultaneously. In addition, the cross-correlation between gyroscope measurements and gyroscope-compensated gradiometer measurements is analyzed. The MEKF algorithm is modified accordingly to cope with the correlation problem. Simulation scenarios with two different attitude modes are built to test the algorithm. With a gradiometer of 0.1 E (1 E = 10−9 s−2) accuracy and a navigation-grade gyroscope, attitude determination accuracy of several arcsecs is obtained. Real data from the GOCE (gravity field and steady-state ocean circulation explorer) spacecraft are also used to test the algorithm. Yaw, pitch, and roll angle errors of 2.8 arcsec, 20.9 arcsec, and 11.3 arcsec are achieved, respectively. The method can directly estimate a spacecraft's attitude relative to the Earth-centered Earth-fixed (ECEF) frame and is promising for high-precision spacecraft attitude determination in Earth-oriented missions. • The spaceborne gravity gradiometer is used for spacecraft attitude determination. • The attitude states and instrument biases are simultaneously estimated. • The correlation between the process and measurement noises is analyzed. • High-precision attitude determination relative to the ECEF frame is realized. [ABSTRACT FROM AUTHOR]

Summary: In the postcapture stage, relative motion could exist between the target and the robot end‐effector, which is called unfirm capture. Unmodeled and time‐varying dynamic and kinematic coupling in unfirm capture cases obstructs the estimation of target inertia properties and relative motion states. To solve this problem, vision navigation information and general dynamic equations are combined to compensate unknown coupling dynamics based on the extended Kalman filter. To avoid disturbing force and torque reducing the precision of the state estimation, a recursive least square multiplicative extended Kalman filter is developed. By minimizing deviations between expected statistics and real statistics of process noise, this novel filter estimates parameters of the external disturbance. Simulations are carried out to demonstrate the efficiency and effectiveness of the proposed filter. [ABSTRACT FROM AUTHOR]

This work presents a multiplicative extended Kalman filter (MEKF) for estimating the relative state of a multirotor vehicle operating in a GPS-denied environment. The filter fuses data from an inertial measurement unit and altimeter with relative-pose updates from a keyframe-based visual odometry or laser scan-matching algorithm. Because the global position and heading states of the vehicle are unobservable in the absence of global measurements such as GPS, the filter in this article estimates the state with respect to a local frame that is colocated with the odometry keyframe. As a result, the odometry update provides nearly direct measurements of the relative vehicle pose, making those states observable. Recent publications have rigorously documented the theoretical advantages of such an observable parameterization, including improved consistency, accuracy, and system robustness, and have demonstrated the effectiveness of such an approach during prolonged multirotor flight tests. This article complements this prior work by providing a complete, self-contained, tutorial derivation of the relative MEKF, which has been thoroughly motivated but only briefly described to date. This article presents several improvements and extensions to the filter while clearly defining all quaternion conventions and properties used, including several new useful properties relating to error quaternions and their Euler-angle decomposition. Finally, this article derives the filter both for traditional dynamics defined with respect to an inertial frame, and for robocentric dynamics defined with respect to the vehicle's body frame, and provides insights into the subtle differences that arise between the two formulations. [ABSTRACT FROM AUTHOR]

We present a novel algorithm for online, real-time orientation estimation. Our algorithm integrates gyroscope data and corrects the resulting orientation estimate for integration drift using accelerometer and magnetometer data. This correction is computed, at each time instance, using a single gradient descent step with fixed step length. This fixed step length results in robustness against model errors, e.g., caused by large accelerations or by short-term magnetic field disturbances, which we numerically illustrate using Monte Carlo simulations. Our algorithm estimates a three-dimensional update to the orientation rather than the entire orientation itself. This reduces the computational complexity by approximately 1/3 with respect to the state of the art. It also improves the quality of the resulting estimates, specifically when the orientation corrections are large. We illustrate the efficacy of the algorithm using experimental data. [ABSTRACT FROM AUTHOR]

The employment of embedded cameras in navigation and guidance of Unmanned Aerial Vehicles (UAV) has attracted the focus of many academic researches. In particular, for the multirotor UAV, the camera is widely employed for applications performed in indoor environments, where the GNSS signal is often unreliable and electromagnetic interference can be a concern. In the literature, images are mostly adopted for position and velocity estimation, rather than attitude estimation. This paper proposes an attitude determination method for multirotor aerial vehicles using pairs of vector measurements taken from a downward-facing strapdown camera. The method is composed of three modules. The first one detects and identifies the visible landmarks by processing the images. The second module computes the vector measurements related to the direction from the camera to the landmarks. The third module estimates attitude from the vector measurements. In the last module, a version of the Multiplicative Extended Kalman Filter (MEKF) with sequential update is proposed as estimation method. The overall method is evaluated via Monte Carlo simulations, showing that it is effective in determining the vehicle's attitude and revealing its properties. [ABSTRACT FROM AUTHOR]

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In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms.

A major advance of using the quaternion to describe body orientation is that the kinematics equation is linear and the quaternion is also globally nonsingular. However, the algebraic constraint of unit norm needs to be maintained. An improved nonlinear constrained filter algorithm is proposed for the spacecraft attitude estimation problem subject to a unit quaternion norm constraint. First, by comparing the quaternion norm of a priori and a posteriori estimate, it is proved that the Multiplicative Extended Kalman filter can not gain the optimal solution under nonlinear constraint. Then, a generalized quadratically constrained optimization object function is developed by effective combination of QUEST algorithm and Multiplicative Kalman filter. During the predicting state, the attitude and its covariance propagation models are used to modify the cost function. During the measurement update phase, the quaternion normalization is explicitly maintained in a globally optimal manner by solving the eigenvalue-eigenvector problem and therefore the local linearization is avoided. Compared with the Multiplicative Extended Kalman filter, numerical simulation result demonstrates the precision, stability and convergence of the presented algorithm. [ABSTRACT FROM AUTHOR]

Abstract: Multiplicative Extended Kalman Filter (MEKF) is one of the most widely used satellite attitude estimation methods. However, the linearization errorʼs influence is an inherent limitation of this method. In this paper, we aim to analyze this linearization error in the typical satellite attitude determination system with star sensors and gyros. The formulation of linearization error is first derived and the curvature metric is then employed to measure the linearization error. Additionally, we show the reason why linearization error has influence on the performance of MEKF. Based on these analyses, we point out that star sensorsʼ sampling frequency, initial estimated error and accuracy of gyroʼs measurement model are the factors that could enlarge the system modelʼs linearization error. They all affect the linearization error and attitude determination accuracy by decreasing the predicted accuracy. More concretely, the influence of star sensorʼs sampling frequency is large, while initial estimated error and gyroʼs measurement error within a certain range have little influence on MEKF. Finally, combined with plenty of experiments, validity of the above analyses is verified. [Copyright &y& Elsevier]

In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms. [ABSTRACT FROM AUTHOR]