Spacecraft Attitude Estimation Research Articles

A meticulous covariance adaptive Kalman filter for satellite attitude estimation

Aiming at the problems of model errors, non-Gaussian noise and measurement anomaly in the spacecraft attitude estimation system, this article proposes an improved adaptive filtering method based on covariance matching, which solves the problems of simultaneous dynamics model error and measurement model error in the attitude estimation system, and at the same time, effectively reduces the effects of non-Gaussian noise and large outlier situations occurring in the vector measurement sensor. Firstly, an adaptive filtering algorithm based on the innovation sequence estimation covariance is investigated under the framework of multiplicative extended Kalman filter (MEKF), which is used to correct process noise covariance, then the Sage–Husa adaptive Kalman filtering (SHAKF) method is combined to correct the measurement noise covariance, and finally the meticulous covariance adaptive multiplicative extended Kalman filter is designed. The proposed algorithm uses both innovation and SHAKF methods to correct the two covariance matrices simultaneously. Several attitude estimation simulation scenarios are set up to simulate the proposed algorithm in the presence of model errors, non-Gaussian noise, and large outlier. The simulation results demonstrate that the proposed algorithm outperforms the conventional algorithms in terms of estimation accuracy and robustness.

Slow-Spinning Spacecraft Cross-Range Scaling and Attitude Estimation Based on Sequential ISAR Images

Slow-Spinning Spacecraft Cross-Range Scaling and Attitude Estimation Based on Sequential ISAR Images

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

This paper proposes a novel robust adaptive filter that combines smooth variable structure filter and extended Kalman filter for the spacecraft attitude estimation with model uncertainty originating from gyro drift, parameter error, and installation error. The proposed filter employs the extended Kalman filter based on quaternion and fuses an adaptive factor and smooth variable structure filter to improve robustness to the model uncertainty and noise. To improve the robustness of the extended Kalman filter, an adaptive factor that tunes the predicted covariance matrix is utilized to design the attitude estimation strategy. Moreover, to further decrease the impact of the suddenly rapid maneuvering and improve its robust effect of model uncertainty induced by dynamic error, gyro drift, and so on, a smooth variable structure estimation strategy founded on sliding mode theory is derived and utilized for the satellite attitude estimation. Thereby, a novel filtering algorithm is proposed by incorporating an adaptive factor and a smooth variable structure estimation strategy. Simulation results indicate that our proposed algorithm delivers exceptional robustness and achieves high precision and accuracy in satellite attitude estimation compared with the traditional extended Kalman filter.

Spacecraft attitude estimation based on temperature measurements in cuboid configuration

In any spacecraft mission it is vital to have knowledge about the attitude. In this context, multiple ways can be employed to estimate the current attitude of the spacecraft. As temperature sensors are cheap and lightweight they appear to be a viable alternative. A method is investigated to estimate the attitude of a spacecraft based on twelve temperature sensors in a cuboid configuration. The method relies on a proposed mathematical model governing the temperature and attitude dynamics and employs non-linear observer design. Further, it is investigated if the attitude estimation is still possible if some of the sensors are malfunctioning. The proposed algorithms are validated using real mission data.

Error-Covariance Reset in the Multiplicative Extended Kalman Filter for Attitude Estimation

This paper presents a study of the reset step in the multiplicative extended Kalman filter (MEKF). This filter is widely used for spacecraft attitude estimation, which typically involves estimating the attitude and gyro drift in real time using external sensors such as star trackers. The basic idea of the MEKF is to use the quaternion or direction-cosine matrix as the “global” attitude parameterization and a three-component state vector for the “local” parameterization of attitude errors. The true attitude is expressed as the product of the error attitude and the estimate rather than as the sum of the error and the estimate. The reset operation moves the local error to the global variable. This reset does not add new information, but it changes the reference frame for the attitude error covariance. This results in an error-covariance reset that is very different from the measurement update of the error covariance in the MEKF. The effects of using an error-covariance reset in the MEKF are analyzed in this work. The results from this work can be applied to any application involving attitude estimation as part of its process, such as inertial navigation.

Robust filtering for spacecraft attitude estimation systems with multiplicative noises, unknown measurement disturbances and correlated noises

Unknown measurement disturbances and correlated noise caused by jitter or vibration phenomena during spacecraft operation and the complex external environment are important topics for spacecraft attitude estimation. This paper studies the problem of spacecraft attitude estimation for nonlinear systems with multiplicative noises, unknown measurement disturbances and correlated noises. In addition, a two-step prediction framework is used to complete the noise decoupling. This paper aims to design a robust filter that minimizes the upper bound of the prediction error covariance and estimation error covariance in the presence of multiplicative noises, correlated noises and unknown measurement disturbances. The prediction gain and filtering gain of the robust filter are designed to minimize the upper bound. Finally, the simulation results verify the effectiveness of the proposed filter.

A novel stochastically stable variational Bayesian Kalman filter for spacecraft attitude estimation

AbstractIn the context of nonlinear systems, variational Bayesian filters play an important and alternative role to sampling‐based Monte Carlo methods. Although they have been used in conjunction with derivatives of Kalman filters, their behavior, both in terms of convergence, stability, and a solution without a stepwise approximation procedure, has not been well explored. In this paper, we propose a novel, stochastically stable, stepwise approximation‐free variational Bayesian Kalman filter (hence, termed as VBKF) for nonlinear systems. The proposed filter, unlike other posterior distribution estimation methods, is very flexible with the number of parameters that should be known a priori, offers an excellent convergence rate, stochastic stability, and more specifically in its ability to handle non‐Gaussian, unknown, inaccurate and drifting noise models. Furthermore, one of the key advantages of the proposed solution is that it is stepwise approximation‐free, and as such, less computationally demanding. We also prove that the proposed filter is stochastically stable using the Posterior Cramér–Rao Lower Bound. In addition to the stability, by using Lyapunov function, we show that the estimation errors are exponentially bounded by the mean square error under certain conditions. In addition to this, we also demonstrate the practical applicability of the proposed approach by developing a novel filter for estimating the attitude of spacecrafts using star cameras and gyro‐sensors. We then evaluate the efficacy of the novel filter for attitude estimation, and thus that of the VBKF, using a set of detailed simulations mimicking different initialization errors that are common in attitude estimation. Our results show that the proposed approach offers an excellent convergence rate within conventional bounds, better root mean square error when compared against several of the common, and state‐of‐the‐art methods.

Magnetometer-Only Kalman Filter Based Algorithms for High Accuracy Spacecraft Attitude Estimation (A Comparative Analysis)

Kalman Filter (KF) based algorithms are the most frequently employed attitude estimation algorithms. Typically, a fully observable system necessitates the use of two distinct sensor types. Therefore, relying on a single sensor, such as a magnetometer, for spacecraft attitude estimation is deemed to be a challenge. The present investigation centers on utilizing magnetometers as the exclusive sensor. Several KF based estimation algorithms have been designed and evaluated to give the designer of spacecraft Attitude and Orbit Control System (AOCS) the choice of a suitable algorithm for his mission based on quantitative measures. These algorithms are capable of effectively addressing nonlinearity in both process and measurement models. The algorithms under examination encompass the Extended Kalman Filter (EKF), Sequential Extended Kalman Filter (SEKF), Pseudo Linear Kalman Filter (PSELIKA), Unscented Kalman Filter (USKF), and Derivative Free Extended Kalman Filter (DFEKF). The comparison of the distinct algorithms hinges on key performance metrics, such as estimation error for each axis, computation time, and convergence rate. The resulting algorithms provide numerous benefits, such as diverse levels of high estimation accuracy (with estimation errors ranging from 0.014o to 0.14o), varying computational demands (execution time ranges from 0.0536s to 0.0584s), and the capability to converge despite large initial attitude estimation errors (which reached 170o). These properties render the algorithms appropriate for utilization by spacecraft designers in all operational modes, supplying high-precision attitude estimations better than (0.5o) despite high magnetometer noise levels, which reached (200 nT).

Adaptive robust maximum correntropy cubature Kalman filter for spacecraft attitude estimation

In this paper, an adaptive robust maximum correntropy cubature Kalman filter (AMCCKF) for spacecraft attitude estimation is proposed. The main aim is to enable the algorithm to resist the influence of noise non-Gaussian and insufficient statistical information on process noise in the system. Based on the maximum correntropy criterion in this study, the robust filtering algorithm is derived by establishing the regression model. In addition, the Cauchy kernel function is used to replace the Gaussian kernel function in the cost function to prevent a singular matrix from appearing in algorithm operation. Furthermore, the process noise is corrected by an adaptive fading factor. The quaternion normalization problem is solved by constructing a minimum constraint cost function using additive quaternion property. The simulation results show that the proposed AMCCKF algorithm has better estimation accuracy and robustness under the conditions of non-Gaussian noise and insufficient statistical information of process noise.

Improved Maximum Correntropy Unscented Kalman Filter for Spacecraft Attitude Estimation

Improved Maximum Correntropy Unscented Kalman Filter for Spacecraft Attitude Estimation

Three-axis high-accuracy spacecraft attitude estimation via sequential extended Kalman filtering of single-axis magnetometer measurements

Magnetometer is a highly advantageous sensor for determining a spacecraft’s attitude. This article provides a solution to the problem of spacecraft attitude estimation using magnetometer measurements only. To ensure full observability of spacecraft attitude states, it is necessary to use at least two types of sensors. Consequently, utilizing a single sensor, such as the magnetometer, poses a significant challenge for any attitude estimation algorithm, including the extended Kalman filter (EKF). Moreover, implementing the EKF algorithm, or any other attitude estimation algorithm, is computationally intensive. To address these issues, an algorithm has been developed that estimates spacecraft attitude angles and attitude rates using a sequential extended Kalman filter (SEKF). This algorithm offers numerous benefits over those found in the literature such as high accuracy, low computational resource requirements, the ability to converge even with large initial attitude and angular velocity estimation errors, and the ability to function even if two of the three measurement channels of the magnetometer are not functioning. With these benefits, the developed SEKF algorithm is capable of operating in all spacecraft operational modes, delivering accurate performance and computation time. In spite of measurements with large noise values, the high accuracy achieved by the SEKF algorithm enables the magnetometer to serve as the sole source of attitude information, even if one or two magnetometer measurement channels are not functioning.

Calibration Method of MEMS Gyroscopes Using a Robot Manipulator

Inertial measurement units composed of microelectromechanical systems (MEMS) gyroscopes are widely used sensors for small spacecraft and nanosatellite attitude estimation, control, and orientation. This is due to the fact that when developing nanosatellites, it is convenient to use devices of small dimensions and low energy consumption, which are advantages of MEMS sensors. However, one of the significant disadvantages of these measuring devices is their relatively low accuracy, which is related to systematic and random errors. For this reason, this article proposes a method for calibrating MEMS-based angular rate sensors using a robot manipulator for partial elimination of these errors. There are high-precision rotary calibration stands on the market that are designed to set angular rates and orientations when testing products of various types and accuracy classes. Similarly, a robot manipulator represents a possible option for performing this task. As a result, a modified six-position method as a sequence for performing laboratory calibration using a robot joint for high-precision rotation is proposed. The features of the results of processing experimental measurement data of tests have been validated on MEMS angular rate sensors. After calibration, the quality of MEMS gyroscope output data using this calibration approach was significantly improved.

Spacecraft attitude estimation under attitude tracking maneuver during close-proximity operations

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.

Multiplicative extended Kalman filter ignoring initial conditions for attitude estimation using vector observations

AbstractIn 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.

Decomposed Algorithm for Spacecraft Attitude Estimation in Stellar Correction Mode

Decomposed Algorithm for Spacecraft Attitude Estimation in Stellar Correction Mode

Geomagnetic storms in the context of spacecraft attitude estimation under different noise levels

This study examines geomagnetic storm conditions for attitude estimation of a spacecraft having magnetometers with various measurement noise levels at low Earth orbit. The geomagnetic field models are introduced by taking the external field effects into account. It is important to discuss the limitations of the models and the measurements that are being used. Therefore, the external effects are evaluated under different noise levels of magnetometer to determine and discuss the suppression level caused by the noise levels in a general framework. External magnetic field effects are examined by the ratio to noise under various magnetometer standard deviations up to 300 nT. An analysis is carried out for attitude estimation using Kalman-type filter in order to determine what noise level is acceptable on a particular sensor with a specified attitude requirement, magnetic field model, and space weather conditions.This study indicates that external magnetic fields are vital for establishing attitude processes based on magnetometers with varying noise on which the spacecraft relies for accuracy.

A combined configuration (αβ filter- TRIAD algorithm) for spacecraft attitude estimation based on in-Orbit Flight Data

A combined configuration (αβ filter- TRIAD algorithm) for spacecraft attitude estimation based on in-Orbit Flight Data

Attitude Estimation of On-Orbit Spacecraft Based on the U-Linked Network

Real-time attitude estimation of on-orbit spacecraft is a core task in various space applications. Most of the existing methods are based on long-term observation by high-resolution sensors, such as space-borne cameras and ground-based radars. However, when the observation period is limited, it is difficult to obtain target instantaneous attitude information by these methods. To achieve instantaneous attitude estimation from a single camera image, a U-Linked network (ULNet) is proposed in this work. The prior structural constraints of key points are used to reflect the relationship between three-dimensional (3D) target attitude parameters and two-dimensional (2D) images. In this way, target attitude estimation can be solved through the feature point regression when the large-perspective image dataset can be built. The simulation results confirm the feasibility of the proposed method. Besides, the estimation performance of the proposed method also is investigated under different imaging observation conditions.

Instantaneous Attitude Estimation of Spacecraft Utilizing Joint Optical-and-ISAR Observation

Estimation of the instantaneous attitude of spacecraft plays significant roles in space situation awareness activities, such as on-orbit status monitoring and collision warning. With the rapid development of both optical sensors and inverse synthetic aperture radar (ISAR), it becomes possible to achieve accurate instantaneous attitude estimation of spacecraft by multistatic optical-and-ISAR joint observation. In view of this, this article proposes a novel spacecraft attitude estimation method based on a joint optical-and-ISAR observation system, which includes one optical sensor and two ISARs. Specifically, the proposed method first estimates the orientation and the length of typical components utilizing optical and ISAR images with the same observation instant. Then, it solves the target instantaneous rotation vector from the orientation, length, and Doppler of typical components, and finally, it obtains the instantaneous attitude of the spacecraft. Experimental results have verified the effectiveness of the proposed method.

Compensation Filtering for Spacecraft Attitude Estimation Using Error-Covariance Reconstruction

Traditional spacecraft attitude estimation algorithms normally require the assumption that the true quaternion approximates to the estimated value. Otherwise, it may lead to a large truncation error. However, this assumption is difficult to be always satisfied during practical applications. To alleviate it, this article proposes a new scheme to reconstruct the error covariance matrix to minimize this truncation error. Specifically, the recursive formulas of measurement updates used in traditional algorithms are recalculated with the quaternion derived from the attitude update, which can reduce the influence caused by the initial conditional errors and inaccurate attitude estimations. This new scheme is then applied to the quaternion attitude estimators. It is shown that the error covariances of the proposed algorithms are theoretically bounded. Simulations for a low-earth-orbit spacecraft state estimation are performed. Through updating the estimated quaternion and then reconstructing the error covariance, the comparison results show that the proposed algorithms thus reduce the introduction of truncation error and thus achieve better performance than traditional algorithms in terms of robustness and convergence rate.