REKF and RUKF for pico satellite attitude estimation in the presence of measurement faults

When a pico satellite is under normal operational condi- tions, whether it is extended or unscented, a conventional Kalman filter gives sufficiently good estimation results. However, if the measurements are not reliable because of any kind of malfunc- tions in the estimation system, the Kalman filter gives inaccurate results and diverges by time. This study compares two different robust Kalman filtering algorithms, robust extended Kalman filter （REKF） and robust unscented Kalman filter （RUKF）, for the case of measurement malfunctions. In both filters, by the use of de- fined variables named as the measurement noise scale factor, the faulty measurements are taken into the consideration with a small weight, and the estimations are corrected without affecting the characteristic of the accurate ones. The proposed robust Kalman filters are applied for the attitude estimation process of a pico satel- lite, and the results are compared.

Real-Time Position and Attitude Estimation for Homing and Docking of an Autonomous Underwater Vehicle Based on Bionic Polarized Optical Guidance

As an important tool for marine exploration, the autonomous underwater vehicle(AUV) must home in and dock at a docking station(DS) to be recharged, repaired, or to exchange information at set intervals. However, the complex and hostile underwater environment makes this process challenging. This study proposes a real-time method based on polarized optical guidance for determining the position and attitude of the AUV relative to its DS. Four polarized artificial underwater landmarks are positioned at the DS, which are recognized by the AUV vision system. Compared with light intensity, the polarization of a light beam is known to be better maintained at greater propagation distances, especially in underwater environments. The proposed method, which is inspired by the ability of marine animals to communicate, calculates the pose parameters in less than 10 ms without any other navigational information. The simulation results reveal that the angle errors are small and the position errors are no more than 0.116 m within 100 m in the coastal ocean. The results of underwater experiments further demonstrate the feasibility of the proposed method, which extends the operating distance of the AUV beyond what is currently possible while maintaining the precision of traditional optical guidance.

Marginalized particle filter for spacecraft attitude estimation from vector measurements

An algorithm based on the marginalized particle filters （MPF） is given in details in this paper to solve the spacecraft attitude estimation problem： attitude and gyro bias estimation using the biased gyro and vector observations. In this algorithm, by marginalizing out the state appearing linearly in the spacecraft model, the Kalman filter is associated with each particle in order to reduce the size of the state space and computational burden. The distribution of attitude vector is approximated by a set of particles and estimated using particle filter, while the estimation of gyro bias is obtained for each one of the attitude particles by applying the Kalman filter. The efficiency of this modified MPF estimator is verified through numerical simulation of a fully actuated rigid body. For comparison, unscented Kalman filter （UKF） is also used to gauge the performance of MPE The results presented in this paper clearly derfionstrate that the MPF is superior to UKF in coping with the nonlinear model.

Aircraft attitude estimation of MEMS sensor based on modified particle filter

The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on modified particle filter is proposed.The aircraft attitude is optimized by the conjugate gradient method,and the drift error of gyroscope is reduced.Moreover,the particle weight is updated by the observed value to obtain an optimized state estimate.Finally,the conjugate gradient method and the modified particle filter are weightily combined to determine the optimal weighting factor.The attitude estimation is carried out with STM32 and MEMS sensor as the core to design system.The experimental results show that the static and dynamic attitude estimation performances of the aircraft are improved.The performances are well,the attitude data is relatively stable,and the tracking characteristics are better.Moreover,it has better robustness and stability.

Application of the sun line-of-sight vector in the optimal attitude estimation of deep-space probe

This paper proposed an optimal algorithm using the sun line-of-sight vector to improve the probe attitude estimation accuracy in deep-space mission.Firstly,the elaborate analysis of the attitude estimation error from vector observations was done to demonstrate that the geometric relation between the reference vectors is an important factor which influences the accuracy of attitude estimation.Then,with introduction of the sun line-of-sight vector,the attitude quaternion obtained from the star-sensor was converted into a pair of mutually perpendicular reference vectors perpendicular to the sun vector.The normalized weights were calculated according to the accuracy of the sensors.Furthermore,the optimal attitude estimation in the least squares sense was achieved with the quaternion estimation method.Finally,the results of simulation demonstrated the validity of the proposed optimal algorithm based on the practical data of the Deep Impact mission.

Underwater square-root cubature attitude estimator by use of quaternion-vector switching and geomagnetic field tensor

This paper presents a kind of attitude estimation algorithm based on quaternion-vector switching and square-root cubature Kalman filter for autonomous underwater vehicle(AUV).The filter formulation is based on geomagnetic field tensor measurement dependent on the attitude and a gyro-based model for attitude propagation. In this algorithm, switching between the quaternion and the three-component vector is done by a couple of the mathematical transformations. Quaternion is chosen as the state variable of attitude in the kinematics equation to time update, while the mean value and covariance of the quaternion are computed by the three-component vector to avoid the normalization constraint of quaternion. The square-root forms enjoy a continuous and improved numerical stability because all the resulting covariance matrices are guaranteed to stay positively semidefinite. The entire square-root cubature attitude estimation algorithm with quaternion-vector switching for the nonlinear equality constraint of quaternion is given. The numerical simulation of simultaneous swing motions in the three directions is performed to compare with the three kinds of filters and the results indicate that the proposed filter provides lower attitude estimation errors than the other two kinds of filters and a good convergence rate.

Flight Vehicle Attitude Determination Using the Modified Rodrigues Parameters

There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator （MEAE）, whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator （SEAE）, whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE, and simulation results demonstrate the efficacy of the presented algorithm.

Attitude sensor fault diagnosis based on Kalman filter of discrete-time descriptor system

To diagnose the fault of attitude sensors in satellites, this paper proposes a novel approach based on the Kalman filter of the discrete-time descriptor system. By regarding the sensor fault term as the auxiliary state vector, the attitude measurement system subjected to the attitude sensor fault is modeled by the discrete-time descriptor system. The condition of estimability of such systems is given. And then a Kalman filter of the discrete-time descriptor system is established based on the methodology of the maximum likelihood estimation. With the descriptor Kalman filter, the state vector of the original system and sensor fault can be estimated simultaneously. The proposed method is able to esti-mate an abrupt sensor fault as well as the incipient one. Moreover, it is also effective in the multiple faults scenario. Simulations are conducted to confirm the effectiveness of the proposed method.

UKF-based attitude determination method for gyroless satellite

UKF (unscented Kalman filtering) is a new filtering method suitable to nonlinear systems. The method need not linearize nonlinear systems at the prediction stage of filtering, which is indispensable in EKF ( extended Kalman filtering) . As a result, the linearization error is avoided, and the filtering accuracy is greatly improved. UKF is applied to the attitude determination for gyroless satellite. Simulations are made to compare the new filter with the traditional EKF. The results indicate that under same conditions, compared with EKF, UKF has faster convergence speed, higher filtering accuracy and more stable estimation performance.

Unscented Kalman Filter for Autonomous Warship Attitude Determination

To address a problem of autonomous attitude determination algorithm using gravitational field and geomagnetic field observation, a new recursive optimization autonomous attitude estimation algorithm is proposed. The algorithm is based on unscented Kalman filter(UKF), and can synchronously provide the attitude rate information. The simulated results show that the measurement precision of the method could be increased by 2 times compared to that of the common methods.

Gradient Descent Algorithm for Small UAV Parameter Estimation System

A gradient descent algorithm with adjustable parameter for attitude estimation is developed,aiming at the attitude measurement for small unmanned aerial vehicle(UAV)in real-time flight conditions.The accelerometer and magnetometer are introduced to construct an error equation with the gyros,thus the drifting characteristics of gyroscope can be compensated by solving the error equation utilized by the gradient descent algorithm.Performance of the presented algorithm is evaluated using a self-proposed micro-electro-mechanical system(MEMS)based attitude heading reference system which is mounted on a tri-axis turntable.The on-ground,turntable and flight experiments indicate that the estimation attitude has a good accuracy.Also,the presented system is compared with an open-source flight control system which runs extended Kalman filter(EKF),and the results show that the attitude control system using the gradient descent method can estimate the attitudes for UAV effectively.

Fuzzy Sliding Mode Observer for Vehicular Attitude Heading Reference System

In low-cost Attitude Heading Reference Systems (AHRS), the measurements made by Micro Electro-Mechanical Systems (MEMS) type sensors are affected by uncertainties, noises and unknown disturbances. In this paper, considering the robustness of sliding mode observers against structured and unstructured uncertainties, and also exogenous inputs, the process of design and implementation of a sliding mode observer (SMO) is proposed based on a linearized model of the AHRS. To decrease the chattering phenomenon is the main difficulty of the SMO. Through smoothing the discontinuity term, the tracking performance of the observer is attenuated. Boundary layer technique, for example, using a saturation term, is the common smoother to remove the chattering drawbacks. However, through poor tracking performance, the high range chattering could not be removed by this method. Therefore, a knowledge-based Mamdani-type fuzzy SMO (FSMO) is proposed to decrease the chattering effects intelligently, which in turn could obtain the high accuracy tracking performance of the SMO. Following proving the stability of the proposed SMOs based on direct Lyapunov’s method, the performance of the proposed observers is compared with that of the extended Kalman filter through simulation and real experiments of an AHRS.

Adaptive robust cubature Kalman filtering for satellite attitude estimation

This paper is concerned with the adaptive robust cubature Kalman filtering problem for the case that the dynamics model error and the measurement model error exist simultaneously in the satellite attitude estimation system. By using Hubel-based robust filtering methodology to correct the measurement covariance formulation of cubature Kalman filter, the proposed filtering algorithm could effectively suppress the measurement model error. To further enhance this effect and reduce the impact of the dynamics model error, two different adaptively robust filtering algorithms,one with the optimal adaptive factor based on the estimated covariance matrix of the predicted residuals and the other with multiple fading factors based on strong tracking algorithm, are developed and applied for the satellite attitude estimation. The quaternion is employed to represent the global attitude parameter, and three-dimensional generalized Rodrigues parameters are introduced to define the local attitude error. A multiplicative quaternion error is derived from the local attitude error to maintain quaternion normalization constraint in the filter. Simulation results indicate that the proposed novel algorithm could exhibit higher accuracy and faster convergence compared with the multiplicative extended Kalman filter, the unscented quaternion estimator, and the adaptive robust unscented Kalman filter.

Simultaneous state and actuator fault estimation for satellite attitude control systems

In this paper, a new nonlinear augmented observer is proposed and applied to satellite attitude control systems. The observer can estimate system state and actuator fault simultaneously. It can enhance the performances of rapidly-varying faults estimation. Only original system matrices are adopted in the parameter design. The considered faults can be unbounded, and the proposed augmented observer can estimate a large class of faults. Systems without disturbances and the fault whose finite times derivatives are zero piecewise are initially considered, followed by a discussion of a general situation where the system is subject to disturbances and the finite times derivatives of the faults are not null but bounded. For the considered nonlinear system, convergence conditions of the observer are provided and the stability analysis is performed using Lyapunov direct method. Then a feasible algorithm is explored to compute the observer parameters using linear matrix inequalities （LMIs）. Finally, the effectiveness of the proposed approach is illustrated by considering an example of a closed-loop satellite attitude control system. The mance in estimating states and actuator faults. It also successfully. simulation results show satisfactory perfor- shows that multiple faults can be estimated

Magnetometer-only linear attitude estimation for bias momentum pico-satellite

Satellite attitude information is essential for pico-satellite applications requiring light-weight,low-power,and fast-computation characteristics.The objective of this study is to provide a magnetometer-only attitude estimation method for a low-altitude Earth orbit,bias momentum pico-satellite.Based on two assumptions,the spacecraft spherical symmetry and damping of body rates,a linear kinematics model of a bias momentum satellite's pitch axis is derived,and the linear estimation algorithm is developed.The algorithm combines the linear Kalman filter(KF) with the classic three-axis attitude determination method(TRIAD).KF is used to estimate satellite's pitch axis orientation,while TRIAD is used to obtain information concerning the satellite's three-axis attitude.Simulation tests confirmed that the algorithm is suited to the time-varying model errors resulting from both assumptions.The estimate result keeps tracking satellite attitude motion during all damping,stable,and free rotating control stages.Compared with nonlinear algorithms,such as extended Kalman filer(EKF) and square root unscented Kalman filer(SRUKF),the algorithm presented here has an almost equal performance in terms of convergence time and estimation accuracy,while the consumption of computing resources is much lower.

DOA estimation for attitude determination on communication satellites

In order to determine an appropriate attitude of three-axis stabilized communication satellites, this paper describes a novel attitude determination method using direction of arrival （DOA） estimation of a ground signal source. It differs from optical measurement, magnetic field measurement, inertial measurement, and global positioning system （GPS） attitude determination. The proposed method is characterized by taking the ground signal source as the attitude reference and acquiring attitude information from DOA estimation. Firstly, an attitude measurement equation with DOA estimation is derived in detail. Then, the error of the measurement equation is analyzed. Finally, an attitude determination algorithm is presented using a dynamic model, the attitude measurement equation, and measurement errors. A developing low Earth orbit （LEO） satellite which tests mobile communication technology with smart antennas can be stabilized in three axes by corporately using a magnetometer, reaction wheels, and three-axis magnetorquer rods. Based on the communication satellite, simulation results demonstrate the effectiveness of the method. The method could be a backup of attitude determination to prevent a system failure on the satellite. Its precision depends on the number of snapshots and the input signal-to-noise ratio （SNR） with DOA estimation.

Star-sensor-based predictive Kalman filter for satellite attitude estimation

A real-time attitude estimation algorithm, namely the predictive Kalman filter, is presented . This algorithm can accurately estimate the three-axis attitude of a satellite using only star sensor measurements. The implementation of the filter includes two steps: first, predicting the torque modeling error, and then estimating the attitude. Simulation results indicate that the predictive Kalman filter provides robust performance in the presence of both significant errors in the assumed model and in the initial conditions.

Interlaced Attitude Estimation for Spacecraft Using Vector Observations

This paper proposes an interlaced attitude estimation method for spacecraft using vector observations,which can simultaneously estimate the constant attitude at the very start and the attitude of the body frame relative to its initial state.The arbitrary initial attitude,described by constant attitude at the very start,is determined using quaternion estimator which requires no prior information.The multiplicative extended Kalman-lter(EKF)is competent for estimating the attitude of the body frame relative to its initial state since the initial value of this attitude is exactly known.The simulation results show that the proposed algorithms could achieve better performance compared with the state-of-the-art algorithms even with extreme large initial errors.Meanwhile,the computational burden is also much less than that of the advanced nonlinear attitude estimators.

基于惯性辅助跟踪的未知对应姿态估计方法

针对特征点对应关系未知的姿态估计问题,提出了1种基于惯性辅助跟踪的未知对应姿态估计方法。与利用惯性信息在数据处理层面优化先验位姿选取的方法不同,该方法在数据采集层面融合图像信息和惯性信息,从而提高了姿态估计和特征点匹配的准确性和稳健性。本文提出了1种融合特征点跟踪和运动矢量约束跟踪的混合跟踪新方法,构建了二维和三维点集的初始匹配权重矩阵。基于该匹配权重矩阵建立优化目标函数,并利用改进软分配算法交替优化姿态估计和二维/三维点集匹配关系。利用二维精密转台搭载合作立体靶标进行算法性能测试,结果表明:在方位角/俯仰角为±50°内,该方法的成功率为99%,姿态估计精度优于0.15°,单次测量耗时约17 ms,并且在视觉遮挡情况下仍可保持较高的成功率。

九轴MEMS微型AHRS设计及其在矢量水听器中的应用

为了精确测量矢量水听器的姿态,设计了一种体积为20 mm×20 mm×5 mm、重量为1.8 g的微型航姿参考系统(AHRS)。利用微机电系统(MEMS)陀螺仪测定角速度,用四元数等效旋转矢量算法求解姿态角;采用扩展卡尔曼滤波器对姿态角估计值进行修正,并估计出MEMS陀螺仪的角速度漂移量。测试结果表明,所提AHRS的俯仰、横滚和航向角误差均方根值分别为0.04°、0.04°和0.34°。最后,将AHRS集成到矢量水听器中,并在加窗直方图统计波达方向估计算法中加入姿态修正。海上实验结果表明,对于航速为8 kn的目标船,经AHRS修正后的单矢量水听器方位角误差均方根值约为3.8°,减小了平台运动导致的方位测量误差。