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.

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.

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.

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.

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.

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.

A Beam Stabilization Algorithm Based on Nonlinear Observer for Low Cost Satcom-on-the-Move

A beam stabilization algorithm was proposed for low cost satcom-on-the-move （SOTM） to stabilize the vehicle-mounted antenna beam. The proposed algorithm utilizes the nonlinear observel to estimate the vehicle＇s attitude information based on inertial measurement unit. Then the estimated angles and angular velocities are used to stabilize the antenna beam. Experiment results show tha｜ the proposed algorithm can stabilize the antenna beam when the tracking information is available, indicating that it is competent to the SOTM system.

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.

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.

Regularized Robust Filter for Spacecraft Attitude Determination

A modified regularized robust filter is proposed for spacecraft attitude determination in the presence of relative misalignment of attitude sensors. The filter is designed to minimize the worst-possible residual norm on condition that there is parametric uncertainty in the measurement model. The weighting matrix of the residual norm is designed to minimize the upper bound of the estimation error variance. The performance of the proposed attitude determination robust filter is illustrated with the use of real test data from a real three-floated gyroscope. Simulation results demonstrate that the attitude estimation accuracy is improved by using the proposed algorithm.

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.

Design and experimental study of a new flapping wing rotor micro aerial vehicle

A three-wing Flapping Wing Rotor Micro Aerial Vehicle(FWR-MAV)which can perform controlled flight is introduced and an experimental study on this vehicle is presented.A mechanically driven flapping rotary mechanism is designed to drive the three flapping wings and generate lift,and control mechanisms are designed to control the pose of the FWR-MAV.A flight control board for attitude control with robust onboard attitude estimation and a control algorithm is also developed to perform stable hovering flight and forward flight.A series of flight tests was conducted,with hovering flight and forward flight tests performed to optimize the control parameters and assess the performance of the FWR-MAV.The hovering flight test shows the ability of the FWR-MAV to counteract the moment generated by rotary motion and maintain the attitude of the FWR-MAV in space;the experiment of forward flight shows that the FWR-MAV can track the desired attitude.

Adaptive Kalman filter for MEMS IMU data fusion using enhanced covariance scaling

MEMS(micro-electro-mechanical-system)IMU(inertial measurement unit)sensors are characteristically noisy and this presents a serious problem to their effective use.The Kalman filter assumes zero-mean Gaussian process and measurement noise variables,and then recursively computes optimal state estimates.However,establishing the exact noise statistics is a non-trivial task.Additionally,this noise often varies widely in operation.Addressing this challenge is the focus of adaptive Kalman filtering techniques.In the covariance scaling method,the process and measurement noise covariance matrices Q and R are uniformly scaled by a scalar-quantity attenuating window.This study proposes a new approach where individual elements of Q and R are scaled element-wise to ensure more granular adaptation of noise components and hence improve accuracy.In addition,the scaling is performed over a smoothly decreasing window to balance aggressiveness of response and stability in steady state.Experimental results show that the root mean square errors for both pith and roll axes are significantly reduced compared to the conventional noise adaptation method,albeit at a slightly higher computational cost.Specifically,the root mean square pitch errors are 1.1∘under acceleration and 2.1∘under rotation,which are significantly less than the corresponding errors of the adaptive complementary filter and conventional covariance scaling-based adaptive Kalman filter tested under the same conditions.