Vector‐Based Adaptive Attitude Observer and Controller on Special Orthogonal Group

An adaptive attitude observer‐controller scheme is proposed for attitude tracking of a rigid body. In the derived observer, the vector measurements are directly utilized to estimate gyro bias, and thus estimates of gyro bias are obtained independent to attitude estimates. The proposed observer is even robust towards fluctuation of gyro bias. Then an adaptive controller is proposed on the Special Orthogonal Group to track the reference trajectory subject to uncertain inertia parameters. This controller belongs to the non‐certainty‐equivalent framework, and the vector signals are also utilized into estimation of inertia parameters. It is ensured that the estimates of inertia parameters can converge towards real values to some degrees. Simulation results compared with previous observer and controller schemes verify the effectiveness of the proposed scheme.     

A coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise

We propose a new algorithm for estimating constant biases in gyro measurements of angular velocity, and demonstrate that the resulting estimates converge to the true bias values exponentially fast. The new observer is then combined with a nonlinear attitude tracking control strategy in a certainty equivalence fashion, and the combination shown via Lyapunov analysis to produce globally stable closed-loop dynamics, with asymptotically perfect tracking of any commanded attitude sequence. The analysis is then extended to consider the effects of stochastic measurement noise in the gyro in addition to the bias. A simulation is given for a rigid spacecraft tracking a specified, time-varying attitude sequence to illustrate the theoretical claims.     

基于Marginalized粒子滤波的卫星姿态估计算法

针对具有矢量观测的卫星姿态估计问题。提出一种基于Marginalized粒予滤波（MPF）的算法．采用Rao-Blackwellization技术，将卫星模型状态向量中的线性状态部分（陀螺漂移）和非线性状态部分（卫星姿态）分开处理，从而使得估计的方差降低．以较少的运算量获得较好的估计效果．通过引入解决含等式约束条件的估计问题方法，保证了姿态四元数的归一化．将所提出的方法应用于某型号卫星．仿真验证了用该算法处理卫星姿态估计问题的优越性．     

Nonlinear Complementary Filters on the Special Orthogonal Group

This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group $SO(3)$ driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on $SO(3)$, termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.      

Global attitude and gyro bias estimation based on set-valued observers

The problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations. A Set-Valued Observer (SVO) is proposed that has no singularities and that, for any initial conditions, provides a bounding set with guarantees of containing the actual (unknown) rotation matrix. The sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias. Conditions for the boundedness of the estimated sets are established and implementation details are discussed. The feasibility of the technique is demonstrated in simulation.     

Nonlinear observer design for GNSS-aided inertial navigation systems with time-delayed GNSS measurements

Global navigation satellite system (GNSS) receivers suffer from an internal time-delay of up to several hundred milliseconds leading to a degeneration of position accuracy in high-dynamic systems. With the increasing interest in GNSS navigation, handling of time-delays will be vital in high accuracy applications with high velocity and fast dynamics. This paper presents a nonlinear observer structure for estimating position, linear velocity, and attitude (PVA) as well as accelerometer and gyro biases, using inertial measurements and time-delayed GNSS measurements. The observer structure consists of four parts; (a) attitude and gyro bias estimation, (b) time-delayed translational motion observer estimating position and linear velocity, (c) input delays for inertial and magnetometer measurements, and (d) a faster than real-time simulator. The delayed PVA and gyro bias estimates are computed using a uniformly semiglobally exponentially stable (USGES) nonlinear observer. The high-rate inertial measurements are delayed and synchronized with the GNSS measurements in the state observer. The fast simulator integrates the inertial measurements from the delayed state estimate to provide a state estimate at current time. The sensor measurements are carefully synchronized and the estimation procedure for the GNSS receiver delay is discussed. Experimental data from a small aircraft are used to validate the results.     

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 MPF. The results presented in this paper clearly demonstrate that the MPF is superior to UKF in coping with the nonlinear model.     

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.     

Distributed observer‐based leader‐follower attitude consensus control for multiple rigid bodies using rotation matrices

This paper addresses the distributed observer‐based leader‐follower attitude consensus control problem for multiple rigid bodies. An intrinsic distributed observer is proposed for each follower to estimate the leader's trajectory, which is only available to a subset of followers. The proposed observer can guarantee that the estimated attitude evolves on rotation matrices all the time, and it provides us with a simple way to design the attitude consensus control law. The dynamics of rigid bodies and distributed observer are both modeled directly on rotation matrices, so that the singularity and ambiguity can be avoided. Furthermore, adopting the idea of disturbance observer on vector space, a gyro bias observer on the rotation matrices is proposed. Based on the distributed observer, three types of attitude consensus control law are proposed, which are respectively on the basis of full‐state, biased angular velocity, and external disturbance combined with biased angular velocity. Finally, the SimMechanics experiments are provided to illustrate effectiveness of the proposed theoretical results.     

Vector-Based Attitude Filter for Space Navigation

This paper presents the design and performance evaluation of a novel integrated attitude filter with application to space navigation. The design is based directly on the sensor measurements as opposed to traditional solutions that resort to rotation parameterizations. The information provided by a low-cost star tracker is merged with the measurements of a triaxial rate gyro to provide accurate estimates of the attitude. The proposed multirate solution also includes the estimation of rate gyro bias and tuning procedures. Simulation and experimental results, including ground truth data for performance evaluation purposes, are shown that illustrate the attainable performance in the presence of realistic measurements provided by low-cost star trackers.     

自主姿态测量算法研究

航姿系统一般不实时计算速度和位置信息,无法补偿地球自转和表观运动引起的分量误差,同时陀螺漂移较大,载体长时间持续机动时,出现姿态精度不高,甚至发散的问题。提出了一种基于卡尔曼滤波的姿态融合算法,将等效陀螺漂移列入系统状态,利用卡尔曼滤波的新息对运动状态进行判别,在一定条件下,用加速度计的输出作为量测量进行卡尔曼滤波的量测更新过程。实验结果表明,所提出的姿态融合算法考虑了陀螺漂移,能提高载体长时间机动时的姿态精度。     

Globally exponentially stable attitude observer with Earth velocity estimation

This paper presents a novel observer for attitude estimation based on a triad of high‐grade rate gyros aided by a body‐fixed vector measurement of a constant inertial vector, departing from the majority of solutions that consider at least two of these vectors. A cascade approach is proposed, where the first block estimates a vector that is related to the angular velocity of the Earth and a second block estimates the attitude. While the topological characteristics are relaxed in the attitude observer so that global exponential stability is achieved, an additional stage is also devised that yields estimates directly on the special orthogonal group, preserving global convergence of the estimation error. Simulation results with realistic sensor noise were performed, including extensive Monte Carlo runs. These results illustrate the convergence of the proposed solution, as well as the achievable performance and robustness to sensor noise.     

Pose estimation using line-based dynamic vision and inertial sensors

An observer problem from a computer vision application is studied. Rigid body pose estimation using inertial sensors and a monocular camera is considered and it is shown how rotation estimation can be decoupled from position estimation. Orientation estimation is formulated as an observer problem with implicit output where the states evolve on SO(3). A careful observability study reveals interesting group theoretic structures tied to the underlying system structure. A locally convergent observer where the states evolve on SO (3) is proposed and numerical estimates of the domain of attraction is given. Further, it is shown that, given convergent orientation estimates, position estimation can be formulated as a linear implicit output problem. From an applications perspective, it is outlined how delayed low bandwidth visual observations and high bandwidth rate gyro measurements can provide high bandwidth estimates. This is consistent with real-time constraints due to the complementary characteristics of the sensors which are fused in a multirate way.     

UKF based in‐flight calibration of magnetometers and rate gyros for pico satellite attitude determination

In this paper an unscented Kalman filter based procedure for the bias estimation of both the magnetometers and the gyros carried onboard a pico satellite, is proposed. At the initial phase, biases of three orthogonally located magnetometers are estimated as well as the attitude and attitude rates of the satellite. During the initial period after the orbit injection, gyro measurements are accepted as bias free since the precise gyros are working accurately and the accumulated gyro biases are negligible. At the second phase estimated constant magnetometer bias components are taken into account and the algorithm is run for the estimation of the gyro biases that are cumulatively increased by time. As a result, six different bias terms for two different sensors are obtained in two stages, where attitude and attitude rates are estimated regularly. For both estimation phases of the procedure an unscented Kalman filter is used as the estimation algorithm. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

面向皮纳卫星姿态确定的MEMS陀螺磁强计组合滤波系统

针对难以配置高精度部件的皮纳卫星姿态测量系统,当卫星处于阴影区或任何太阳敏感器不可用的状态下,MEMS陀螺与磁强计的组合便成为卫星在轨姿态测量精度的重要保障.本文基于MEMS陀螺与磁强计的低功耗、全轨、全天时、最小姿态敏感组合,提出一种适用于皮纳卫星在轨运行的滤波系统方案.该方案通过滑窗ARMA建模降低陀螺随机噪声的影响,并由姿态滤波器估计所得的零偏在线去除陀螺常值分量,以保证其建模的长期有效性.本文以浙江大学皮星二号卫星搭载的敏感部件以及姿态测量算法为研究基础,结合在轨实测数据,仿真对比表明,该系统方案有效降低了陀螺随机噪声,抑制比达50％以上;陀螺零偏估计精度提高310％,可达到0.001°/s;姿态确定精度提升190％,可达1.2127°.该系统方案是对皮纳卫星姿态确定最小系统精度提升及实用方案设计的有益探索.     

基于重力四元数的陀螺漂移估计与补偿

为提高钻探中的钻具姿态测量精度,提出一种基于重力四元数的MEMS惯性随钻姿态测量方法.采用MEMS惯性器件构建钻具姿态测量系统,把加速度计数据解算的姿态四元数作为观测四元数,陀螺仪数据解算的姿态四元数作为误差四元数;然后将陀螺仪漂移融入误差四元数,建立重力四元数估计陀螺仪误差四元数的模型,采用最小二乘法估计陀螺仪三轴漂移,进而补偿陀螺仪姿态四元数;通过补偿后的姿态四元数解算出钻具姿态.最后设计了转台、振动台实验和钻进模拟实验,实验结果表明,姿态四元数补偿后的井斜角和工具面角漂移由平均10 °/h减小到约0.2 °/h,方位角误差由平均12 °/h减小到约0.46 °/h,实现了加速度计补偿陀螺的三轴漂移,表明该方法能够有效提高钻具的姿态测量精度.     

应用于多旋翼MAVs的姿态测量系统

应用一个三轴加速度计、三个单轴角速率陀螺和一个三轴磁强计等微机械惯性传感器,设计廉价轻量姿态测量系统,研究了姿态角推算算法。在以往的姿态测量系统中,陀螺偏差和动加速度的影响限制其应用。将角速度陀螺的误差作为状态量导入到系统,动加速度作为噪音项导入到观测方程中,然后利用扩展卡尔曼滤波器来构成姿态估计算法来降低误差。实际飞行中对比商用高精度传感器和多次室外飞行测试表明,设计的系统能够应于旋翼MAVs。     

环形激光陀螺的零偏热效应补偿模型

热效应对激光陀螺零偏的影响非常明显且难以精确建模。根据对环形激光陀螺的大量温度试验的数据,分析了温度变化、温度梯度与温变速率对陀螺零偏漂移影响的规律,进而提出了一种适用于工程应用的环形激光陀螺的零偏热效应补偿方法。经试验验证,此模型能在一定程度上改善热效应对环形激光陀螺零偏稳定性的影响,为建立最后的误差补偿模型,进一步提高环形激光陀螺的精度打下基础。     

基于神经网络观测器的卫星姿态控制系统陀螺故障诊断

针对基于解析模型的卫星姿态控制系统陀螺故障诊断方法存在设计复杂、参数求解困难的问题,提出一种基于神经网络观测器的陀螺故障诊断方法。由系统内的冗余关系导出故障诊断逻辑,实现对陀螺故障的检测和隔离;同时利用先验模型知识和神经网络的非线性建模特性对陀螺故障进行估计。仿真结果表明,该方法能够实现对陀螺故障的检测、隔离和估计。     

A nonlinear position and attitude observer on SE(3) using landmark measurements

This paper addresses the problem of position and attitude estimation, based on landmark readings and velocity measurements. A derivation of a nonlinear observer on SE(3) is presented, using a Lyapunov function conveniently expressed as a function of the difference between the estimated and the measured landmark coordinates. The resulting feedback laws are explicit functions of the landmark measurements and velocity readings, exploiting the sensor information directly in the observer. The proposed observer yields almost global asymptotic stabilization of the position and attitude errors and exponential convergence in any closed ball inside the region of attraction. Also, it is shown that the asymptotic convergence of the estimation error trajectories is shaped by the landmark geometry and observer design parameters. The problem of non-ideal velocity readings is also considered, and the observer is augmented to compensate for bias in the angular and linear velocity measurements. The resulting position, attitude, and bias estimation errors are shown to converge exponentially fast to the desired equilibrium points, for bounded initial estimation errors. Simulation results are presented to illustrate the stability and convergence properties of the observer.