Globally exponentially stable cascade observers for attitude estimation

This paper presents the design, analysis, and performance evaluation of a novel cascade observer for attitude estimation. A sensor-based observer, which resorts to rate gyro readings and a set of vector observations, estimates the rate gyro bias. Afterwards, a cascaded observer explicitly estimates the attitude in the form of a rotation matrix based on the rate gyro measurements, the vector observations, and the estimated gyro bias. The overall error dynamics are globally exponentially stable and the proposed system is computationally efficient. Finally, the resulting estimator is successfully evaluated, in simulation and experimentally, with ground truth data in both cases.     

Integrated Design and Accuracy Analysis of Star Sensor and Gyro on the Same Benchmark for Satellite Attitude Determination System

As an important sensor in the navigation systems, star sensors and the gyro play important roles in spacecraft attitude determination system. Complex environmental factors are the main sources of error in attitude determination. The error influence of different benchmarks and the disintegration mode between the star sensor and the gyro is analyzed in theory. The integrated design of the star sensor and the gyro on the same benchmark can effectively avoid the error influence and improves the spacecraft attitude determination accuracy. Simulation results indicate that when the stars sensor optical axis vectors overlap the reference coordinate axis of the gyro in the same benchmark, the attitude determination accuracy improves.      

基于EKF的航天器姿态确算法定及精度分析

采用陀螺和星敏感器组合的方式来进行航天器姿态确定。首先建立了陀螺和星敏感器的测量模型,选择以四元数作为描述航天器姿态的参数,详细推导了在小偏差下以误差姿态角和陀螺常值漂移误差为状态量的滤波状态方程,并且以星敏感器的测量残差作为量测量,采用扩展卡尔曼滤波（Extended Kalman Filter, EKF）算法进行姿态确定;然后进行了仿真分析,仿真结果表明：该算法可以达到较高的姿态确定精度;最后对影响姿态确定精度的硬件因素和软件因素进行了定量的数据分析,得出了有一定意义的结论,从而为工程实践提供理论支持。     

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.     

基于最大熵卡尔曼滤波的机载SINS星敏感器辅助空中标定技术

为增强机载捷联惯导系统（SINS）在自标定过程中的可观测性,提升陀螺仪漂移和加速度计零偏估计的速度和精度,引入星敏感器姿态信息和GPS速度信息,辅助完成捷联惯导系统的空中标定。同时,考虑在实际空中飞行条件下,受气流、电磁干扰等影响,姿态和速度的量测噪声呈非高斯分布且噪声统计特性不精确,导致经典卡尔曼滤波性能降低。为有效利用量测信号中的高阶矩信息,在卡尔曼滤波中采用最大熵准则代替最小均方误差准则,对星敏感器辅助下的机载捷联惯导系统的误差进行标定。仿真结果表明,经最大熵卡尔曼滤波后,惯性器件误差的标定精度明显提升;在采用星敏感器后,对陀螺仪漂移的标定速度和精度都得到了提升。     

基于MIMU和磁力计的姿态更新算法研究

针对传统人体姿态解算算法中存在MEMS陀螺误差发散快的问题,提出一种基于微惯性测量单元( MIMU)及磁力计信息融合的姿态解算算法。该算法利用互补滤波结合PI调节控制完成陀螺零偏校正,然后在加速度计和磁强计的辅助校正下,通过EKF( Expand Kalman Filter)滤波器更新四元数法实现陀螺姿态解算。本算法采用MPU9150传感器模块完成测试实验,实验中对比分析了单独扩展卡尔曼滤波算法与本算法的滤波效果。实验结果表明,本算法能够有效地抑制陀螺的发散,实现稳定地输出高精度姿态数据。     

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。     

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.      

小型尾坐式飞行器航姿参考系统

针对小型尾坐式飞行器姿态实时解算问题,研究了低成本的航姿参考系统(AHRS).由于MEMS惯性器件精度较低,设计了混合卡尔曼滤波器,以姿态四元数和陀螺随机漂移为状态变量,抑制了载体长时间飞行时陀螺漂移造成的累积误差.由于加速度计输出值在除重力加速度之外的附加加速度较大时不可信,完善了判断载体运动状态的方法,根据加速度计的实际输出,选择加速度值或者磁场强度作为观测量.实验结果表明,设计的算法在精度和计算效率方面都能满足控制系统的需求,更加适用于对实时性有较高要求的飞行器.     

基于UKF的两轮自平衡机器人姿态最优估计研究

针对扩展卡尔曼滤波器(EKF)设计困难并且容易发散的问题,提出基于采样卡尔曼滤波(UKF)的方法解决滤波器设计及收敛问题,并补偿低成本的惯性传感器陀螺仪和加速度计的误差,从而得到机器人姿态的最优估计．将滤波后的模型应用到两轮自平衡机器人系统,实验结果表明UKF参数设计简单,姿态估计误差小于EKF,方差估计优于EKF,估计精度、计算量基本与EKF相当．因此,UKF能够满足两轮自平衡机器人快速机动过程中的实时姿态估计要求．     

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.     

Application of Kalman filtering to the calibration and alignment ofinertial navigation systems

The development of Kalman filters for the calibration and alignment of complex inertial guidance systems is presented. The attitude error equation is augmented by gyro and accelerometer model parameters. The mechanization of the algorithm involves preprocessing the raw measurements to reduce the computational load. Results for simulated data show that preprocessing has very little effect on the performance of the filter. Other topics discussed include gyro and accelerometer models and a technique for generating parameter excitation trajectories     

Optimal estimation for the satellite attitude using star tracker measurements

An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.     

三轴稳定卫星姿态控制周期的仿真研究

针对三轴稳定卫星的姿态控制系统,在离散事件仿真器OMNeT 的基础上,建立了以陀螺、星敏感器为敏感器,以反作用飞轮为执行机构的三轴稳定卫星的闭环控制系统.对于卫星姿态控制系统中控制周期的选取作了初步的分析,最后采用双矢量定姿算法和PID控制算法,设定多种控制周期,对该卫星在对地定向模式下的控制精度进行了仿真,仿真结果清楚的显示了控制周期对姿态控制精度的影响.     

Image motion compensation system for the shuttle infrared telescope facility

The shuttle infrared telescope facility (SIRTF) is mounted in the orbiter on the instrument pointing system (IPS) and requires that the image at the focal plane be stabilized to better than 0.25 arcsec in order to achieve the scientific goals of the device. Current estimates of IPS performance accuracy indicate that additional stabilization will be necessary to meet the SIRTF requirements. An image motion compensation system, utilizing a charge coupled device (CCD) star tracker located at the focal plane and a steerable mirror in the SIRTF optical path, has been designed to work in conjunction with the IPS. The CCD tracks multiple stars simultaneously and through the use of a high-performance microcomputer generates three-axis attitude errors and gyro drift estimates to correct disturbances not compensated for the IPS control system. The SIRTF control system is described in detail and performance is analyzed with respect to system noise inputs, environmental disturbances, and error sources such as bending and feed-forward scale factor. It is concluded that the SIRTF accuracy and stability requirements can be met with this design.     

一种天文/惯性导航系统组合模式的研究

本文以姿态误差四元数与陀螺漂移误差之间的关系为基础,构建了系统状态方程;针对天文/惯性组合导航系统,以姿态四元数误差为观测值,具体推导了系统量测方程。利用卡尔曼滤波,对天文/惯性组合系统的融合方案进行了仿真,仿真结果较好的实现了对陀螺漂移误差的估计。     

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.     

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.     

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.     

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.