Self‐alignment and calibration of a MEMS IMU: Improving observability and estimability by rotary motions of IMU

The stationary self‐alignment and calibration (SSAC) for a low‐cost MEMS IMU is quite challenging due to the poor observability of an inertial system under static condition and the significant sensor errors of MEMS inertial sensors. This research proposes to employ IMU rotations to improve the system observability and estimability regarding the SSAC of a low‐cost MEMS IMU. IMU rotations about the X, Y, and Z axes are employed in this paper. The analytic estimation algorithm for each error state is derived and the observability of the system with IMU rotation is analyzed. As the observability analysis will not provide clues about how well an error state can be estimated, the estimability analysis is also conducted based on the eigenvalues and eigenvectors from the covariance matrix in the Kalman filter. Tests are conducted with a tri‐axial turntable to verify the improvements on system observability and estimability brought by IMU rotations. Of both theoretical analysis and results indicated with proper IMU rotations, only azimuth error still remains unobservable, and the IMU rotation also significantly improves the estimability of all error states, including the unobservable azimuth.     

具有非完整约束移动机器人的超宽带-惯导-里程计融合定位与能观测性分析

为解决现有超宽带-惯导组合定位系统在轮式移动机器人的定位精度低、依赖高精度IMU等问题,提出了一种采用误差状态卡尔曼滤波融合超宽带-惯导-里程计的定位算法,利用里程计的线速度测量和由非完整约束隐含的伪测量,提高了移动机器人的位置和姿态估计精度. 同时,对于由多传感器测量模型组成的非线性系统,通过基于李导数的能观性秩条件分析方法对该系统的能观测性进行了详细的理论分析与数学证明,得到了系统局部弱可观的条件,从而确定了系统状态可以被无偏估计所需要的测量输出以及控制输入. 仿真结果表明,在满足能观测性条件时,本文提出的方法能够有效地获得移动机器人较准确的六自由度位姿,且相比传统方法显著提升了定位精度.     

Mobile robot localization with gyroscope and constrained Kalman filter

The odometry information used in mobile robot localization can contain a significant number of errors when robot experiences slippage. To offset the presence of these errors, the use of a low-cost gyroscope in conjunction with Kalman filtering methods has been considered by many researchers. However, results from conventional Kalman filtering methods that use a gyroscope with odometry can unfeasible because the parameters are estimated regardless of the physical constraints of the robot. In this paper, a novel constrained Kalman filtering method is proposed that estimates the parameters under the physical constraints using a general constrained optimization technique. The state observability is improved by additional state variables and the accuracy is also improved through the use of a nonapproximated Kalman filter design. Experimental results show that the proposed method effectively offsets the localization error while yielding feasible parameter estimation.     

A novel motion-based online temporal calibration method for multi-rate sensors fusion

Accurate and robust calibration is an essential prerequisite for multi-rate sensors fusion. However, most existing calibration methods ignore the temporal calibration and assumed the timestamps of the multi-rate sensors are precisely aligned; more importantly, many approaches are designed for offline calibration. For these reasons, this paper develops a novel online temporal calibration method for multi-rate sensors fusion based on the motion constrains of the sensors. In this new calibration framework, the high update rate inertial measurement unit (IMU) is utilized as the unified calibrating references, while other moderate or low-frequency target sensors can be estimated based on the reference IMU. As a result, the targetless, online, and high-precision temporal self-calibration can be achieved. During the calibration, an improved multi-state constraint Kalman filter (I-MSCKF) algorithm is proposed for both position and temporal states estimation of the multi-rate sensors to establish a multi-constraint filter and correct the temporal offset error in a real-time manner. Furthermore, the motion constraints models in the two-dimensional (2D) planar and three-dimensional (3D) space are developed from per-sensor ego-motion to enhance the robust and reliable abilities of the proposed temporal self-calibration method. Experimental results demonstrate that the proposed method can accurately and online estimate the temporal offset error and transformation parameters, which significantly improves the performance of moving trajectory estimation for robots equipped with the multi-rate sensors.     

Attitude determination algorithm using state estimation including lever arms between center of gravity and IMU

In this paper, an enhanced attitude determination algorithm is proposed to decrease the estimation error by including an additive state variable for the lever arm. Attitude determination generally is carried out by measurements from an IMU (inertial measurement unit), which is typically located at the center of gravity of the vehicle. The IMU lever arm, which spans the distance between the IMU and the center of gravity, causes extra acceleration in the accelerometer and increases the error in attitude estimates. However, if the extra accelerations caused by the lever arm can be removed from the measurements of accelerometers, the increased attitude error caused by the IMU lever arm can be prevented. Because an IMU lever arm is fixed in a vehicle after installation, it can be considered as an additive element of the state vector in Kalman filter for attitude determination. The proposed algorithm is composed of a quaternion-based Kalman filter and includes an estimation of the IMU lever arm. In addition, in order to determine components of lever arm, the gross measure of modal observability is investigated for the system. An evaluation of the proposed algorithm is carried out by simulations with a noise model based on an actual IMU. Evaluations through simulations show that the proposed algorithm improves the performance with regard to errors.     

A Kalman Filter-Based Algorithm for IMU-Camera Calibration: Observability Analysis and Performance Evaluation

Vision-aided inertial navigation systems (V-INSs) canprovide precise state estimates for the 3-D motion of a vehicle when no external references (e.g., GPS) are available. This is achieved bycombining inertial measurements from an inertial measurement unit (IMU) with visual observations from a camera under the assumption that the rigid transformation between the two sensors is known. Errors in the IMU-camera extrinsic calibration process cause biases that reduce the estimation accuracy and can even lead to divergence of any estimator processing the measurements from both sensors. In this paper, we present an extended Kalman filter for precisely determining the unknown transformation between a camera and an IMU. Contrary to previous approaches, we explicitly account for the time correlation of the IMU measurements and provide a figure of merit (covariance) for the estimated transformation. The proposed method does not require any special hardware (such as spin table or 3-D laser scanner) except a calibration target. Furthermore, we employ the observability rank criterion based on Lie derivatives and prove that the nonlinear system describing the IMU-camera calibration process is observable. Simulation and experimental results are presented that validate the proposed method and quantify its accuracy.      

基于IMU阵列的标定方法

微电子机械系统(MEMS)技术的发展使惯性传感器行业发生了革命性的变化,这使得生产惯性传感器阵列成为可能。然而,低成本的惯性测量系统会受到比例因子和轴失准误差的影响,从而造成位置和姿态估计的精度降低。在单个IMU校正的基础上,设计了一套基于IMU阵列的标定方法,该标定方法为了解决传统六面法在标定IMU阵列过程中方向激励不足的问题,设计了正20面的校正装置,该标定方法不仅能够估计出IMU阵列中单个IMU的比例因子、轴失准误差和偏置,还能估计出阵列中不同IMU之间的坐标轴对齐误差。通过把标定结果和官方所给的校正参数进行对比,可以得到经过本文所提的IMU阵列标定方法得到的标定结果能够达到工厂标定结果的百分之五十到百分之九十。     

一种自适应残差补偿算法在移动机器人姿态估计中的应用研究

针对两轮移动机器人MEMS IMU姿态估计的数据融合问题,提出一种以卡尔曼滤波为基础的自适应残差补偿算法。该算法结合惯性传感器误差模型与移动机器人姿态模型构建卡尔曼滤波器,利用卡尔曼滤波量测更新的加速度残差自适应补偿非重力载体位移加速度对姿态估计的影响。实验结果表明,该算法有效的融合了MEMS IMU姿态测量数据,抑制了传感器随机漂移误差,同时自适应补偿了非重力载体位移加速度。     

MEMS陀螺仪漂移和噪声的分析和补偿

对陀螺仪数据分析的传统方法是使用kalman滤波器做尾数据处理来降低随机误差,由于陀螺仪传感器随着外界环境的变化的影响会有非线性误差,传统的kalman滤波算法处理的是线性误差,因此引进了适用于非线性系统的EKF滤波.为了快速滤除系统在实际环境中产生的噪声,对传统的中值滤波算法进行了改进,降低其计算复杂度,提出差分-均值中值滤波法.本文首先使用阿伦(ALLAN)方差分析了陀螺仪的误差特性,对于这些误差源分别提出了偏移校正的方法,之后建立自动回归-滑动平均模型(ARMA模型)对陀螺仪数据进行误差建模分析,最后使用EKF算法降低随机误差.实验结果表明该方法比传统的方法滤波效果好、计算复杂度低、实时性好.     

基于自适应Kalman滤波的MEMS陀螺随机误差分析

针对某型MEMS陀螺随机误差较大、精度不高的问题,通过时间序列分析法,建立自回归滑动平均 ARMA(Auto-Regressive and Moving Average)模型,采用ARMA(2,1)模型将预处理后的MEMS陀螺随机误差进行建模.设计基于ARMA模型的经典Kalman滤波器.静态试验和恒定速率试验结果表明在经典Kalman滤波器作用下,静态试验下其均值与均方差下降32.62%和66.31%;恒定速率试验下,其均值有明显的降低,其均方差减小了一个数量级.针对经典Kalman滤波器不能解决振动试验中大振幅时滤波发散问题,提出一种新的自适应Kalman滤波法,通过寻找合适的标定因子s解决滤波发散问题.振动试验结果表明,当振幅为100°时,滤波后的均值和均方差分别下降8.25%和8.36%.     

基于加速度分离算法的姿态测量方法研究

针对运动状态下探测器姿态解算精度不高的问题,提出了一种基于加速度分离算法的姿态测量方法。首先,分别利用椭球拟合法和建模法对加速度计、陀螺仪进行误差补偿,保证了MEMS传感器初始测量数据的精度。其次,提出了一种分离运动加速度的方法,以消除运动对加速度计测量数据的影响。最后,结合加速度分离算法实现了基于卡尔曼滤波器的高精度姿态解算。模拟实验结果表明,该姿态测量方法具有较高的精度和抗干扰能力,在变加速运动时姿态误差减小了70%以上,满足了设计的要求。     

基于多传感器的运动姿态测量算法

在基于MEMS传感技术的运动姿态测量中, 陀螺仪信号的漂移和载体线性加速度与重力加速度的叠加是影响测量结果准确性的主要原因, 实践中一般采用静态补偿和滤波技术减小测量误差. 基于自主研发的惯性测量单元, 设计了一种新型两级扩展卡尔曼滤波器: 基于四元数的运动姿态测量模型, 首先构造自适应加速度误差协方差矩阵, 消除载体线性加速度, 再采用多传感器融合技术进行数据融合, 修正陀螺仪信号漂移产生的误差. 实验表明, 本文算法结果与业界认可的动作捕捉系统Xsens的测量结果一致, 可有效满足应用需求.     

Inertial-Aided Metric States and Surface Normal Estimation using a Monocular Camera

In this paper, a visual inertial fusion framework is proposed for estimating the metric states of a Micro Aerial Vehicle (MAV) using optic flow (OF) and a homography model. Aided by the attitude estimation from the on-board Inertial Measurement Unit (IMU), the computed homography matrix is reshaped into a vector and directly fed into an Extend Kalman Filter (EKF). The sensor fusion method is able to recover metric distance, speed, acceleration bias and surface normal of the observed plane. We further consider reducing the size of the filter by using only part of the homography matrix as the system observation. Simulation results show that these smaller filters have reduced observability compared with the filter using the complete homography matrix, however it is still possible to estimate the metric states as long as one of the axes is linearly excited. Experiments using real sensory data show that our method is superior to the homography decomposition method for state and slope estimation. The proposed method is also validated in closed-loop flight tests of a quadrotor.     

基于改进MSCKF算法的室内机器人定位方法

针对传统多状态约束卡尔曼滤波算法(MSCKF)在实现机器人室内定位时,速度和位置状态方程需要对IMU中加速度计的测量数据进行积分,存在漂移和累计误差,且加速度计受重力干扰问题,本文提出改进MSCKF算法.改进MSCKF算法避免使用加速度计传感器,利用轮式里程计传感器对平移测量较为精确的优点,将IMU中陀螺仪和轮式里程计的数据进行融合,改进MSCKF算法的扩展卡尔曼(EKF)状态方程.首先利用陀螺仪传感器的角速度数据得到改进EKF姿态方程,然后利用轮式里程计传感器的平移数据,结合姿态方程中的旋转信息得到改进EKF速度和位置方程.最后在机器人操作系统(ROS)上实现MSCKF及其改进算法,并结合Turtlebot2机器人在室内进行实验验证.实验结果表明,改进MSCKF算法的运动轨迹更接近于真实轨迹,定位精度较改进前所有提高,改进前平均闭环误差是0.429 m,改进后平均闭环误差是0.348 m.     

基于误差状态卡尔曼滤波估计的旋翼无人机输入饱和控制

针对GPS（global positioning system）信号缺失环境下无人机自主飞行控制问题,设计了一种基于视觉与IMU（inertial measurement unit）融合的误差状态卡尔曼滤波（ESKF）框架,并在此基础上提出了一种新的输入饱和控制方法以进一步缓解视野约束以及运动模糊问题．不同于传统的扩展卡尔曼滤波（EKF）框架,本文设计的滤波框架是对误差状态进行更新与校正,而不是直接对系统状态进行估计．由于误差状态是小量,并且其线性程度较高,因此相对于系统状态局部线性化而言,误差状态的局部线性化的模型误差更小,进而可以提高状态估计的精度．基于ESKF框架得到的全状态估计,本文提出了一种新的线性与双曲正切混合的饱和函数,进而设计了输入饱和控制器并通过李亚普诺夫函数证明了闭环系统平衡点的渐近稳定性．最后,在旋翼无人机平台上的对比实验结果表明：本文ESKF方法得到的状态估计精度更高．另外,本文所提出的输入饱和控制方法有助于保证视觉特征在视野之内,并且比有界积分控制方法有更好的暂态以及稳态性能．     

Compensation for Periodic Star Sensor Measurement Error on Satellite

A novel method based on the least squares estimation and the augmented Kalman filter (KF) is proposed to identify and compensate for the star sensor measurement error due to the periodic star sensor alignment change. For the satellite attitude determination system, the periodic star sensor measurement error causes periodic variations in the gyroscope bias estimate. Thus, the gyroscope bias estimate is adopted as an indicator for the identification of the periodic star sensor measurement error. The high performance of the proposed method is illustrated through numerical simulations with the use of the real gyroscope data. It is shown that the proposed method is effective.     

A Rotating Sonar and a Differential Encoder Data Fusion for Map-Based Dynamic Positioning

In this paper, a dynamic positioning system using a rotating sonar and a differential encoder is proposed. The method is implemented by employing an indirect feedback Kalman filter. The state equation is written for encoder propagation and its error characteristic. A measurement equation describes a map-based measurement equation based on rotating sonar sensor data. In other words, sonar data compensates for the system and navigation errors of the differential encoder. The positioning system calculates the position and headings of a mobile robot. The real-time calculation is performed by a map-based measurement update utilizing wide-angle beam characteristics of the sonar sensor and the Kalman filter. In addition, an observability analysis for the positioning system is performed. Experimental results show that the proposed hybrid positioning system successfully provides accurate position and headings in real-time. The position and heading errors arc bounded within few centimeters and within few degrees, respectively.     

基于视觉/惯导的无人机组合导航算法研究

目前视觉惯性组合导航系统多采用优化紧/松耦合以及滤波紧/松耦合算法,应用误差状态卡尔曼滤波能够将较低频率的视觉位姿信息提升到与惯性信息同步的频率;提出一种基于自适应卡尔曼滤波的视觉惯导组合导航算法,首先考虑到系统建模与传感器测量误差,采用自适应渐消卡尔曼滤波进行导航解算,通过实时计算遗忘因子,以调节历史数据的权重,可抑制建模误差,提高组合导航系统性能,然后针对视觉SLAM解算过程造成的视觉位姿信息滞后于惯导信息的问题,提出一种延时补偿方法;仿真实验表明,采用延时补偿的自适应渐消卡尔曼滤波算法能够有效抑制建模误差,并降低视觉位姿信息滞后带来的影响,提高无人机组合导航的解算精度,姿态、速度、位置解算精度分别达到5°、0.5m/s、0.4m以内。     

基于改进卡尔曼滤波的陀螺仪误差补偿算法

针对基于卡尔曼滤波的MEMS陀螺仪误差补偿算法中量测噪声方差选取不准确的问题,提出一种基于改进卡尔曼滤波的陀螺仪误差补偿算法.卡尔曼滤波通常采用统计特性估计得到固定的量测噪声方差,无法自适应地估计不同环境下陀螺仪噪声特性.该算法将卡尔曼滤波与神经网络相融合,使用卡尔曼滤波新息矩阵作为神经网络输入,通过神经网络得到新息协方差矩阵,以此自适应地估计卡尔曼滤波量测噪声方差.将该算法应用到陀螺仪信号误差补偿中,使用Allan方差分析法对原始信号以及误差补偿后的陀螺仪信号进行分析,实验结果表明该算法能够有效地抑制陀螺仪随机误差,提高MEMS陀螺仪的精度.     

利用惯性传感器的人体运动空间轨迹追踪

人体运动的空间轨迹追踪是一种利用传感器技术和计算机技术来分析记录人体的运动过程的方法.为了实现人体运动轨迹的空间追踪,本文设计了一种人体可穿戴式的人体运动捕捉系统,通过佩戴在人体关节点的惯性传感器单元来获取肢体的实时姿态信息.惯性传感器由加速度传感器、角速度传感器和磁力计构成.通过微控制单元获取传感器数据,利用低通滤波和卡尔曼滤波来更新四元数,再将预处理后的数据由蓝牙模块实时发送到电脑端.本文通过对肢体运动的不同角度的实验,证明了利用惯性传感器可以追踪人体肢体、运动的空间轨迹.