Attitude estimation by divided difference filter in quaternion space
Attitude estimation by divided difference filter in quaternion space
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DOI：
10.1016/j.actaastro.2011.12.022
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发表时间：
2012-06-01
影响因子：
3.5
通讯作者：
Karimaghaee, Paknoush
中科院分区：
文献类型：
--
作者：
Ahmadi, Mohammad;Khayatian, Alireza;Karimaghaee, Paknoush
基于四元数误差连续-离散时间模型，研究了差分滤波在方位估计中的应用。DDF是一种非线性估计器，与泰勒展开的扩展卡尔曼滤波(EKF)不同，它利用多项式近似作为Stirling插值公式的多变量扩展，并且不需要导数。DDF可以基于一阶和二阶Stirling插值法，称为一阶分割差分滤波(DDF1)和二阶分割差分滤波(DDF2)。方向运动学定义在四元数向量空间中，与欧拉角表示不同，该空间不存在任何奇异性问题。该非线性姿态模型是一种精确的误差模型，与刚体动力学无关。该非线性过程模型包括六个误差状态，其中误差状态方程中只包含四元数误差向量的非标量元素。为了减小估计误差协方差矩阵的发散性，从系统状态中去掉了四元数误差向量中服从单位范数约束的第四个元素。测量系统为MARC传感器，由三轴速率陀螺、三轴加速度计和三轴磁强计组成。根据磁强计和加速度计的基本原理和四元数向量空间的性质，建立了磁强计和加速度计的非线性测量模型。针对所提出的非线性定向模型，从均方根误差、误差范数曲线下的捕获面积、估计状态方差和计算量等方面比较了DDF、EKF和Unscented Kalman Filter(UKF)三种滤波器在不同采样频率下的性能。结果表明，在相同的初始角度误差条件下，DDFS和UKF比EKF具有更好的鲁棒性。与无迹卡尔曼滤波(UKF)相比，DDF的性能更好，但UKF的计算量更小。在DDF1和DDF2中，DDF2的S性能略好，但计算量较大。在没有初始角度误差条件的情况下，这四种滤波器的性能是相同的，特别是当考虑低噪声水平条件时。(C)2012爱思唯尔有限公司。保留所有权利。
This article considers the application of Divided Difference Filter (DDF) to the orientation estimation, based on a quaternion-error continuous-discrete time model. DDF is a nonlinear estimator that in contrast to Taylor's expansion of extended Kalman Filter (EKF), exploit the polynomial approximations as a multivariable extension of Stirling's interpolation formula and require no derivatives. The DDF can be based on 1st and 2nd order Stirling's interpolation, which is named the divided difference filter-1st order (DDF1) and the divided difference filter-2nd order (DDF2). The orientation kinematics is defined in a quaternion vector space that unlike the Euler angle representation does not have any singularity problem. The presented nonlinear orientation model is an exact error model and is independent of the rigid body dynamics. The nonlinear process model includes six error-states in which only non-scalar elements of quaternion error vector are included in the error-state equations. The fourth element of quaternion error vector, which obeys unit norm constraint, is removed from system states to alleviate the estimated error covariance matrix divergence. The measurement system is a MARC sensor, which consists of a tri-axial rate gyro, a tri-axial accelerometer and a tri-axial magnetometer. The nonlinear measurement model is obtained based on the principals of magnetometer and accelerometer and the properties of the quaternion vector space. For the presented nonlinear orientation model, the performance of three filters namely DDF, EKF and Unscented Kalman Filter (UKF) is compared for different sampling frequencies in terms of the rms error, the captured area under the error norm curve, the estimated state variance and the computational cost. It is shown that under the same initial angle-error conditions, DDFs and UKF are more robust than EKF. The DDFs perform better than unscented Kalman filter (UKF) although the computational load for UKF is less. Among DDF1 and DDF2, DDF2's performance is slightly better but with more computation load. In the case of no initial angle-error conditions, the performance of the four filters is the same especially when the low noise level condition is considered. (c) 2012 Elsevier Ltd. All rights reserved.