College of Mechanical Engineering and Automation, National University of Defense Technology, Changsha 410073, China.
Sensors (Basel). 2012;12(6):8157-75. doi: 10.3390/s120608157. Epub 2012 Jun 12.
This paper presents an improved iterative nonlinear calibration method in the gravitational field for both low-grade and high-grade triaxial accelerometers. This calibration method assumes the probability density function of a Gaussian distribution for the raw outputs of triaxial accelerometers. A nonlinear criterion function is derived as the maximum likelihood estimation for the calibration parameters and inclination vectors, which is solved by the iterative estimation. First, the calibration parameters, including the scale factors, misalignments, biases and squared coefficients are estimated by the linear least squares method according to the multi-position raw outputs of triaxial accelerometers and the initial inclination vectors. Second, the sequence quadric program method is utilized to solve the nonlinear constrained optimization to update the inclination vectors according to the estimated calibration parameters and raw outputs of the triaxial accelerometers. The initial inclination vectors are supplied by normalizing raw outputs of triaxial accelerometers at different positions without any a priori knowledge. To overcome the imperfections of models, the optimal observation scheme is designed according to some maximum sensitivity principle. Simulation and experiments show good estimation accuracy for calibration parameters and inclination vectors.
本文提出了一种改进的迭代非线性标定方法，用于对低等级和高等级三轴加速度计的重力场进行标定。该标定方法假设三轴加速度计原始输出的概率密度函数服从高斯分布。推导了一个非线性判据函数作为标定参数和倾斜向量的最大似然估计，通过迭代估计来求解。首先，根据三轴加速度计的多位置原始输出和初始倾斜向量，通过线性最小二乘法估计标定参数，包括标度因子、失准角、偏差和平方系数。其次，利用序列二次规划方法求解非线性约束优化问题，根据估计的标定参数和三轴加速度计的原始输出更新倾斜向量。初始倾斜向量由不同位置的三轴加速度计原始输出归一化提供，无需任何先验知识。为了克服模型的不完善性，根据一些最大灵敏度原理设计了最优观测方案。仿真和实验结果表明，标定参数和倾斜向量的估计精度良好。
