• 论文 • 上一篇    

基于改进Levenberg-Marquardt算法的加速度计标定模型研究

李萌, 王淑娟   

  1. 哈尔滨工程大学数学科学学院, 哈尔滨 150001
  • 收稿日期:2021-03-05 发布日期:2022-09-09

李萌, 王淑娟. 基于改进Levenberg-Marquardt算法的加速度计标定模型研究[J]. 数值计算与计算机应用, 2022, 43(3): 248-258.

Li Meng, Wang Shujuan. RESEARCH ON CALIBRATION MODEL OF ACCELEROMETER BASED ON IMPROVED LEVENBERG-MARQUARDT ALGORITHM[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(3): 248-258.

RESEARCH ON CALIBRATION MODEL OF ACCELEROMETER BASED ON IMPROVED LEVENBERG-MARQUARDT ALGORITHM

Li Meng, Wang Shujuan   

  1. School of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
  • Received:2021-03-05 Published:2022-09-09
对MEMS加速度计的标定模型进行研究是提高MEMS加速度计精度的重要方法.本文提出一种基于改进Levenberg-Marquardt算法的加速度计标定模型.基于静态多位置翻转法进行标定,根据误差建立数学模型即非线性最小二乘的求最小值问题,由于原始Levenberg-Marquardt算法在迭代求解最优估计值下降慢以及计算量大等问题,通过充分利用算法每次迭代的计算结果设置步长因子,获取最优估计值迭代次数减少,并在理论上证明了改进算法的收敛性.又针对标定后存在数值偏离真实值的问题,提出利用传感器状态信息对标定模型进行改进,使用改进标定模型的数值实验效果良好.
Research on the calibration model of MEMS accelerometer is an important method to improve the accuracy of MEMS accelerometer. An accelerometer calibration model based on improved Levenberg-Marquardt algorithm is proposed in this paper. Based on the static multi-position inversion method for calibration, according to the error to establish a mathematical model, namely the nonlinear least square minimization problem. Because the original Levenberg-Marquardt algorithm is slow to decrease and has a large amount of computation in solving the optimal estimate, the iterative times of obtaining the optimal estimate are reduced by making full use of the calculation results of each iteration of the algorithm to set the step factor, and the convergence of the improved algorithm is proved theoretically. In view of the problem that the value deviates from the real value after calibration, it is proposed to use the sensor state information to improve the calibration model, and the numerical experiments using the improved calibration model have good results.

MR(2010)主题分类: 

()
[1] 何志锋. 冰雪运动应用智能可穿戴设备的可行性研究[C]. 张家口:2017科技冬奥论坛暨体育科技产品展示会论文摘要汇编. 2017, 10-11.
[2] 刘泳庆, 蔡旭旦, 张蓓, 陈小平, 杨志良. 卫星导航系统在越野滑雪运动中的应用[C]. 北京:第十一届中国卫星导航年会. 2020, 1-3.
[3] 刘宇, 季廷洪, 向高林, 张欣, 龚爽, 宁莉莎. 基于Kalman滤波和六位置法的加速度计标定补偿[J]. 压电与声光, 2016, 38(01):94-98.
[4] Nourmohammadi H, Keighobadi J. Design and experimental evaluation of indirect centralized and direct decentralized integration scheme for low-cost INS/GNSS system[J]. Gps Solutions, 2018, 22(3):1-18.
[5] 秦永元. 惯性导航[M]. 北京:科学出版社, 2014, 35-47.
[6] Xing H, Bo H, Lin Z, Guo M. Modeling and Compensation of Random Drift of MEMS Gyroscopes Based on Least Squares Support Vector Machine Optimized by Chaotic Particle Swarm Optimization[J]. Sensors, 2017, 17(10):2335.
[7] Claudia C. Meruane Naranjo. Analysis and Modeling of MEMS based Inertial Sensors[J]. Kungliga Tekniska Hgskolan. 2008, 10-17.
[8] 秦永元, 张洪钺, 汪叔华. 卡尔曼滤波与组合导航原理[M]. 西安:西北工业大学出版社, 1998, 33-37.
[9] Ranjbaran S, Ebadollahi S. Fast and precise solving of non-linear optimisation problem for field calibration of triaxial accelerometer[J]. Electronics Letters, 2018, 54(3):148-150.
[10] Powell M J. Convergence properties of a class of minimization algorithms[J]. Optimization Letters, 1975, 1-27.
[1] 翟娜, 李亚娟, 邓重阳. 迭代逼近坐标[J]. 数值计算与计算机应用, 2022, 43(1): 112-124.
[2] 陈国茗, 于腾腾, 刘新为. 带自适应学习率的加速随机方差缩减梯度法[J]. 数值计算与计算机应用, 2021, 42(3): 215-225.
[3] 刘芳芳, 杨超. 一种提高SpMV向量化性能的新型稀疏矩阵存储格式[J]. 数值计算与计算机应用, 2014, 35(4): 269-276.
[4] 张春敏,  杨月婷. 两种混合共轭梯度法的全局收敛性[J]. 数值计算与计算机应用, 2012, 33(2): 92-98.
[5] 姚国柱, 廖安平, 段雪峰. 矩阵方程$AXB=C$的最小二乘Hamilton解[J]. 数值计算与计算机应用, 2009, 30(1): 48-57.
阅读次数
全文


摘要