超声波三维定位系统中基线长度与误差传递关系的分析

Analysis of relationship between baseline length and error transfer in ultrasonic 3D positioning system

分析了空气介质中三维超声波定位系统的误差传递模型,通过实验得到了不同基线长度下误差敏感度的分布。三维超声定位系统的定位误差主要取决于超声测距误差和运算过程中误差传递两个方面,本文主要研究运算过程中误差传递的关系。首先,建立了定位坐标相对于超声波传播距离的偏微分方程,进而通过全微分方程推导得到误差传递关系,即误差灵敏度ε的表达式;由ε的表达式可知,接收阵列基线的相对长度和测距误差符号方向(差模测距误差和共模测距误差)直接影响误差灵敏度;然后,分别在长基线和短基线条件下,讨论共模和差模测距误差对误差灵敏度的影响,通过实验给出误差灵敏度的空间分布图。实验结果表明:长基线超声定位系统中定位误差是差模和共模测距误差共同作用结果;短基线超声定位系统中定位误差主要来源于差模测距误差,共模测距误差可以忽略,且短基线系统中差模测距误差条件下误差灵敏度要比长基线系统误差灵敏度大很多;长、短基线下灵敏度误差等高线均以类似俄罗斯套娃的形式逐层分布;误差灵敏度的空间分布图也解释了超声定位中误差分布不均匀的现象。最后,本文给出了提高定位精度的措施。

In this paper,the error transfer model of three-dimensional ultrasonic positioning(TDUP)system in air medium is provided.The distribution of error sensitivity under different baseline length is obtained through experiments.The positioning accuracy of the TDUP system mainly depends on the distance measurement error and the error transmission brought by the process of calculation.This paper is focused on the study of the error transition.Firstly,the partial differential equations of the positioning coordinates with respect to the ultrasonic propagation distance are established,and the error transfer model,the expression of the error sensitivityε,is derived by the total differential equation.According to the expression ofε,the relative length of the receiving array baseline and the direction of the distance error symbol(differential mode distance error and common mode distance error)directly affect the error sensitivity.The spatial distribution of error sensitivity is given by experiment.Next,under the condition of long baseline and short baseline,the influences of common mode and differential mode distance errors on the error sensitivity are discussed,and the spatial distribution of error sensitivity is given through experiments.The experimental results show that the positioning error in the long baseline ultrasound positioning system is the result of the combination of differential mode and common mode distance error.The positioning error in the short baseline ultrasonic positioning system mainly comes from the differential mode distance error,and the common mode ranging error could be ignored.In addition,the error sensitivity of short baseline system is much higher than that of long baseline system under the condition of difference mode.T The contour of sensitivity error is distributed layer by layer in the form of Russian dolls.The spatial distribution of error sensitivity further explains the uneven distribution of errors in ultrasonic localization.Finally,the paper proposes solutions to improve the positioning accuracy.