Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (4): 1461-1469.doi: 10.13229/j.cnki.jdxbgxb20200294

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

Xue-zhi YAN1(),Zi-ting WANG1,Xin WANG2()   

  1. 1.College of Communication Engineering，Jilin University，Changchun 130022，China
    2.School of Mechanical and Aerospace Engineering，Jilin University，Changchun 130022，China
  • Received:2020-05-05 Online:2021-07-01 Published:2021-07-14
  • Contact: Xin WANG E-mail:yanxz@jlu.edu.cn;wxin@jlu.edu.cn

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Abstract:

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 sensitivity ε, is derived by the total differential equation. According to the expression of ε, 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.

Key words: three-dimensional ultrasonic localization, error sensitivity, long and short baseline, error transmission, air medium

CLC Number: 

  • TN911.72

Fig.1

Principle of three-dimensional ultrasonic positioning based on TOA"

Fig.2

Common mode error sensitivity of long baseline ultrasounic positioning system"

Fig.3

Differential mode error sensitivity of long baseline ultrasonic positioning system"

Fig.4

Common mode error sensitivity of short baseline ultrasonic positioning system"

Fig.5

Differential mode error sensitivity of short baseline ultrasonic positioning system"

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