Statistical Calibration and Comparative Modelling of an Infrared Distance Sensor Using Regression Techniques
Keywords:
Embedded systems, Infrared distance sensor, Least squares method, Linear regression, Measurement accuracy, Real-time implementation, Robotics, Sensor calibrationAbstract
This paper presents a statistical calibration approach to improve the accuracy of infrared (IR) triangulation distance sensors. These sensors operate by emitting infrared light toward a target and measuring the position of the reflected beam on a detector, where the reflection angle varies with distance. However, the output voltage does not exhibit a perfectly linear relationship with distance due to optical distortions, surface reflectivity variations, and electronic noise. Experimental data were collected using an Arduino-based acquisition system over a measurement range of 5 cm to 30 cm, representative of typical robotics and automation applications. A theoretical inverse model was first evaluated to estimate distance directly from voltage readings. However, practical deviations resulted in noticeable estimation errors. To address this limitation, a least-squares linear regression model was developed to establish an optimized voltage-to-distance mapping. Model performance was evaluated using the coefficient of determination (R²), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). Experimental results demonstrate that the calibrated model significantly reduces estimation error compared to the raw theoretical model, improving measurement reliability while maintaining computational simplicity suitable for real-time embedded systems.
References
C. Kim and G.-S. Kim, “Calibration of environmental sensor data using a linear regression technique,” International Journal of Trend in Scientific Research and Development, 2017.
R. Fang, S. Collingwood, Y. Zhang, J. B. Stanford, C. Porucznik, and D. Sleeth, “Optimizing Air Quality Monitoring: Comparative Analysis of Linear Regression and Machine Learning in Low-Cost Sensor Calibration,” Aerosol and Air Quality Research, vol. 25, no. 1–4, Apr. 2025.
V. Villena Martínez et al., “A quantitative comparison of calibration methods for RGB-D sensors using different technologies,” Sensors, 2017.
V. Yogesh, L. Grevinga, J. H. Buurke, P. H. Veltink, and C. T. M. Baten, “Novel calibration method for improved UWB sensor distance measurement in the context of application for 3D analysis of human movement,” Engineering Science and Technology an International Journal, vol. 58, pp. 101844–101844, Sep. 2024.
T. Stoyanov, R. Mojtahedzadeh, H. Andreasson, and A. J. Lilienthal, “Comparative evaluation of range sensor accuracy for indoor mobile robotics and automated logistics applications,” Robotics and Autonomous Systems, vol. 61, no. 10, pp. 1094–1105, Oct. 2013.
M. Shah, R. D. Eastman, and T. H. Hong, “An overview of robot sensor calibration methods for evaluation of perception systems,” National Institute of Standards and Technology (NIST), 2012.
Q. Ma and G. S. Chirikjian, “Sensor calibration, modelling, and simulation,” in Springer Handbook, Springer, 2018.
J. Fraden, Handbook of Modern Sensors. Cham, Switzerland: Springer, 2016.
D. C. Montgomery, Introduction to Linear Regression Analysis. Hoboken, NJ, USA: Wiley, 2012.
S. Haykin, Adaptive Filter Theory. Upper Saddle River, NJ, USA: Pearson, 2013.
Sharp Corporation, “GP2Y0A21YK0F datasheet,”
Arduino, “Analog input processing,”
