Aneta Predrag Prijić, Aleksandar Ilić, Zoran Dragoslav Prijić, Emilija Živanović, Branislav Randjelović

DOI Number
First page
Last page


Many sensors exhibit nonlinear dependence between their input and output variables and specific techniques are often applied for the linearization of their transfer characteristics. Some of them include additional analog circuits, while the others are based on different numerical procedures. One commonly used software solution is Progressive Polynomial Approximation. This method for sensor transfer function linearization shows strong dependence on the order of selected nodes in the linearization vector. There are several modifications of this method which enhance its effectiveness but require extensive computational time. This paper proposes the methodology that shows improvement over Progressive Polynomial Approximation without additional increase of complexity. It concerns the order of linearization nodes in linearization vector. The optimal order of nodes is determined on the basis of sensor transfer function concavity. The proposed methodology is compared to the previously reported methods on a set of analytical functions. It is then implemented in the temperature measurement system using a set of thermistors with negative temperature coefficients. It is shown that its implementation in the low-cost microcontrollers integrated into the nodes of reconfigurable sensor networks is justified.


Sensor Linearization, Progressive Polynomial Approximation, Reconfigurable Sensor Networks, NTC Thermistor

Full Text:



J. Rivera-Mejia, M. Carrillo-Romero, and G. Herrera-Ruiz, “Self-compensation to build reconfigurable measurement systems”, IEEE Instrumentation & Measurement Magazine, vol. 16, pp. 10–19, 2013.

D. Vasiljević, Č. Žlebič, G. Stojanović, M. Simić, L. Manjakkal, Z. Stamenković, “Cost-effective sensors and sensor nodes for monitoring environmental parameters”, Facta Universitatis, Series: Electronics and Energetics, vol. 31, no. 1, pp. 11-23, 2018.

C. Renneberg and T. Lehmann, “Analog circuits for thermistor linearization with Chebyshev optimal linearity error”, In Proc. of 18th European Conference on Circuit Theory Design, Seville, Spain, August 2007, pp. 910–913.

J. Lukić, D. Živanović and D. Denić, “A compact and cost-effective linearization circuit used for angular position sensors”, Facta Universitatis, Series: Automatic Control and Robotics, vol. 14, no. 2, pp. 123–134, 2015.

N. Khachab and M. Ismail, “Linearization techniques for nth-order sensor models in MOS VLSI technology”, IEEE Transactions on Circuits and Systems, vol. 38, no. 12, pp. 1439–1450, December 1991.

S. Jasko and G. Simon, “CSP-based sensor network architecture for reconfigurable measurement systems”, IEEE Transactions on Instrumentation and Measurement, vol. 60, no. 6, pp. 2104–2117, June 2011.

A. Žorić, D. Martinović and S. Obradović, “A simple 2D digital calibration routine for transducers”, Facta Universitatis, Series: Electronic and Energetics, vol. 19, no. 2, pp. 197-207, 2006.

L. Bengtsson, “Lookup table optimization for sensor linearization in small embedded systems”, Journal of Sensor Technology, vol. 2, pp. 177–184, 2012.

J. E. Brignell, “Software techniques for sensor compensation”, Sensors and Actuators, A, vol. 25, pp. 29–35, 1991.

A. Pašić and J. Dowling, “Linearising calibration methods for a generic embedded sensor interface (GESI)”, In Proc. of 1st International Conference on Sensing Technology, November 2005, pp. 185–190.

F. Shangchun, Z. Qiuli, Q. Jie, and Z. Pengcheng, “The temperature compensation of high precision pressure sensor based on the cubic spline interpolation”, MAPAN Journal of Metrology Society of India, vol. 21, no. 3, pp. 167–170, 2006.

R. Burden and J. Faires, Numerical Analysis, 8-th ed. Thomson Higher Education, 2005.

R. B. Srivastava and P. K. Srivastava “Comparison of Lagrange’s and Newton’s interpolating polynomials”, Journal of Experimental Science, vol. 3, no. 1, pp. 1-4, 2012.

C. Bluemm, R. Weiss, R. Weigel, and D. Brenk, “Correcting non-linearity and temperature influence of sensors through B-spline modeling”, In Proc. of IEEE International Symposium on Industrial Electronics, July 2010, pp. 3356–3361.

G. van der Horn and J. L. Huijsing, Integrated Smart Sensors Design and Calibration. Springer, 1998.

K. F. Lyahou, G. van der Horn, and J. H. Huijsing, “A noniterative polynomial 2-D calibration method implemented in a microcontroller”, IEEE Transactions on Instrumentation and Measurement, vol. 46, no. 4, pp. 752–757, August 1997.

J. Rivera, M. Carrillo, M. Chacon, G. Herrera, and G. Bojorquez, “Self-calibration and optimal response in intelligent sensors design based on artificial neural networks”, Sensors, vol. 7, pp. 1509–1529, 2007.

T. Nenov and S. Ivanov, “Linearization of characteristics of relative humidity sensor and compensation of temperature impact”, Sensors and Materials, vol. 19, no. 2, pp. 95–106, 2007.

J. Rivera, G. Herrera, M. Chacon, P. Acosta, and M. Carrillo, “Improved progressive polynomial algorithm for self-adjustment and optimal response in intelligent sensors”, Sensors, vol. 8, pp. 7410–7427, 2008.

J. Fraden, Handbook of Modern Sensors Physics, Designs, and Applications, 4th ed., New York: Springer, 2010.

J. Carr, Sensors and Circuits: Sensors, Transducers, and Supporting Circuits for Electronic Instrumentation, Measurement, and Control, Prentice Hall, 1993.

J. M. Dias Pereira, O. Postolache, and P. S. Girao, “PDF-based progressive polynomial calibration method for smart sensors linearization”, IEEE Transactions on Instrumentation and Measurement, vol. 58, no. 9, pp. 3245–3252, September 2009.

J. M. Dias Pereira, O. Postolache, and P. S. Girao, “Adaptive self-calibration algorithm for smart sensors”, In Proc. of IMTC 2005 - Instrumentation and Measurement Technology Conference, May 2005, pp. 648–652.

S. Rahili, J. Ghaisari, and A. Golfar, “Intelligent selection of calibration points using a modified progressive polynomial method”, IEEE Transactions on Instrumentation and Measurement, vol. 61, no. 9, pp. 2519–2523, September 2012.

B. Baker, “Thermistors in single supply temperature sensing circuits”, Microchip Technology Inc., Tech. Rep. AN685, 2004. Available at: http://ww1.microchip.com/downloads/en/AppNotes/00685b.pdf

NI USB-TC01 Thermocouple Measurement Device with NI Instant DAQ Technology, National Instruments, 2014, Data Sheet. Available at: http://www.ni.com/datasheet/pdf/en/ds-215.


  • There are currently no refbacks.

ISSN: 0353-3670