Lookup Table Optimization for Sensor Linearization in Small Embedded Systems


This paper treats the problem of designing an optimal size for a lookup table used for sensor linearization. In small embedded systems the lookup table must be reduced to a minimum in order to reduce the memory footprint and intermediate table values are estimated by linear interpolation. Since interpolation introduces an estimation uncertainty that increases with the sparseness of the lookup table there is a trade-off between lookup table size and estimation precision. This work will present a theory for finding the minimum allowed size of a lookup table that does not affect the overall precision, i.e. the overall precision is determined by the lookup table entries’ precision, not by the interpolation error.

Share and Cite:

L. E. Bengtsson, "Lookup Table Optimization for Sensor Linearization in Small Embedded Systems," Journal of Sensor Technology, Vol. 2 No. 4, 2012, pp. 177-184. doi: 10.4236/jst.2012.24025.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] W. Gawronski, F. Baher and E. Gama, “Track-Level-Compensation Look-Up Table Improves Antenna Poiting Precision,” 2006. http://ipnpr.jpl.nasa.gov/progress_report/42-164/164E.pdf
[2] R. A. Barlow, P. Bobbio, E. Carlier, G. Grawer, N. Voumard and R. Gjelsvik, “The Beam Energy Tracking System of the LHC Beam Dumping System”, The 10th International Conferences on Accelerators & Large Experiment Physics Control Systems, Geneva, 10-14 October, 2005, p. 02.056-4.
[3] P. Gaydecki, “New Real-Time Algorithms for Arbitrary, High Precision Function Generation with Applications to Acoustic Transducer Excitation,” Journal of Physics: Conference Series, Vol. 178, 2009, pp. 12-15. doi:10.1088/1742-6596/178/1/012015
[4] P. Hung, H. Fahmy, O. Mencer and M. J. Flynn, “Fast Division with a Small Lookup Table,” 2002. http://arith.stanford.edu/~hung/papers/asilomar.pdf
[5] M. D. Ercegovac, T. Lang, J.-M. Muller and A. Tisserand, “Reciprocation, Square Root, Inverse Square Root and Some Elementary Functions Using Small Multipliers,” IEEE Transactions on Computers, Vol. 49, No. 7, 2000, pp. 628-637.
[6] H. Hassler and N. Takagi, “Functions Evaluation by Table Look-up and Addition.” Proceedings of the 12th IEEE Symposium Computer Arithmetic, Bath, 19-21 July 1995, pp. 10-16. doi:10.1109/ARITH.1995.465382
[7] W. F. Wong and E. Goto, “Fast Evaluation of the Elementary Functions in Single Precision,” IEEE Transactions on Computers, Vol. 44, No. 3, 1995, pp. 453-457. doi:10.1109/12.372037
[8] E. Balestrieri, P. Daponte and S. Rapuano, “A State of the Art on ADC Error Compensation Methods,” IEEE Transactions on Instrumentation and Measurement, Vol. 54, No. 4, 2005, pp. 1388-1394. doi:10.1109/TIM.2005.851083
[9] A. C. Dent and C. F. N. Cowan, “Linearization of Analog-to-Digital Converters,” IEEE Transactions on Circuits and Systems, Vol. 37, No. 6, 1990, pp. 729-737. doi:10.1109/31.55031
[10] M. Frey and H.-A. Loeliger, “On Flash A/D Converters with Low-Precision Comparators,” Proceedings of IEEE International Symposium on Circuits and Systems, Greece, 21-24 May 2006, pp. 3926-3929.
[11] S. A. Jawed, “Analog-to-Digital Converter Design for Non-Uniform Quantization”, Master Thesis, University of Linkoping, Linkoping, 2004. http://liu.diva-portal.org/smash/get/diva2:19990/FULLTEXT01
[12] M. Pascale, “Microcontrollers CORDIC Methods”, 2004. http://www.drdobbs.com/184404244
[13] S. L. Gaverick, K. Fujino, D. T. McGrath and R. D. Baertsch, “A Programmable Mixed-Signal ASIC for Power Metering,” IEEE Journal of Solid-State Circuits, Vol. 26, No. 12, 1991, pp 2008-2016. doi:10.1109/4.104195
[14] E. Laulainen, L. Koskinen, M. Kosunen and K. Halonen, “Compass Tilt Compensation Algorithm Using CORDIC,” Proceedings of the 2008 IEEE International Symposium on Circuits and Systems, Vol. 1-10, 2008, pp 1188-1191.
[15] M. Beckman and L. Chioye, “Precision Thermocouple Measurement with the ADS1118,” Texas Instruments, 2011. http://www.ti.com/lit/an/sbaa189/ sbaa189.pdf
[16] J. Julicher, “Simplified Thermocoupld Interfaces and PIC micro MCUs,” Microchip Technology, 2002.
[17] Mathworks, “Look-up Tables and Polynomials,” 2000. http://radio.feld.cvut.cz/matlab/toolbox/rtw/rtw_ug/opt_mod4.html
[18] B. C. Baker, “Precision Temperature-Sensing with RTD Circuits”, 2008. http://ww1.microchip.com/downloads/en/appnotes/00687c.pdf
[19] J. Day and S. Bible, “Piecewise Linear Interpolation on PIC12/14/16 Series Microcontrollers,” 2004. http://ww1.microchip.com/downloads/en/AppNotes/00942A.pdf
[20] J. M. D. Pereira, P. M. B. S. Girao and O. Postolache, “Fitting Transducer Characteristics to Measured Data,” IEEE Instrumentation & Measurement Magazine, Vol. 4, No. 4, 2001, pp. 26-39.
[21] H. Erdem, “Implementation of Software-Based Sensor Linearization Algorithms on Low-Cost Microcontrollers,” ISA Transactions, Vol. 49, No. 4, 2010, pp. 552-558. doi:10.1016/j.isatra.2010.04.004
[22] P. Hille, R. Hohler and H. Strack, “A Linearisation and Compensation Method for Integrated Sensors,” Sensors and Actuators A, Vol. 44, No. 2, 1994, pp. 95-102. doi:10.1016/0924-4247(94)00795-0
[23] “PIC32MX1XX/2XX Data Sheet,” Microchip Technology Inc., 2011. http://ww1.microchip.com/downloads/en/DeviceDoc/61168D.pdf
[24] K. Post, “Interpolated Table Lookups Using SSE2 [1/2],” 2010. http://rawstudio.org/blog/?p=457
[25] G. Bucci, M. Faccio and C. Landi “New ADC with Piecewise Linear Characteristic: Case Study—Implementation of a Smart Humidity Sensor”. IEEE Transactions on Instrumentation and Measurements, Vol. 49, No. 6, 2000, pp. 1154-1166.
[26] S. Khan, A. H. M. Z. Alam, S. M. Ahmmad, I. B. Tijani, M. A. Hasan, L. W. Adetunji, S. F. Abdulazeez, S. H. M. Zaini, S. A. Othman and S. S. Khan, “On the Issue of Linearizing a Sensor Characteristic over a Wider Response Range”, Proceedings of the International Conference on Computer and Communication Engineering, Kuala Lumpur, 13-15 May 2008, pp. 72-76.
[27] Microchip, “Temperature Sensor Design Guide”, Microchip Inc., 2009. http://ww1.microchip.com/downloads/en/DeviceDoc/21895d.pdf
[28] B. Trump “Analog Linearization of Resistance Temperature Detectors,” Analog Application Journal, Vol. 4Q, 2011, pp. 21-24.
[29] J. E. Brignell, “Software Techniques for Sensor Compensation,” Sensors and Actuators A, Vol. 25, No. 1-3, 1991, pp. 29-35.
[30] B. Stringham, J. Leonard and S. Yakimchuk, “A Universal Sensor Linearizing Circuit,” Computers and Electronics in Agriculture, Vol. 4, No. 1, 1989, pp. 81-84. doi:10.1016/0168-1699(89)90016-1
[31] D. K. Anvekar and B. S. Sonde, “Transducer Output Signal Processing Using Dual and Triple Microprocessor Systems,” IEEE Transactions on Instrumentation and Measurement, Vol. 38, No. 3, 1989, pp.834-836. doi:10.1109/19.32204
[32] A. Flammini, D. Marioli and A. Taroni, “Transducer Output Signal Processing Using an Optimal Look-up Table in Microcontroller-Based Systems,” Electronics Letters, Vol. 33, No. 14, 1997, pp. 1197-1198. doi:10.1049/el:19970809
[33] A. Flammini, D. Marioli and A. Taroni, “Application of an Optimal Look-up Table to Sensor Data Processing,” IEEE Transactions on Instrumentation and Measurement, Vol. 48, No. 4, 1999, pp. 813-816. doi:10.1109/19.779179
[34] P. N. Mahana and F. N. Trofimenkoff, “Transducer Output Signal Processing Using an 8-Bit Microcontroller,” IEEE Transactions on Instrumentation and Measurement, Vol. 35, No. 2, 1986, pp. 182-186.
[35] “Sensors, Excitation and Linearization”, 2007. http://media.wiley.com/product_data/excerpt/33/07803601/0780360133-2.pdf
[36] Microchip, “PIC18FXX8 Data Sheet,” Microchip Inc., 2003. http://www.micrchip.com/wwwproducts/Devices.aspx?dDocName=en010301
[37] S. Y. C. Catunda, O. R. Saavedra, J. V. FonsecaNeto and R. A. Morais, “Look-up Table and Breakpoints Determination for Piecwise Linear Approximation Functions Using Evolutionary Computation,” IMTC 2003, Instrumentation and Measurement Technology Conference, Vail, 20-22 May 2003, pp. 435-440.
[38] L. Rade and B. Westergren, “Mathematics Handbook for Science and Engineering”, 3rd Edition, Studentlitteratur, Lund, 1995.
[39] P. Pohl, G. Eriksson and G. Dahlquist,“Numeriska Metoder”, 5th Edition, ILiber Tryck, Stockholm, 1982.
[40] E. O. Doeblin, “Measurement Systems—Application and Design,” 4th Editio, McGraw-Hill, Singapore, 1990.
[41] B. Cipra, “How Number-Theory Got the Best of the Pentium Chip”, Science, Vol. 267, No. 5295, 1995, p. 175. doi:10.1126/science.267.5195.175

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.