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Theoretical and Practical Limits in Position Estimation Based on Received Signal Strength Measurements

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Abstract

In this study, theoretical limits in position estimation in Wireless Sensor Network (WSN) using a trilateration method are derived in the form of probability density functions (PDFs) and compared with practical limits obtained via received signal strength (RSS) measurements in an anechoic chamber. In particular, the PDF of the radius of error of an unknown node’s position has been derived as having a Nakagami-m distribution. The theoretical PDFs is validated via Kolmogorov–Smirnov hypothesis tests at 95% confidence level against the empirical results of position estimation in a 4 m × 4 m area using the RSS measured in an ideal environment of an anechoic chamber. High-resolution equipment is used in the RSS measurements to ensure the inaccuracies due to limited-capability WSN equipment can be quantified. A lower bound of positioning accuracy to be expected in real environments via the received signal strength method has been established to be in the range of 11 cm from the true position with 95% confidence level. Better results cannot be expected in the real environments with bigger variations than the variations observed in the anechoic chamber unless a more sophisticated algorithm, equipment with better resolution and/or more precise measurement methods are employed.

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References

  1. (2013) CC2420 datasheet [Online]. http://www.ti.com/lit/ds/symlink/cc2420.pdf. Accessed: 28 January, 2018.

  2. Al Alawi, R. (2011). RSSI based location estimation in wireless sensors networks. In 17th IEEE international conference on networks (pp. 118–122). https://doi.org/10.1109/ICON.2011.6168517.

  3. Alsindi, N., et al. (2014). An empirical evaluation of a probabilistic RF signature for WLAN location fingerprinting. IEEE Transactions Wireless Communications, 13(6), 3257–3268. https://doi.org/10.1109/TWC.2014.041714.131113.

    Article  Google Scholar 

  4. Bensky, A. (2016). Wireless positioning technologies and applications, ch. 1, sec. 3 (2nd ed., pp. 7–10). Norwood, MA: Artech House.

    Google Scholar 

  5. Berber, S. M., et al. (2014). Measurement and mean power estimation in indoor wireless channel based on higher order Kalman filtering. IEEE Transactions on Instrumentation and Measurements, 63, 2771–2778. https://doi.org/10.1109/TIM.2014.2320832.

    Article  Google Scholar 

  6. Boano, C. A., et al. (2014). Mitigating the adverse effects of temperature on low-power wireless protocols. In IEEE 11th international conference on mobile ad hoc and sensor system (pp. 336–344). IEEE. https://doi.org/10.1109/MASS.2014.14.

  7. Bryant, G. H. (1993). Wireless positioning technologies and applications. Bristol: Peregrinus.

    Google Scholar 

  8. Chen, Y., & Terzis, A. (2010). On the mechanisms and effects of calibrating RSSI measurements for 802.15.4 radios. In Wireless sensor networks: 7th European conference (pp. 256–271). Berlin: Springer. https://doi.org/10.1007/978-3-642-11917-0_17.

  9. Chizhik, D., et al. (2012). Radio wave diffusion indoors and throughput scaling with cell density. IEEE Transactions Wireless Communications, 11, 3284–3291. https://doi.org/10.1109/TWC.2012.062012.111779.

    Article  Google Scholar 

  10. Coluccia, A. (2013). Reduced-bias ML-based estimators with low complexity for self-calibrating RSS ranging. IEEE Transactions Wireless Communications, 12(3), 1220–1230. https://doi.org/10.1109/TWC.2013.011713.120557.

    Article  Google Scholar 

  11. Gezici, S. (2008). A survey on wireless position estimation. Wireless Personal Communications, 44(3), 263–282. https://doi.org/10.1007/s11277-007-9375-z.

    Article  Google Scholar 

  12. Goldsmith, A. (2005). Wireless communications, ch. 3, sec. 2 (p. 79). Cambridge: Cambridge University Press.

    Book  Google Scholar 

  13. Jiang, J. A., et al. (2013). A distributed RSS-based localization using a dynamic circle expanding mechanism. IEEE Sensors Journal, 13(10), 3754–3766. https://doi.org/10.1109/JSEN.2013.2258905.

    Article  Google Scholar 

  14. Kendall, M., & Stuart, A. (1977). The advanced theory of statistics (4th ed., Vol. 1). London: Charles Griffin and Company Ltd.

    MATH  Google Scholar 

  15. Konings, D., et al. (2017). Do RSSI values reliably map to RSS in a localization system? In 2nd workshop on recent trends in telecommunication research (RTTR) (pp. 1–5). https://doi.org/10.1109/RTTR.2017.7887867.

  16. Lee, W. Y., et al. (2012). Mobile robot navigation using wireless sensor networks without localization procedure. Wireless Personal Communications, 62(2), 257–275. https://doi.org/10.1007/s11277-010-0052-2.

    Article  Google Scholar 

  17. Liu, Y., et al. (2017). RSS-based ranging by leveraging frequency diversity to distinguish the multiple radio paths. IEEE Transactions on Mobile Computing, 16, 1121–1135. https://doi.org/10.1109/TMC.2016.2579619.

    Article  Google Scholar 

  18. MacCartney, G. R, Jr., et al. (2015). Indoor office wideband millimeter-wave propagation measurements and channel models at 28 and 73 GHz for ultra-dense 5G wireless networks. IEEE Access, 3, 2388–2424. https://doi.org/10.1109/ACCESS.2015.2486778.

    Article  Google Scholar 

  19. Marsaglia, G., et al. (2003). Evaluating Kolmogorov’s distribution. Journal of Statistical Software, 8(18), 1–4. https://doi.org/10.18637/jss.v008.i18.

    Article  Google Scholar 

  20. Mohd Azmi, K. (2017). Derivations of probability density functions for indoor position estimation. Technical report, The University of Auckland.

  21. Mohd Azmi, K., et al. (2016). Channel parameters and distance estimation in wireless sensor networks based on maximum likelihood estimation method. In International conference on computing and communication engineering (pp. 400–405). IEEE. https://doi.org/10.1109/ICCCE.2016.91.

  22. Ning, C., et al. (2016). Outdoor location estimation using received signal strength-based fingerprinting. Wireless Personal Communications, 89(2), 365–384. https://doi.org/10.1007/s11277-016-3270-4.

    Article  Google Scholar 

  23. Papoulis, A., & Pillai, S. U. (2002). Probability, random variables and stochastics processes (4th ed.). New York: McGraw-Hill.

    Google Scholar 

  24. Pivato, P., et al. (2011). Accuracy of RSS-based centroid localization algorithms in an indoor environment. IEEE Transactions on Instrumentation and Measurement, 60(10), 3451–3460.

    Article  Google Scholar 

  25. Rappaport, T. S. (1996). Wireless communications, ch.3, sec. 11 (1st ed., pp. 123–133). Upper Saddle River, NJ: Prentice Hall PTR.

    Google Scholar 

  26. Sharma, G., & Kumar, A. (2017). Dynamic range normal bisector localization algorithm for wireless sensor networks. Wireless Personal Communications, 97(3), 4529–4549. https://doi.org/10.1007/s11277-017-4736-8.

    Article  Google Scholar 

  27. Shnidman, D. A. (1995). Efficient computation of the circular error probability (CEP) Integral. IEEE Transactions Automatic Control, 40(8), 1472–1474. https://doi.org/10.1109/9.402244.

    Article  MathSciNet  MATH  Google Scholar 

  28. Silva, H. D., et al. (2016). Body attenuation and path loss exponent estimation for RSS-based positioning in WSN. Wireless Personal Communications, 94(3), 1–23. https://doi.org/10.1007/s11277-016-3653-6.

    Article  Google Scholar 

  29. Wang, Y., et al. (2013). Propagation characteristics of the LTE indoor radio channel with persons at 2.6 GHz. IEEE Antennas and Wireless Propagation Letters, 12, 991–994. https://doi.org/10.1109/LAWP.2013.2275811.

    Article  Google Scholar 

  30. Weiss, A. J. (2003). On the accuracy of a cellular location system based on RSS measurements. IEEE Transactions on Vehicular Technology, 52(6), 1508–1518. https://doi.org/10.1109/TVT.2003.819613.

    Article  Google Scholar 

  31. Xue, W., et al. (2017). Improved Wi-Fi RSSI measurement for indoor localization. IEEE Sensors Journal, 17, 2224–2230. https://doi.org/10.1109/JSEN.2017.2660522.

    Article  Google Scholar 

  32. Yiğitler, H., et al. (2017). On log-normality of RSSI in narrowband receivers under static conditions. IEEE Signal Processing Letters, 24, 367–371. https://doi.org/10.1109/LSP.2017.2657332.

    Article  Google Scholar 

  33. Zanella, A. (2016). Best practice in RSS measurements and ranging. IEEE Communications Surveys & Tutorials, 18, 2662–2686. https://doi.org/10.1109/COMST.2016.2553452.

    Article  Google Scholar 

  34. Zhang, Y., et al. (2009). The design and implementation of a RSSI-based localization system. In 5th international conference on wireless communications, networking and mobile computing (pp. 1–4). https://doi.org/10.1109/WICOM.2009.5303968.

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Authors and Affiliations

  1. The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Kaiyisah Hanis Mohd Azmi, Stevan M. Berber & Michael J. Neve

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  1. Kaiyisah Hanis Mohd Azmi
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  2. Stevan M. Berber
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  3. Michael J. Neve
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Correspondence to Kaiyisah Hanis Mohd Azmi.

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Mohd Azmi, K.H., Berber, S.M. & Neve, M.J. Theoretical and Practical Limits in Position Estimation Based on Received Signal Strength Measurements. Wireless Pers Commun 111, 1295–1311 (2020). https://doi.org/10.1007/s11277-019-06915-9

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