Characterisation of Received Signal Strength Perturbations using Allan Variance

Chunbo Luo, Pablo Casaseca-de-la-Higuera, Sally McClean, Gerard Parr, Peng Ren

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The received signal strength (RSS) of wireless signalsconveys important information that has been widely used in wirelesscommunications, localisation and tracking. Traditional RSS-basedresearch and applications model the RSS signal using a deterministiccomponent plus a white noise term. This paper investigates theassumption of white noise to have a further understanding of theRSS signal and proposes a methodology based on the Allan Variance (AVAR) to characterise it. Using AVAR, we model the RSS unknown perturbations as correlated random terms. These terms can account for both coloured noise or other effects such as shadowing or small scale fading. Our results confirm that AVAR can be used to obtain a flexible model of the RSS perturbations, as expressed by coloured noise components . The study is complemented by introducing two straightforward applications of the proposed methodology: 1) The modelling and simulation of RSS noise using Wiener processes, and 2) RSS localisation using the extended Kalman filter.
LanguageEnglish
Pages873-889
Number of pages17
JournalIEEE Transactions on Aerospace and Electronic Systems
Volume54
Issue number2
Early online date3 Nov 2017
DOIs
Publication statusPublished - 11 Apr 2018

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White noise
Extended Kalman filters

Keywords

  • Received Signal Strength (RSS)
  • coloured noise
  • Allan variance
  • Kalman filter
  • RSS simulation
  • RSS based localization

Cite this

Luo, Chunbo ; Casaseca-de-la-Higuera, Pablo ; McClean, Sally ; Parr, Gerard ; Ren, Peng. / Characterisation of Received Signal Strength Perturbations using Allan Variance. In: IEEE Transactions on Aerospace and Electronic Systems. 2018 ; Vol. 54, No. 2. pp. 873-889.
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title = "Characterisation of Received Signal Strength Perturbations using Allan Variance",
abstract = "The received signal strength (RSS) of wireless signalsconveys important information that has been widely used in wirelesscommunications, localisation and tracking. Traditional RSS-basedresearch and applications model the RSS signal using a deterministiccomponent plus a white noise term. This paper investigates theassumption of white noise to have a further understanding of theRSS signal and proposes a methodology based on the Allan Variance (AVAR) to characterise it. Using AVAR, we model the RSS unknown perturbations as correlated random terms. These terms can account for both coloured noise or other effects such as shadowing or small scale fading. Our results confirm that AVAR can be used to obtain a flexible model of the RSS perturbations, as expressed by coloured noise components . The study is complemented by introducing two straightforward applications of the proposed methodology: 1) The modelling and simulation of RSS noise using Wiener processes, and 2) RSS localisation using the extended Kalman filter.",
keywords = "Received Signal Strength (RSS), coloured noise, Allan variance, Kalman filter, RSS simulation, RSS based localization",
author = "Chunbo Luo and Pablo Casaseca-de-la-Higuera and Sally McClean and Gerard Parr and Peng Ren",
note = "Reference text: [1] A. Wadhwa, U. Madhow, J. P. Hespanha, and B. M. Sadler, “Following an RF trail to its source,” in Proc. of the 49th Annual Allerton Conf. on Comm., Contr., and Computing, Sep. 2011. [2] I. Guvenc, C. T. Abdallah, R. Jordan, and O, “Enhancements to RSS based indoor tracking systems using Kalman filters,” GSPx & International, 2003. [3] X. Li, “RSS-based location estimation with unknown pathloss model,” IEEE Trans. Wireless Commun., vol. 5, no. 12, pp. 3626 –3633, Dec. 2006. [4] M. Mertens, M. Ulmke, and W. Koch, “Ground target tracking with RCS estimation based on signal strength measurements,” IEEE Trans. Aerosp. Electron. Syst., vol. 52, no. 1, pp. 205–220, Feb. 2016. [5] A. Weiss, “On the accuracy of a cellular location system based on RSS measurements,” IEEE Trans. Veh. Technol., vol. 52, no. 6, pp. 1508 – 1518, Nov. 2003. [6] T. Roos, P. Myllymaki, and H. Tirri, “A statistical modeling approach to location estimation,” IEEE Trans. Mobile Comput., vol. 1, no. 1, pp. 59 – 69, Jan. 2002. [7] H. Friis, “A note on a simple transmission formula,” in Pro. IRE. 34, 1946, pp. 254–256. [8] A. Goldsmith, Wireless communications. Cambridge University Press, 2005. [9] J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed. Wiley, Nov. 2000. [10] T. S. Rappaporat, Wireless Communications - Principle and Practice. Prentice-Hall, 1996. [11] J. G. Proakis, Digital communications, 4th ed. New York: McGraw- Hill, Inc., 2001. [12] H. Hashemi, “The indoor radio propagation channel,” Proceedings of the IEEE, vol. 81, pp. 943–968, 1993. [13] A. Demir, “Phase noise in oscillators: DAEs and colored noise sources,” in 1998 IEEE/ACM International Conference on Computer- Aided Design, Nov. 1998, pp. 170–177. [14] A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. (1993-2003), vol. 47, no. 5, pp. 655–674, May 2000. [15] A. Demir, “Phase noise and timing jitter in oscillators with colorednoise sources,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. (1993-2003), vol. 49, no. 12, pp. 1782–1791, Dec. 2002. [16] M. Gudmundson, “Correlation model for shadow fading in mobile radio systems,” Electronics Letters, vol. 27, pp. 2145–2146, 1991. [17] S. Wyne, A. Singh, F. Tufvesson, and A. Molisch, “A statistical model for indoor office wireless sensor channels,” Wireless Commu- nications, IEEE Transactions on, vol. 8, pp. 4154–4164, 2009. [18] A. Aubry, V. Carotenuto, A. D. Maio, and A. Farina, “Radar phase noise modeling and effects-part ii: pulse doppler processors and sidelobe blankers,” IEEE Trans. Aerosp. Electron. Syst., vol. 52, no. 2, pp. 712–725, Apr. 2016. [19] K. Pahlavan and A. Levesque, Wireless Information Networks, ser. Wiley Series in Telecommunications and Signal Processing. Wiley, 2005. [20] R. Zekavat and R. Buehrer, Handbook of Position Location: Theory, Practice and Advances, ser. IEEE Series on Digital & Mobile Communication. John Wiley & Sons, 2011. [21] P. H¨anggi and P. Jung, “Colored noise in dynamical systems,” Advances in Chemical Physics, vol. 89, pp. 239 – 326, 1995. [22] Y. Stebler, S. Guerrier, J. Skaloud, and M. P. Victoria-Feser, “Generalized method of wavelet moments for inertial navigation filter design,” IEEE Trans. Aerosp. Electron. Syst., vol. 50, no. 3, pp. 2269–2283, Jul. 2014. 14 [23] Z. Malkin, “Application of the allan variance to time series analysis in astrometry and geodesy: A review,” IEEE Trans. Ultrason., Ferroelect., Freq. Control, vol. 63, no. 4, pp. 582–589, Apr. 2016. [24] D. Allan, “Statistics of atomic frequency standards,” Proceedings of the IEEE, vol. 54, no. 2, pp. 221 – 230, Feb. 1966. [25] X. Chen, D. Schonfeld, and A. Khokhar, “Localization and trajectory estimation of mobile objects using minimum samples,” IEEE Trans. Veh. Technol., vol. 58, no. 8, pp. 4439 –4446, Oct. 2009. [26] C. Luo, S. McClean, G. Parr, L. Teacy, and R. Nardi, “UAV position estimation and collision avoidance using the extended Kalman filter,” IEEE Trans. Veh. Technol., vol. 62, no. 6, pp. 2749–2762, 2013. [27] D. Arora and M. McGuire, “Lower bounds on mobile terminal localisation in an urban area,” IET Commun., vol. 5, no. 9, pp. 1182 –1191, June 2011. [28] S. Cameron, S. Hailes, S. McClean, and et al., “Suaave: Combining aerial robots and wireless networking,” in SUAAVE. University of Oxford, University College London, University of Ulster, Feb. 2010, pp. 1–14. [29] D. C. Cox, R. R. Murray, and A. W. Norris, “800 MHz attenuation measured in and around suburban houses,” Bell Labs Tech. J., vol. 63, pp. 921–954, 1984. [30] S. Seidel and T. Rappaport, “914 MHz path loss prediction models for indoor wireless communications in multifloored buildings,” IEEE Trans. Antennas Propag., vol. 40, no. 2, pp. 207–217, Feb. 1992. [31] A. Einstein, Investigations on the Theory of the Brownian Movement, ser. Dover Books on Physics. Dover Publications, 1956. [32] R. Short, L. Mandel, and R. Roy, “Correlation functions of a dye laser: Comparison between theory and experiment,” Phys. Rev. Lett., vol. 9, no. 49, pp. 647–650, Aug. 1982. [33] L. C. Ng, “On the application of Allan variance method for ring laser gyro performance characterization,” Oct., p. 29, 1993. [34] G. M. Ljung and G. E. P. Box, “On a measure of lack of fit in time series models,” Biometrika, vol. 65, no. 2, pp. 297–303, 1978. [35] “IEEE standard definitions of physical quantities for fundamental frequency and time metrology - random instabilities,” IEEE Std 1139-1999, pp. 1–36, 1999. [36] D. Allan, “Should the classical variance be used as a basic measure in standards metrology?” IEEE Transactions on Instrumentation and Measurement, vol. IM-36, pp. 646–654, 1987. [37] N. J. Kasdin, “Discrete simulation of colored noise and stochastic processes and 1/f� power law noise generation,” IEEE Proc., vol. 83, no. 5, pp. 802–827, May 1995. [38] J. Timmer and M. Knig, “On generating power law noise,” Astron- omy and Astrophysics, vol. 300, pp. 707–710, 1995. [39] S. Robitzsch, L. Murphy, and J. Fitzpatrick, “An analysis of the received signal strength accuracy in 802.11a networks using atheros chipsets: A solution towards self configuration,” in IEEE GLOBE- COM Workshops (GC Wkshps). IEEE, Dec. 2011, pp. 1429–1434. [40] F. Vernotte, E. Lantz, J. Groslambert, and J. Gagnepain, “Oscillator noise analysis: multivariance measurement,” Instrumentation and Measurement, IEEE Transactions on, vol. 42, no. 2, pp. 342–350, Apr 1993. [41] C. Luo, P. C. de-la Higuera, S. McClean, G. Parr, and C. Grecos, “Analysis of coloured noise in received signal strength using the Allan Variance,” in 22nd European Signal Processing Conference (EUSIPCO), 2014, pp. 994–998. [42] C. Phillips and E. W. Anderson, “CRAWDAD data set cu/antenna (v. 2009-05-08),” Downloaded from http:// crawdad .cs .dartmouth .edu/cu/antenna, May 2009. [43] S. Haykin, Adaptive Filter Theory. Pearson Education, 2014. [44] J. Bendat and A. Piersol, Random Data: Analysis and Measurement Procedures, ser. Wiley Series in Probability and Statistics. John Wiley & Sons, 2010. [45] P. Embrechts and M. Maejima, Selfsimilar Processes. Princeton, NJ, USA: Princeton University Press, 2002. [46] S. M. Kay, Fundamentals of Statistical Signal Processing. Estimation Theory. Upper Saddle River, New Jersey (USA): Prentice–Hall, 1993. [47] A. Sayed, A. Tarighat, and N. Khajehnouri, “Network-based wireless location: challenges faced in developing techniques for accurate wireless location information,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 24 – 40, July 2005. [48] R. Malaney, “Nuisance parameters and location accuracy in lognormal fading models,” IEEE Trans. Wireless Commun., vol. 6, no. 3, pp. 937 –947, Mar. 2007. [49] N. Patwari, J. Ash, S. Kyperountas, I. Hero, A.O., R. Moses, and N. Correal, “Locating the nodes: cooperative localization in wireless sensor networks,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 54 – 69, July 2005. [50] J.-C. Chen, “Improved maximum likelihood location estimation accuracy in wireless sensor networks using the cross-entropy method,” in Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, Apr. 2009, pp. 1325 –1328.",
year = "2018",
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}

Characterisation of Received Signal Strength Perturbations using Allan Variance. / Luo, Chunbo; Casaseca-de-la-Higuera, Pablo; McClean, Sally; Parr, Gerard; Ren, Peng.

In: IEEE Transactions on Aerospace and Electronic Systems, Vol. 54, No. 2, 11.04.2018, p. 873-889.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Characterisation of Received Signal Strength Perturbations using Allan Variance

AU - Luo, Chunbo

AU - Casaseca-de-la-Higuera, Pablo

AU - McClean, Sally

AU - Parr, Gerard

AU - Ren, Peng

N1 - Reference text: [1] A. Wadhwa, U. Madhow, J. P. Hespanha, and B. M. Sadler, “Following an RF trail to its source,” in Proc. of the 49th Annual Allerton Conf. on Comm., Contr., and Computing, Sep. 2011. [2] I. Guvenc, C. T. Abdallah, R. Jordan, and O, “Enhancements to RSS based indoor tracking systems using Kalman filters,” GSPx & International, 2003. [3] X. Li, “RSS-based location estimation with unknown pathloss model,” IEEE Trans. Wireless Commun., vol. 5, no. 12, pp. 3626 –3633, Dec. 2006. [4] M. Mertens, M. Ulmke, and W. Koch, “Ground target tracking with RCS estimation based on signal strength measurements,” IEEE Trans. Aerosp. Electron. Syst., vol. 52, no. 1, pp. 205–220, Feb. 2016. [5] A. Weiss, “On the accuracy of a cellular location system based on RSS measurements,” IEEE Trans. Veh. Technol., vol. 52, no. 6, pp. 1508 – 1518, Nov. 2003. [6] T. Roos, P. Myllymaki, and H. Tirri, “A statistical modeling approach to location estimation,” IEEE Trans. Mobile Comput., vol. 1, no. 1, pp. 59 – 69, Jan. 2002. [7] H. Friis, “A note on a simple transmission formula,” in Pro. IRE. 34, 1946, pp. 254–256. [8] A. Goldsmith, Wireless communications. Cambridge University Press, 2005. [9] J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed. Wiley, Nov. 2000. [10] T. S. Rappaporat, Wireless Communications - Principle and Practice. Prentice-Hall, 1996. [11] J. G. Proakis, Digital communications, 4th ed. New York: McGraw- Hill, Inc., 2001. [12] H. Hashemi, “The indoor radio propagation channel,” Proceedings of the IEEE, vol. 81, pp. 943–968, 1993. [13] A. Demir, “Phase noise in oscillators: DAEs and colored noise sources,” in 1998 IEEE/ACM International Conference on Computer- Aided Design, Nov. 1998, pp. 170–177. [14] A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. (1993-2003), vol. 47, no. 5, pp. 655–674, May 2000. [15] A. Demir, “Phase noise and timing jitter in oscillators with colorednoise sources,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. (1993-2003), vol. 49, no. 12, pp. 1782–1791, Dec. 2002. [16] M. Gudmundson, “Correlation model for shadow fading in mobile radio systems,” Electronics Letters, vol. 27, pp. 2145–2146, 1991. [17] S. Wyne, A. Singh, F. Tufvesson, and A. Molisch, “A statistical model for indoor office wireless sensor channels,” Wireless Commu- nications, IEEE Transactions on, vol. 8, pp. 4154–4164, 2009. [18] A. Aubry, V. Carotenuto, A. D. Maio, and A. Farina, “Radar phase noise modeling and effects-part ii: pulse doppler processors and sidelobe blankers,” IEEE Trans. Aerosp. Electron. Syst., vol. 52, no. 2, pp. 712–725, Apr. 2016. [19] K. Pahlavan and A. Levesque, Wireless Information Networks, ser. Wiley Series in Telecommunications and Signal Processing. Wiley, 2005. [20] R. Zekavat and R. Buehrer, Handbook of Position Location: Theory, Practice and Advances, ser. IEEE Series on Digital & Mobile Communication. John Wiley & Sons, 2011. [21] P. H¨anggi and P. Jung, “Colored noise in dynamical systems,” Advances in Chemical Physics, vol. 89, pp. 239 – 326, 1995. [22] Y. Stebler, S. Guerrier, J. Skaloud, and M. P. Victoria-Feser, “Generalized method of wavelet moments for inertial navigation filter design,” IEEE Trans. Aerosp. Electron. Syst., vol. 50, no. 3, pp. 2269–2283, Jul. 2014. 14 [23] Z. Malkin, “Application of the allan variance to time series analysis in astrometry and geodesy: A review,” IEEE Trans. Ultrason., Ferroelect., Freq. Control, vol. 63, no. 4, pp. 582–589, Apr. 2016. [24] D. Allan, “Statistics of atomic frequency standards,” Proceedings of the IEEE, vol. 54, no. 2, pp. 221 – 230, Feb. 1966. [25] X. Chen, D. Schonfeld, and A. Khokhar, “Localization and trajectory estimation of mobile objects using minimum samples,” IEEE Trans. Veh. Technol., vol. 58, no. 8, pp. 4439 –4446, Oct. 2009. [26] C. Luo, S. McClean, G. Parr, L. Teacy, and R. Nardi, “UAV position estimation and collision avoidance using the extended Kalman filter,” IEEE Trans. Veh. Technol., vol. 62, no. 6, pp. 2749–2762, 2013. [27] D. Arora and M. McGuire, “Lower bounds on mobile terminal localisation in an urban area,” IET Commun., vol. 5, no. 9, pp. 1182 –1191, June 2011. [28] S. Cameron, S. Hailes, S. McClean, and et al., “Suaave: Combining aerial robots and wireless networking,” in SUAAVE. University of Oxford, University College London, University of Ulster, Feb. 2010, pp. 1–14. [29] D. C. Cox, R. R. Murray, and A. W. Norris, “800 MHz attenuation measured in and around suburban houses,” Bell Labs Tech. J., vol. 63, pp. 921–954, 1984. [30] S. Seidel and T. Rappaport, “914 MHz path loss prediction models for indoor wireless communications in multifloored buildings,” IEEE Trans. Antennas Propag., vol. 40, no. 2, pp. 207–217, Feb. 1992. [31] A. Einstein, Investigations on the Theory of the Brownian Movement, ser. Dover Books on Physics. Dover Publications, 1956. [32] R. Short, L. Mandel, and R. Roy, “Correlation functions of a dye laser: Comparison between theory and experiment,” Phys. Rev. Lett., vol. 9, no. 49, pp. 647–650, Aug. 1982. [33] L. C. Ng, “On the application of Allan variance method for ring laser gyro performance characterization,” Oct., p. 29, 1993. [34] G. M. Ljung and G. E. P. Box, “On a measure of lack of fit in time series models,” Biometrika, vol. 65, no. 2, pp. 297–303, 1978. [35] “IEEE standard definitions of physical quantities for fundamental frequency and time metrology - random instabilities,” IEEE Std 1139-1999, pp. 1–36, 1999. [36] D. Allan, “Should the classical variance be used as a basic measure in standards metrology?” IEEE Transactions on Instrumentation and Measurement, vol. IM-36, pp. 646–654, 1987. [37] N. J. Kasdin, “Discrete simulation of colored noise and stochastic processes and 1/f� power law noise generation,” IEEE Proc., vol. 83, no. 5, pp. 802–827, May 1995. [38] J. Timmer and M. Knig, “On generating power law noise,” Astron- omy and Astrophysics, vol. 300, pp. 707–710, 1995. [39] S. Robitzsch, L. Murphy, and J. Fitzpatrick, “An analysis of the received signal strength accuracy in 802.11a networks using atheros chipsets: A solution towards self configuration,” in IEEE GLOBE- COM Workshops (GC Wkshps). IEEE, Dec. 2011, pp. 1429–1434. [40] F. Vernotte, E. Lantz, J. Groslambert, and J. Gagnepain, “Oscillator noise analysis: multivariance measurement,” Instrumentation and Measurement, IEEE Transactions on, vol. 42, no. 2, pp. 342–350, Apr 1993. [41] C. Luo, P. C. de-la Higuera, S. McClean, G. Parr, and C. Grecos, “Analysis of coloured noise in received signal strength using the Allan Variance,” in 22nd European Signal Processing Conference (EUSIPCO), 2014, pp. 994–998. [42] C. Phillips and E. W. Anderson, “CRAWDAD data set cu/antenna (v. 2009-05-08),” Downloaded from http:// crawdad .cs .dartmouth .edu/cu/antenna, May 2009. [43] S. Haykin, Adaptive Filter Theory. Pearson Education, 2014. [44] J. Bendat and A. Piersol, Random Data: Analysis and Measurement Procedures, ser. Wiley Series in Probability and Statistics. John Wiley & Sons, 2010. [45] P. Embrechts and M. Maejima, Selfsimilar Processes. Princeton, NJ, USA: Princeton University Press, 2002. [46] S. M. Kay, Fundamentals of Statistical Signal Processing. Estimation Theory. Upper Saddle River, New Jersey (USA): Prentice–Hall, 1993. [47] A. Sayed, A. Tarighat, and N. Khajehnouri, “Network-based wireless location: challenges faced in developing techniques for accurate wireless location information,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 24 – 40, July 2005. [48] R. Malaney, “Nuisance parameters and location accuracy in lognormal fading models,” IEEE Trans. Wireless Commun., vol. 6, no. 3, pp. 937 –947, Mar. 2007. [49] N. Patwari, J. Ash, S. Kyperountas, I. Hero, A.O., R. Moses, and N. Correal, “Locating the nodes: cooperative localization in wireless sensor networks,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 54 – 69, July 2005. [50] J.-C. Chen, “Improved maximum likelihood location estimation accuracy in wireless sensor networks using the cross-entropy method,” in Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, Apr. 2009, pp. 1325 –1328.

PY - 2018/4/11

Y1 - 2018/4/11

N2 - The received signal strength (RSS) of wireless signalsconveys important information that has been widely used in wirelesscommunications, localisation and tracking. Traditional RSS-basedresearch and applications model the RSS signal using a deterministiccomponent plus a white noise term. This paper investigates theassumption of white noise to have a further understanding of theRSS signal and proposes a methodology based on the Allan Variance (AVAR) to characterise it. Using AVAR, we model the RSS unknown perturbations as correlated random terms. These terms can account for both coloured noise or other effects such as shadowing or small scale fading. Our results confirm that AVAR can be used to obtain a flexible model of the RSS perturbations, as expressed by coloured noise components . The study is complemented by introducing two straightforward applications of the proposed methodology: 1) The modelling and simulation of RSS noise using Wiener processes, and 2) RSS localisation using the extended Kalman filter.

AB - The received signal strength (RSS) of wireless signalsconveys important information that has been widely used in wirelesscommunications, localisation and tracking. Traditional RSS-basedresearch and applications model the RSS signal using a deterministiccomponent plus a white noise term. This paper investigates theassumption of white noise to have a further understanding of theRSS signal and proposes a methodology based on the Allan Variance (AVAR) to characterise it. Using AVAR, we model the RSS unknown perturbations as correlated random terms. These terms can account for both coloured noise or other effects such as shadowing or small scale fading. Our results confirm that AVAR can be used to obtain a flexible model of the RSS perturbations, as expressed by coloured noise components . The study is complemented by introducing two straightforward applications of the proposed methodology: 1) The modelling and simulation of RSS noise using Wiener processes, and 2) RSS localisation using the extended Kalman filter.

KW - Received Signal Strength (RSS)

KW - coloured noise

KW - Allan variance

KW - Kalman filter

KW - RSS simulation

KW - RSS based localization

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DO - 10.1109/TAES.2017.2768278

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JO - IEEE Transactions on Aerospace and Electronic Systems

T2 - IEEE Transactions on Aerospace and Electronic Systems

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