© The Institution of Engineering and Technology
For localisation algorithms of wireless sensor networks (WSNs), the communication overhead and the computational complexity are two main bottlenecks that should be considered beside the positioning accuracy. In this study, the authors focus on cooperative localisation in WSNs and propose a low-complexity distributed cooperative localisation algorithm by employing variational message passing (VMP) on factor graphs. In order to decrease the communication overhead, Gaussian parametric message representation is adopted. With regard to the non-Gaussian messages caused by the non-linear ranging model, they approximate them to Gaussian messages by exploiting second-order Taylor expansion to reduce the computational complexity. Simulation results show that the proposed algorithm performs quite similar to sum-product algorithm over a wireless network and Gaussian VMP algorithm based on minimising Kullback–Leibler divergence with lower computational complexity.
References
-
-
1)
-
16. Ihler, A.T., Fisher, J.W., Moses, R.L., et al: ‘Nonparametric belief propagation for self-localization of sensor networks’, IEEE J. Sel. Areas Commun., 2005, 23, (4), pp. 809–819 (doi: 10.1109/JSAC.2005.843548).
-
2)
-
4. Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J.: ‘Global positioning system: theory and practice’ (Springer-Verlag, Wien, 2001).
-
3)
-
25. Rice, S.O.: ‘Mathematical analysis of random noise’ (Bell Telephone Labs Inc., New York, , 1944).
-
4)
-
9. Li, B., Wu, N., Wang, H., et al: ‘Expectation-maximisation-based localisation using anchors with uncertainties in wireless sensor networks’, IET Commun., 2014, 8, (11), pp. 1977–1987 (doi: 10.1049/iet-com.2014.0025).
-
5)
-
18. Lien, J., Ferner, U.J., Srichavengsup, W., et al: ‘A comparison of parametric and sample-based message representation in cooperative localization’, Int. J. Navig. Obs., 2012, p. 10, .
-
6)
-
20. Li, B., Wu, N., Wang, H., et al: ‘Gaussian message passing-based cooperative localization on factor graph in wireless networks’, Singal Process., 2015, 111, pp. 1–12 (doi: 10.1016/j.sigpro.2014.12.001).
-
7)
-
13. Caceres, M.A., Sottile, F., Garello, R., et al: ‘Hybrid GNSS-ToA localization and tracking via cooperative unscented Kalman filter’. IEEE 21st Int. Symp. on Personal, Indoor and Mobile Radio Communications Workshops (PIMRC Workshops), Istanbul, Turkey, September 2010, pp. 272–276.
-
8)
-
8. Karimand, L., Nasser, N.: ‘Reliable location-aware routing protocol for mobile wireless sensor network’, IET Commun., 2012, 6, (14), pp. 2149–2158 (doi: 10.1049/iet-com.2011.0696).
-
9)
-
22. Riegler, E., Kirkelund, G.E., Manchón, C.N., et al: ‘Merging belief propagation and the mean field approximation: a free energy approach’. Int. Symp. on Turbo Codes and Iterative Information Processing (ISTC), Brest, France, September 2010, pp. 256–260.
-
10)
-
24. Pedersen, C., Pedersen, T., Fleury, B.H.: ‘A variational message passing algorithm for sensor self-localization in wireless networks’. IEEE Int. Symp. on Information Theory Proc. (ISIT), St. Petersburg, Russia, August 2011, pp. 2158–2162.
-
11)
-
8. Lin, L., So, H.C., Chan, F.K.W., et al: ‘A new constrained weighted least squares algorithm for TDOA-based localization’, Signal Process., 2013, 93, (11), pp. 2872–2878 (doi: 10.1016/j.sigpro.2013.04.004).
-
12)
-
12. Lui, K.W.K., Chan, F.K.W., So, H.C.: ‘Semidefinite programming approach for range-difference based source localization’, IEEE Trans. Signal Process., 2008, 57, (4), pp. 1630–1633 (doi: 10.1109/TSP.2008.2010599).
-
13)
-
23. Riegler, E., Kirkelund, G.E., Manchón, C.N., et al: ‘Merging belief propagation and the mean field approximation: a free energy approach’, IEEE Trans. Inf. Theory, 2013, 59, (1), pp. 588–602 (doi: 10.1109/TIT.2012.2218573).
-
14)
-
8. Caceres, M.A., Penna, F., Wymeersch, H., Garello, R.: ‘Hybrid cooperative positioning based on distributed belief propagation’, IEEE J. Sel. Areas Commun., 2011, 29, (10), pp. 1948–1958 (doi: 10.1109/JSAC.2011.111205).
-
15)
-
10. Kschischang, F.R., Frey, B.J., Loeliger, H.-A.: ‘Factor graphs and the sum-product algorithm’, IEEE Trans. Inf. Theory, 2001, 47, pp. 498–519 (doi: 10.1109/18.910572).
-
16)
-
1. Salman, N., Ghogho, M., Kemp, A.H.: ‘Optimized low complexity sensor node positioning in wireless sensor networks’, IEEE Sens. J., 2014, 14, (1), pp. 39–46 (doi: 10.1109/JSEN.2013.2278864).
-
17)
-
21. Wu, N., Li, B., Wang, H., et al: ‘Distributed cooperative localization based on Gaussian message passing on factor graph in wireless networks’, Sci. China Inf. Sci., 2015, 58, (4), pp. 1–15.
-
18)
-
3. Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: ‘A survey on sensor networks’, IEEE Commun. Mag., 2002, 40, (8), pp. 102–114 (doi: 10.1109/MCOM.2002.1024422).
-
19)
-
5. Wymeersch, H., Lien, J., Win, M.Z.: ‘Cooperative localization in wireless networks’, Proc. IEEE, 2009, 97, (2), pp. 427–450 (doi: 10.1109/JPROC.2008.2008853).
-
20)
-
10. Kantas, N., Singh, S.S., Doucet, A.: ‘Distributed maximum likelihood for simultaneous self-localization and tracking in sensor networks’, IEEE Trans. Signal Process., 2012, 60, (10), pp. 5038–5047 (doi: 10.1109/TSP.2012.2205923).
-
21)
-
33. Shen, Y., Wymeersch, H., Win, M.Z.: ‘Fundamental limits of wideband localization-part II: cooperative networks’, IEEE Trans. Inf. Theory, 2010, 56, (10), pp. 4981–5000 (doi: 10.1109/TIT.2010.2059720).
-
22)
-
4. Patwari, N., Ash, J., Kyperountas, S., et al: ‘Locating the nodes: cooperative localization in wireless sensor networks’, IEEE Signal Process. Mag., 2005, 22, (4), pp. 54–69 (doi: 10.1109/MSP.2005.1458287).
-
23)
-
14. Sottile, F., Wymeersch, H., Caceres, M.A., et al: ‘Hybrid GNSS-terrestrial cooperative positioning based on particle filter’. IEEE Global Telecommunications Conf. (GLOBECOM), Houston, TX, USA, December 2011, pp. 1–5.
-
24)
-
3. Gustafsson, F., Gunnarsson, F.: ‘Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements’, IEEE Signal Process. Mag., 2005, 22, (4), pp. 41–53 (doi: 10.1109/MSP.2005.1458284).
-
25)
-
11. Biswas, P., Liang, T.-C., Toh, K.-C., et al: ‘Semidefinite programming approaches for sensor network localization with noisy distance measurements’, IEEE Trans. Autom. Sci. Eng., 2006, 3, (4), pp. 360–371 (doi: 10.1109/TASE.2006.877401).
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