Abstract
Although anchors are the most common in cooperative localizations, they are not the optimal in the class of equality constraints which provide the global reference information for deriving absolute locations. Using Cramér-Rao lower bound (CRLB) to evaluate the localization accuracy, this paper derives the optimal equality constraints that achieve the lowest CRLB trace under given constraint number, and analyzes the feasibility of constructing the optimal constraints before knowing the node ground truth locations. Simulations compare the performance between the anchor-type constraints and the optimal ones, and suggest a cooperative localization algorithm by using the optimal equality constraints.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sadowski, S., Spachos, P.: RSSI-based indoor localization with the internet of things. IEEE Access 6, 30149–30161 (2018)
Kim, H., Granström, K., Gao, L., Battistelli, G., Kim, S., Wymeersch, H.: 5G mmWave cooperative positioning and mapping using multi-model PHD filter and map fusion. IEEE Trans. Wirel. Commun. 19(6), 3782–3795 (2020)
Patwari, N., Ash, J.N., Kyperountas, S., Hero III, A.O., Moses, R.L., Correal, N.S.: Locating the nodes: cooperative localization in wireless sensor networks. IEEE Signal Process. Mag. 22(4), 54–69 (2005)
Jawad, M., Azam, H., Siddiqi, S.J., Imtiaz-Ul-Haq, M., Ahmad, T.: Comparative analysis of localization schemes in conventional vs. next generation cellular networks. In: Proceedings of the 15th International Conference on Emerging Technologies (ICET 2019), pp. 1–6 (2019)
Zhang, P., Wang, Q.: On using the relative configuration to explore cooperative localization. IEEE Trans. Signal Process. 62(4), 968–980 (2014)
Zhang, P., Cao, A., Liu, T.: Bound analysis for anchor selection in cooperative localization. In: Chen, F., Luo, Y. (eds.) Industrial IoT 2017. LNICST, vol. 202, pp. 1–10. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60753-5_1
Huang, J., Liang, J., Luo, S.: Method and analysis of TOA-based localization in 5G ultra-dense networks with randomly distributed nodes. IEEE Access 7, 174986–175002 (2019)
Zhang, P., Yan, N., Zhang, J., Yuen, C.: Optimal minimally constrained system in cooperative localization. In: International Conference on Wireless Communications Signal Processing (WCSP 2015), pp. 1–5 (2015)
Patwari, N., Hero III, A.O., Perkins, M., Correal, N.S., O’Dea, R.J.: Relative location estimation in wireless sensor networks. IEEE Trans. Signal Process. 51(8), 2137–2148 (2003)
Savvides, A., Garber, W., Adlakha, S., Moses, R., Srivastava, M.B.: On the error characteristics of multihop node localization in ad-hoc sensor networks. In: Zhao, F., Guibas, L. (eds.) IPSN 2003. LNCS, vol. 2634, pp. 317–332. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36978-3_21
Niculescu, D., Nath, B.: Ad hoc positioning system (APS). In: Proceedings of the IEEE Global Communication Conference, vol. 5, pp. 2926–2931 (2001)
Langendoen, K., Reijers, N.: Distributed localization in wireless sensor networks: a quantitative comparison. Comput. Netw. 43(4), 499–518 (2003)
Biswas, P., Lian, T.C., Wang, T.C., Ye, Y.: Semidefinite programming based algorithms for sensor network localization. ACM Trans. Sen. Netw. 2(2), 188–220 (2006)
Chan, F.K.W., So, H.C.: Accurate distributed range-based positioning algorithm for wireless sensor networks. IEEE Trans. Signal Process. 57(10), 4101–4105 (2009)
Sun, M., Ho, K.C.: Successive and asymptotically efficient localization of sensor nodes in closed-form. IEEE Trans. Signal Process. 57(11), 4522–4537 (2009)
Vemula, M., Bugallo, M.F., Djuric, P.M.: Sensor self-localization with beacon position uncertainty. Signal Process. 89(6), 1144–1154 (2009)
Garcia, M., Martinez, C., Tomas, J., Lloret, J.: Wireless sensors self-location in an indoor WLAN environment. In: Proceedings of the 2007 International Conference on Sensor Technologies and Applications (SENSORCOMM 2007), pp. 146–151 (2007)
Eren, T., et al.: Rigidity, computation, and randomization in network localization. In: Proceedings of the IEEE Conference on Computer Communication, vol. 4, pp. 2673–2684 (2004)
Bishop, A.N., Fidan, B.I., Anderson, B., Dogançay, K.I., Pathirana, P.N.: Optimality analysis of sensor-target localization geometries. Automatica 46, 479–492 (2010)
Huang, M., Chen, S., Wang, Y.: Minimum cost localization problem in wireless sensor networks. Ad Hoc Netw. 9(3), 387–399 (2011)
Zhang, P., Wang, Q.: Anchor selection with anchor location uncertainty in wireless sensor network localization. In: Proceedings of the IEEE International Conference on Acoustics, Speech, Signal Processing, pp. 4172–4175 (2011)
Priyantha, N.B., Balakrishnan, H., Demaine, E., Teller, S.: Anchor-free distributed localization in sensor networks. Technical report 892, MIT Laboratory for Computer Science (2003)
Ash, J.N., Moses, R.L.: On the relative and absolute positioning errors in self-localization systems. IEEE Trans. Signal Process. 56(11), 5668–5679 (2008)
Shang, Y., Rumi, W., Zhang, Y., Fromherz, M.: Localization from connectivity in sensor networks. IEEE Trans. Parallel Distrib. Syst. 15(11), 961–974 (2004)
Yang, L., Ho, K.C.: On using multiple calibration emitters and their geometric effects for removing sensor position errors in TDOA localization. In: Proceedings of the IEEE International Conference on Acoustics, Speech, Signal Processing, pp. 2702–2705 (2010)
Gorman, J.D., Hero, A.O.: Lower bounds for parametric estimation with constraints. IEEE Trans. Inform. Theory 36(6), 1285–1301 (1990)
Stoica, P., Ng, B.C.: On the Cramér-Rao bound under parametric constraints. IEEE Signal Process. Lett. 5(7), 177–179 (1998)
Zhang, P., Lu, J., Wang, Q.: Performance bounds for relative configuration and global transformation in cooperative localization. ICT Express 2(1), 14–18 (2016). Special Issue on Positioning Techniques and Applications
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Zhang, P., Cheng, F., Lu, J. (2021). Beyond Anchors: Optimal Equality Constraints in Cooperative Localization. In: Peñalver, L., Parra, L. (eds) Industrial IoT Technologies and Applications. Industrial IoT 2020. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 365. Springer, Cham. https://doi.org/10.1007/978-3-030-71061-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-71061-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-71060-6
Online ISBN: 978-3-030-71061-3
eBook Packages: Computer ScienceComputer Science (R0)