Abstract
Cooperative networks of unmanned aerial vehicles (UAV) offer interesting advantages such as increased efficiency and improved accuracy when compared with independently operating UAVs in most applications like remote sensing, mapping, surveillance, exploration, search and rescue, situational awareness, disaster management. However, the quality of the products derived using UAV data is very much dependent on the accuracy with which a UAV can be localized. Although cooperative localization has been shown to improve the localization accuracy of all the UAVs in a network even in global navigation satellite system (GNSS) challenging environments, not all UAVs in a network can achieve equal navigational performance. The objective of this paper is to analyze the various parameters that affect the performance of UAVs in a cooperative network. This paper derives the theoretical performance bound of the localization accuracy that can be achieved by any UAV in the network. This performance bound is derived using posterior Cramér Rao bound and is further used to analyze the effects of various parameters such as network geometry and connectivity, quality of available measurements and the availability of GNSS in the network. Through this analysis, the limitations and the benefits of a cooperative UAV swarm for any application (such as mapping or remote sensing) are presented.
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Blanks, A., Vincent, J., & Phalp, K. (2008). Particle swarm guidance system for autonomous unmanned aerial vehicles in an air defence role. Journal of Navigation, 61(01), 9–29.
Crocker, R. I., Maslanik, J. A., Adler, J. J., Palo, S. E., Herzfed, U. C., & Emery, W. J. (2012). A sensor package for ice surface observations using small unmanned aircraft systems. IEEE Transactions on Geoscience and Remote Sensing, 50(4), 1033–1047.
Gabela, J., Goel, S., Kealy, A., Hedley, M., Moran, B., & Williams, S. (2018). Cramér Rao bound analysis for cooperative positioning in intelligent transportation systems. In Proceedings of the international global navigation satellite systems (IGNSS) conference, February 7–9, 2018, Sydney, Australia. Available at: http://www.ignss2018.unsw.edu.au/sites/ignss2018/files/u80/Papers/IGNSS2018_paper_21.pdf. Accessed 28 October 2018.
Gabrlik, P., La Cour-Harbo, A., Kalvodova, P., Zalud, L., & Janata, P. (2018). Calibration and accuracy assessment in a direct georeferencing system for UAV photogrammetry. International Journal of Remote Sensing, 39(15–16), 4931–4959. https://doi.org/10.1080/01431161.2018.1434331.
Goel, S. (2017). A distributed cooperative UAV swarm localization system: Development and analysis. In Proceedings of the 30th international technical meeting of the satellite division of the institute of navigation (ION GNSS+ 2017), Portland, Oregon, September 25–29, 2017 (pp. 2501–2518).
Goel, S., Kealy, A., Gikas, V., Retscher, G., Toth, C., Brzezinska, D., et al. (2017). Cooperative localization of unmanned aerial vehicles using GNSS, MEMS inertial and UWB sensors. Journal of Surveying Engineering, 13(4), 04017007. https://doi.org/10.1061/(asce)su.1943-5428.0000230.
Goel, S., Kealy, A., & Lohani, B. (2016). Cooperative UAS localization using low cost sensors. ISPRS Annals of Photogrammetry Remote Sensing and Spatial Information Sciences, 3(1), 183–190.
Goel, S., Kealy, A., & Lohani, B. (2018). Development and experimental evaluation of a low-cost cooperative UAV localization network prototype. Journal of Sensor and Actuator Networks., 7(4), 42. https://doi.org/10.3390/jsan7040042.
Gurtner, A., Greer, D. G., Glassrock, R., Mejias, L., Walker, R. A., & Boles, W. W. (2009). Investigation of fish-eye lenses for small-UAV aerial photography. IEEE Transactions on Geoscience and Remote Sensing, 47(3), 709–721.
Hafskjold, B. H., Jalving, B., Hagen, P. E., & Gade, K. (2000). Integrated camera-based navigation. Journal of Navigation, 53(02), 237–245.
Kay, S. M. (1993). Fundamentals of statistical signal processing: Estimation theory (Vol. 1(4), p. 513). Englewood Cliffs, NJ: Prentince Hall.
Larsson, E. G. (2004). Cramér-Rao bound analysis of distributed positioning in sensor networks. IEEE Signal Processing Letters, 11(3), 334–337.
Mourikis, A. I., & Roumeliotis, S. I. (2006). Performance analysis of multirobot cooperative localization. IEEE Transactions on Robotics, 22(4), 666–681.
Penna, F., Caceres, M. A., & Wymeersch, H. (2010). Cramér Rao bound for hybrid GNSS-terrestrial cooperative positioning. IEEE Communications Letters, 14(11), 1005–1007.
Spletzer, J., Das, A. K., Fierro, R., Taylor, C. J., Kumar, V., & Ostrowski, J. P. (2001). Cooperative localization and control for multi-robot manipulation. In Intelligent robots and systems (pp. 631–636).
Taylor, J. H. (1978). The Cramér Rao estimation error lower bound computation for deterministic nonlinear systems. In IEEE conference on decision and control (Vol. 17, pp. 343–344).
Taylor Jr, R. M., Flanagan, B. P., & Uber, J. A. (2003). Computing the recursive posterior Cramér Rao bound for a nonlinear nonstationary system. In Proceedings of IEEE international conference on acoustics, speech and signal processing, April 6–10 (pp. 673–676).
Tichavsky, P., Muravchik, C., & Nehorai, A. (1998). Posterior Cramér Rao bounds for discrete-time nonlinear filtering. IEEE Transactions on Signal Processing, 40, 1386–1396.
Turner, D., Lucieer, A., & Wallace, L. (2014). Direct georeferencing of ultrahigh-resolution UAV imagery. IEEE Transactions on Geoscience and Remote Sensing, 52(5), 2738–2745.
Uto, K., Seki, H., & Saito, G. (2013). Characterization of rice paddies by a UAV-mounted miniature hyperspectral sensor system. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 6(2), 851–860.
Wallace, L., Musk, R., & Lucieer, A. (2014). An assessment of the repeatability of automatic forest inventory metrics derived from UAV-borne laser scanning data. IEEE Transactions on Geoscience and Remote Sensing, 52(11), 71607169.
Wang, W., Peng, Q., & Cai, J. (2009). Waveform-diversity-based millimeter-wave UAV SAR remote sensing. IEEE Transactions on Geoscience and Remote Sensing, 47(3), 691–700.
Wymeersch, H., Lien, J., & Win, M. Z. (2009). Cooperative localization in wireless networks. Proceedings of the IEEE, 97(2), 427–450. https://doi.org/10.1109/JPROC.2008.2008853.
Xing, M., Jiang, X., Wu, R., Zhou, F., & Bao, Z. (2009). Motion compensation for UAV SAR based on raw radar data. IEEE Transactions on Geoscience and Remote Sensing, 47(8), 2870–2883.
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Goel, S., Kealy, A. & Lohani, B. Posterior Cramér Rao Bounds for Cooperative Localization in Low-Cost UAV Swarms. J Indian Soc Remote Sens 47, 671–684 (2019). https://doi.org/10.1007/s12524-018-0899-3
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DOI: https://doi.org/10.1007/s12524-018-0899-3