Relative navigation of autonomous GPS-degraded micro air vehicles


Unlike many current navigation approaches for micro air vehicles, the relative navigation (RN) framework presented in this paper ensures that the filter state remains observable in GPS-denied environments by working with respect to a local reference frame. By subtly restructuring the problem, RN ensures that the filter uncertainty remains bounded, consistent, and normally-distributed, and insulates flight-critical estimation and control processes from large global updates. This paper thoroughly outlines the RN framework and demonstrates its practicality with several long flight tests in unknown GPS-denied and GPS-degraded environments. The relative front end is shown to produce low-drift estimates and smooth, stable control while leveraging off-the-shelf algorithms. The system runs in real time with onboard processing, fuses a variety of vision sensors, and works indoors and outdoors without requiring special tuning for particular sensors or environments. RN is shown to produce globally-consistent, metric, and localized maps by incorporating loop closures and intermittent GPS measurements.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19


  1. 1.

    The PX4 firmware is customized to accept inputs from the onboard computer while also allowing an RC safety pilot to override these commands if necessary. We have subsequently transitioned to using the ROSflight autopilot (Jackson et al. 2016a); see

  2. 2.

    Individual edge covariances can also be combined using the fourth-order analytical approximation presented by Barfoot and Furgale (2014).


  1. Agarwal, P., Tipaldi, G. D., Spinello, L., Stachniss, C., & Burgard, W. (2013). Robust map optimization using dynamic covariance scaling. In IEEE international conference on robotics and automation (pp. 62–69)

  2. Bachrach, A., He, R., & Roy, N. (2010). Autonomous flight in unknown indoor environments. International Journal of Micro Air Vehicles, 1(4), 217–228.

  3. Bachrach, A., Prentice, S., & Roy, N. (2011). RANGE-Robust autonomous navigation in GPS-denied environments. Journal of Field Robotics, 28(5), 644–666.

  4. Bailey, T., Nieto, J., Guivant, J., Stevens, M., & Nebot, E. (2006). Consistency of the EKF-SLAM algorithm. In IEEE/RSJ international conference on intelligent robots and systems (pp. 3562–3568).

  5. Bar-Shalom, Y., Kirubarajan, T., & Li, X. R. (2002). Estimation with applications to tracking and navigation. New York: Wiley.

  6. Barfoot, T. D., & Furgale, P. T. (2014). Associating uncertainty with three-dimensional poses for use in estimation problems. IEEE Transactions on Robotics, 30(3), 679–693.

  7. Blösch, M., Weiss, S., Scaramuzza, D., & Siegwart, R. (2010). Vision based MAV navigation in unknown and unstructured environments. In IEEE international conference on robotics and automation (pp. 21–28)

  8. Carlevaris-Bianco, N., Kaess, M., & Eustice, R. M. (2014). Generic node removal for factor-graph SLAM. IEEE Transactions on Robotics, 30(6), 1371–1385.

  9. Carlone, L., Kira, Z., Beall, C., Indelman, V., & Dellaert, F. (2014). Eliminating conditionally independent sets in factor graphs: A unifying perspective based on smart factors. In IEEE international conference on robotics and automation (pp. 4290–4297).

  10. Censi, A. (2008). An ICP variant using a point-to-line metric. In IEEE international conference on robotics and automation (pp. 19–25).

  11. Chambers, A., Scherer, S., Yoder, L., Jain, S., Nuske, S., & Singh, S. (2014). Robust multi-sensor fusion for micro aerial vehicle navigation in GPS-degraded/denied environments. In American control conference (pp. 1892–1899).

  12. Chong, K. S., & Kleeman, L. (1999). Feature-based mapping in real, large scale environments using an ultrasonic array. International Journal of Robotics Research, 18(1), 3–19.

  13. Chowdhary, G., Johnson, E. N., Magree, D., Wu, A., & Shein, A. (2013). GPS-denied indoor and outdoor monocular vision-aided navigation and control of unmanned aircraft. Journal of Field Robotics, 30(3), 415–438.

  14. Cummins, M., & Newman, P. (2011). Appearance-only SLAM at large scale with FAB-MAP 2.0. International Journal of Robotics Research, 30(9), 1100–1123.

  15. Dellaert, F., & Kaess, M. (2006). Square root SAM: Simultaneous localization and mapping via square root information smoothing. International Journal of Robotics Research, 25(12), 1181–1203.

  16. Fischler, M. A., & Bolles, R. C. (1981). Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6), 381–395.

  17. Forster, C., Carlone, L., Dellaert, F., & Scaramuzza, D. (2015). IMU preintegration on manifold for efficient visual-inertial maximum-a-posteriori estimation (pp. 6–15). Robotics: Science and Systems.

  18. Fraundorfer, F., & Scaramuzza, D. (2012). Visual odometry: Part II: Matching, robustness, optimization, and applications. IEEE Robotics and Automation Magazine, 19(2), 78–90.

  19. Glover, A., Maddern, W., Warren, M., Reid, S., Milford, M., & Wyeth, G. (2012). OpenFABMAP: An open source toolbox for appearance-based loop closure detection. In: IEEE international conference on robotics and automation (pp. 4730–4735).

  20. Grisetti, G., Kummerle, R., Stachniss, C., & Burgard, W. (2010). A tutorial on graph-based SLAM. Intelligent Transportation Systems Council, 2(4), 31–43.

  21. Grzonka, S., Grisetti, G., & Burgard, W. (2012). A fully autonomous indoor quadrotor. IEEE Transactions on Robotics, 28(1), 90–100.

  22. Gutmann, J. S., & Schlegel, C. (1996). AMOS: Comparison of scan matching approaches for self-localization in indoor environments. In: Proceedings of the 1st Euromicro workshop on advanced mobile robots (pp. 61–67).

  23. Jackson, J., Nielsen, J., McLain, T., & Beard, R. (2019). Improving the robustness of visual-inertial extended Kalman filtering. In: IEEE international conference on robotics and automation.

  24. Jackson, J. S., Ellingson, G. S., & McLain, T. W. (2016a). ROSflight: a lightweight, inexpensive MAV research and development tool. In International conference on unmanned aircraft systems (pp. 758–762).

  25. Jackson, J.S., Wheeler, D.O., & McLain, T.W. (2016b). Cushioned extended-periphery avoidance: A reactive obstacle avoidance plugin. In International conference on unmanned aircraft systems (pp. 399–405).

  26. Jones, E., Vedaldi, A., & Soatto, S. (2007). Inertial structure from motion with autocalibration. In ICCV workshop on dynamical vision.

  27. Kaess, M., Ranganathan, A., & Dellaert, F. (2008). iSAM: Incremental smoothing and mapping. IEEE Transactions on Robotics, 24(6), 1365–1378.

  28. Kaess, M., Johannsson, H., Roberts, R., Ila, V., Leonard, J. J., & Dellaert, F. (2012). iSAM2: Incremental smoothing and mapping using the Bayes tree. International Journal of Robotics Research, 31(2), 216–235.

  29. Kim, B., Kaess, M., Fletcher, L., Leonard, J., Bachrach, A., Roy, N., & Teller, S. (2010). Multiple relative pose graphs for robust cooperative mapping. In IEEE International Conference on Robotics and Automation (pp. 3185–3192)

  30. Koch, D. P., McLain, T. W., & Brink, K. M. (2016). Multi-sensor robust relative estimation framework for GPS-denied multirotor aircraft. In International Conference on Unmanned Aircraft Systems (pp. 589–597).

  31. Koch, D. P., Wheeler, D. O., Beard, R. W., McLain, T. W., & Brink, K. M. (2017). Relative multiplicative extended Kalman filter for observable GPS-denied navigation.

  32. Kummerle, R., Grisetti, G., Strasdat, H., Konolige, K., & Burgard, W. (2011). g2o: A general framework for graph optimization. In IEEE international conference on robotics and automation (pp. 3607–3613).

  33. Latif, Y., Cadena, C., & Neira, J. (2013). Robust loop closing over time for pose graph SLAM. International Journal of Robotics Research, 32(14), 1611–1626.

  34. Leishman, R. C., McLain, T. W., & Beard, R. W. (2014). Relative navigation approach for vision-based aerial GPS-denied navigation. Journal of Intelligent and Robotic Systems, 74(1), 97–111.

  35. Leutenegger, S., Lynen, S., Bosse, M., Siegwart, R., & Furgale, P. (2015). Keyframe-based visual-inertial odometry using nonlinear optimization. International Journal of Robotics Research, 34(3), 314–334.

  36. Long, A., Wolfe, K., Mashner, M., & Chirikjian, G. (2012). The banana distribution is Gaussian: A localization study with exponential coordinates. In Robotics: science and systems (p. 8)

  37. Lowry, S., Sunderhauf, N., Newman, P., Leonard, J. J., Cox, D., Corke, P., et al. (2016). Visual place recognition: A survey. IEEE Transactions on Robotics, 32(1), 1–19.

  38. Martinelli, A. (2012). Vision and IMU data fusion: Closed-form solutions for attitude, speed, absolute scale, and bias determination. IEEE Transactions on Robotics, 28(1), 44–60.

  39. Michael, N., Mellinger, D., Lindsey, Q., & Kumar, V. (2010). The GRASP multiple micro-UAV testbed. IEEE Robotics and Automation Magazine, 17(3), 56–65.

  40. Moore, D., Huang, A., Walter, M., Olson, E., Fletcher, L., Leonard, J., & Teller, S. (2009). Simultaneous local and global state estimation for robotic navigation. In: IEEE international conference on robotics and automation (pp. 3794–3799).

  41. Nister, D., & Stewenius, H. (2006). Scalable recognition with a vocabulary tree. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2, 2161–2168.

  42. Olson, E., & Agarwal, P. (2013). Inference on networks of mixtures for robust robot mapping. International Journal of Robotics Research, 32(7), 826–840.

  43. Olson, E., Leonard, J., & Teller, S. (2006). Fast iterative alignment of pose graphs with poor initial estimates. In IEEE international conference on robotics and automation (pp. 2262–2269)

  44. PricewaterhouseCoopers. (2016). Clarity from above: PwC global report on commercial applications of drone technology. Accessed March 30, 2017.

  45. Quigley, M., Conley, K., Gerkey, B., Faust, J., Foote, T., Leibs, J., Wheeler, R., & Ng, A. Y. (2009). ROS: An open-source robot operating system. In: ICRA workshop on open source software.

  46. Raffo, G. V., Ortega, M. G., & Rubio, F. R. (2010). An integral predictive/nonlinear H-infinity control structure for a quadrotor helicopter. Automatica, 46(1), 29–39.

  47. Rehder, J., Gupta, K., Nuske, S., & Singh, S. (2012). Global pose estimation with limited GPS and long range visual odometry. In: IEEE international conference on robotics and automation (pp. 627–633)

  48. Roumeliotis, S.I., & Burdick, J. (2002). Stochastic cloning: a generalized framework for processing relative state measurements. In IEEE International Conference on Robotics and Automation (pp. 1788–1795)

  49. Scaramuzza, D., & Fraundorfer, F. (2011). Visual odometry: Part I: The first 30 years and fundamentals. IEEE Robotics and Automation Magazine, 18(4), 80–92.

  50. Scaramuzza, D., Achtelik, M. C., Doitsidis, L., Friedrich, F., Kosmatopoulos, E., Martinelli, A., et al. (2014). Vision-controlled micro flying robots: From system design to autonomous navigation and mapping in GPS-denied environments. IEEE Robotics and Automation Magazine, 21(3), 26–40.

  51. Scherer, S., Rehder, J., Achar, S., Cover, H., Chambers, A., Nuske, S., et al. (2012). River mapping from a flying robot: State estimation, river detection, and obstacle mapping. Autonomous Robots, 33(1), 189–214.

  52. Scherer, S., Yang, S., & Zell, A. (2015). DCTAM: Drift-corrected tracking and mapping for autonomous micro aerial vehicles. In International conference on unmanned aircraft systems (pp. 1094–1101).

  53. Shen, S., Mulgaonkar, Y., Michael, N., & Kumar, V. (2014). Multi-sensor fusion for robust autonomous flight in indoor and outdoor environments with a rotorcraft MAV. In IEEE international conference on robotics and automation (pp 4974–4981).

  54. Sibley, D., Mei, C., Reid, I.D., & Newman, P. (2009). Adaptive relative bundle adjustment. In Robotics: Science and Systems

  55. Sivic, Zisserman. (2003). Video Google: A text retrieval approach to object matching in videos. IEEE International Conference on Computer Vision, 2, 1470–1477.

  56. Sunderhauf, N., & Protzel, P. (2013). Switchable constraints vs. max-mixture models vs. RRR—a comparison of three approaches to robust pose graph SLAM. In IEEE international conference on robotics and automation (pp. 5198–5203)

  57. Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic robotics. Cambridge: MIT Press.

  58. Tomic, T., Schmid, K., Lutz, P., Domel, A., Kassecker, M., Mair, E., et al. (2012). Toward a fully autonomous UAV: Research platform for indoor and outdoor urban search and rescue. IEEE Robotics and Automation Magazine, 19(3), 46–56.

  59. Weiss, S., & Siegwart, R. (2011). Real-time metric state estimation for modular vision-inertial systems. In IEEE international conference on robotics and automation (pp. 4531–4537).

  60. Weiss, S., Achtelik, M. W., Lynen, S., Chli, M., & Siegwart, R. (2012). Real-time onboard visual-inertial state estimation and self-calibration of MAVs in unknown environments. In IEEE International Conference on Robotics and Automation (pp. 957–964).

  61. Wheeler, D. O., Nyholm, P. W., Koch, D. P., Ellingson, G. J., McLain, T. W., & Beard, R. W. (2016). Relative navigation in GPS-degraded environments. In Encyclopedia of aerospace engineering (pp. 1–10). Hoboken: Wiley

  62. Wheeler, D. O., Koch, D. P., Jackson, J. S., Mclain, T. W., & Beard, R. W. (2018). Relative navigation: A keyframe-based approach for observable GPS-degraded navigation. IEEE Control Systems Magazine, 38(4), 30–48.

  63. Zhang, J., Kaess, M., & Singh, S. (2014). Real-time depth enhanced monocular odometry. In IEEE/RSJ international conference on intelligent robots and systems (pp. 4973–4980).

Download references


This work has been funded by the Center for Unmanned Aircraft Systems (C-UAS), a National Science Foundation Industry/University Cooperative Research Center (I/UCRC) under NSF award Numbers IIP-1161036 and CNS-1650547, along with significant contributions from C-UAS industry members. This work was also supported in part by Air Force Research Laboratory Science and Technology (AFRL S&T) sponsorship. This research was conducted with Government support under and awarded by DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. The authors would like to thank Kevin Brink of the Air Force Research Laboratory Munitions Directorate (AFRL/RW) for his support of this project and for his valuable insights.

Author information

Correspondence to Daniel P. Koch.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wheeler, D.O., Koch, D.P., Jackson, J.S. et al. Relative navigation of autonomous GPS-degraded micro air vehicles. Auton Robot (2020).

Download citation


  • Aerial robotics
  • GPS-denied
  • Navigation
  • GPS-degraded
  • Observable