Graphical Abstract

Relative navigation is a key enabling technology for space missions such as on-orbit servicing and space situational awareness. Given that there are several special advantages of space relative navigation using angles-only measurements from passive optical sensors, angles-only relative navigation is considered as one of the best potential approaches in the field of space relative navigation. However, angles-only relative navigation is well-known for its range observability problem. To overcome this observability problem, many studies have been conducted over the past decades. In this study, we present a comprehensive review of state-of-the-art space relative navigation based on angles-only measurements. The emphasis is on the observability problem and solutions to angles-only relative navigation, where the review of the solutions is categorized into four classes based on the intrinsic principle: complicated dynamics approach, multi-line of sight (multi-LOS) approach, sensor offset center-of-mass approach, and orbit maneuver approach. Then, the flight demonstration results of angles-only relative navigation in the two projects are briefly reviewed. Finally, conclusions of this study and recommendations for further research are presented.
Wang, B. C., Li, S., Mu, J. Z., Hao, X. L., Zhu, W. S., Hu, J. Q. Research advancements in key technologies for space-based situational awareness. Space: Science & Technology, 2020, 2020: 9802793.
Zhu, W. S., Mu, J. Z., Shao, C. B., Hu, J. Q., Wang, B. C., Wen, Z. K., Han, F., Li, S. System design for pose determination of spacecraft using time-of-flight sensors. Space: Science & Technology, 2022, 2022: 9763198.
Battin, R. An Introduction to the Mathematics and Methods of Astrodynamics. New York: AIAA, 1987: 297–312.
Curtis, H. Orbital Mechanics for Engineering Students, 3rd edn. New York: Elsevier, 2014.
Karimi, R. R., Mortari, D. Initial orbit determination using multiple observations. Celestial Mechanics and Dynamical Astronomy, 2011, 109: 167–180.
Fadrique, F. M., Maté, A. Á., Grau, J. J., Sánchez, J. F., García, L. A. Comparison of angles only initial orbit determination algorithms for space debris cataloguing. Journal of Aerospace Engineering, Sciences and Applications, 2012, 4(1): 39–51.
Gooding, R. H. A new procedure for the solution of the classical problem of minimal orbit determination from three lines of sight. Celestial Mechanics and Dynamical Astronomy, 1996, 66(4): 387–423.
Kaufman E., Lovell T. A., Lee, T. Nonlinear observability measure for relative orbit determination with angles-only measurements. The Journal of Astronautical Science, 2016, 63: 60–80.
Gong, B. C., Ma, Y. Q., Zhang, W. F., Li, S., Li, X. Q. Deep-neural-network-based anglesonly relative orbit determination for space non-cooperative target. Acta Astronautica, 2022, https://doi.org/10.1016/j.actaastro.2022.09.024.
Geller, D. K., Lovell, T. A. Angles-only initial relative orbit determination performance analysis using cylindrical coordinates. The Journal of the Astronautical Sciences, 2017, 64(1): 72–96.
Gong, B. C., Zhang, D. G., Zhang, W. F., Yuan, Y. H., Chen, X. Q. Angles-only relative navigation algorithm for space non-cooperative target in cylindrical frame. Journal of Chinese Inertial Technology, 2021, 29(6): 752–762. (in Chinese)
Perez, A. C., Geller, D. K., Lovell, T. A. Non-iterative angles-only initial relative orbit determination with J2 perturbations. Acta Astronautica, 2018, 151: 146–159.
Tombasco, J., Axelrad, P. Observability of relative hybrid elements, given space-based angles-only observations. Journal of Guidance, Control, and Dynamics, 2012, 35(5): 1681–1686.
Gaias, G., D'Amico, S., Ardaens, J. S. Angles-only navigation to a noncooperative satellite using relative orbital elements. Journal of Guidance, Control, and Dynamics, 2014, 37(3): 439–451.
Sullivan, J., D'Amico, S. Nonlinear Kalman filtering for improved angles-only navigation using relative orbital elements. Journal of Guidance, Control, and Dynamics, 2017, 40(9): 2183–2200.
Ardaens, J. S., Gaias, G. A numerical approach to the problem of angles-only initial relative orbit determination in low earth orbit. Advances in Space Research, 2019, 63(12): 3884–3899.
Liu, G. M., Liao, Y., Wen, Y. L. Two-satellite formation-based non-cooperative space target integrated orbit determination. Journal of Astronautics, 2010, 31(9): 2095–2100. (in Chinese)
Chen, T., Xu, S. J. Approach guidance with double-line-of-sight measuring navigation constraint for autonomous rendezvous. Journal of Guidance, Control, and Dynamics, 2011, 34(3): 678–687.
Wang, K., Chen, T., Xu, S. J. A method of double line-of-sight measurement relative navigation. Acta Aeronautica et Astronautica Sinica, 2011, 32(6): 1084–1091. (in Chinese)
Su, J. M., Dong, Y. F. The orbit determination of non-cooperative maneuvering target by applying space-based bearing-only measurement. Aerospace Control, 2011, 29(3): 37–42. (in Chinese)
Zhai, G., Zhang, J. R., Zhang, Y. Co-localization of non-cooperative targets based on multiple space robot system. Robot, 2013, 35(2): 249–256. (in Chinese)
Gao, X. H., Liang, B., Pan, L. Distributed relative navigation of GEO non-cooperative target based on multiple line-of-sight measurements. Journal of Astronautics, 2013, 36(3): 292–299. (in Chinese)
Han, F., Liu, F. C., Wang, Z. L., Du, X., Liu, S. S., Liu, C. Z. Multi light-of-sight angles-only relative navigation by multi collaborative space robot. Acta Aeronautica et Astronautica Sinica, 2021, 42(1): 524147. (in Chinese)
LeGrand, K., DeMars, K., Pernicka, H. Bearings-only initial relative orbit determination. Journal of Guidance, Control, and Dynamics, 2015, 38(9): 1699–1713.
Jia, B., Pham, K. D., Blasch, E., Shen, D., Wang, Z. H., Chen, G. S. Cooperative space object tracking using space-based optical sensors via consensus-based filters. IEEE Transactions on Aerospace and Electronic Systems, 2016, 52(4): 1908–1936.
Andrews, B. A., Geller, D. K. Analysis of angles-only hybrid space-based/ground-based approach for geosynchronous orbit catalog maintenance. The Journal of the Astronautical Sciences, 2022, 69(2): 473–510.
Hippelheuser, J., Elgohary, T. A. Inertial space-based orbit estimation: A new measurement model for multiple observers. Acta Astronautica, 2021, 181: 717–732.
Tasif, T. H., Hippelheuser, J. E., Elgohary, T. A. Analytic continuation extended Kalman filter framework for perturbed orbit estimation using a network of space-based observers with angles-only measurements. Astrodynamics, 2022, 6(2): 161–187.
Hu, Y. P., Bai, X. Z., Chen, L., Yan, H. T. A new approach of orbit determination for LEO satellites based on optical tracking of GEO satellites. Aerospace Science and Technology, 2019, 84: 821–829.
Geller, D. K., Perez, A. Initial relative orbit determination for close-in proximity operations. Journal of Guidance, Control, and Dynamics, 2015, 38(9): 1833–1841.
Gong, B. C., Geller, D. K., Luo, J. J. Initial relative orbit determination analytical covariance and performance analysis for proximity operations. Journal of Spacecraft and Rockets, 2016, 53(5): 822–835.
Gong, B. C., Li, W. D., Li, S., Ma, W. H., Zheng, L. L. Angles-only initial relative orbit determination algorithm for non-cooperative spacecraft proximity operations. Astrodynamics, 2018, 2(3): 217–231.
Gong, B. C., Luo, J. J., Li, S., Li, W. D. Observability criterion of angles-only navigation for spacecraft proximity operations. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2019, 233(12): 4302–4315.
Woffinden, D. C., Geller, D. K. Observability criteria for angles-only navigation. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(3): 1194–1208.
Woffinden, D. C., Geller, D. K. Optimal orbital rendezvous maneuvering for angles-only navigation. Journal of Guidance, Control, and Dynamics, 2009, 32(4): 1382–1387.
Grzymisch, J., Fichter, W. Observability criteria and unobservable maneuvers for in-orbit bearings-only navigation. Journal of Guidance, Control, and Dynamics, 2014, 37(4): 1250–1259.
Grzymisch, J., Fichter, W. Analytic optimal observability maneuvers for in-orbit bearings-only rendezvous. Journal of Guidance, Control, and Dynamics, 2014, 37(5): 1658–1664.
Grzymisch, J., Fichter, W. Optimal rendezvous guidance with enhanced bearings-only observability. Journal of Guidance, Control, and Dynamics, 2015, 38(6): 1131–1140.
Grzymisch, J., Fichter, W. Nonlinear pseudo-measurement filtering for in-orbit bearings-only navigation. IEEE Transactions on Aerospace and Electronic Systems, 2015, 51(4): 2747–2759.
Pi, J., Bang, H. Trajectory design for improving observability of angles-only relative navigation between two satellites. The Journal of the Astronautical Sciences, 2014, 61(4): 391–412.
Li, J. R., Li H. Y., Tang, G. J. Analysis of closed-loop control covariance for autonomous orbital rendezvous using angles-only relative navigation. Journal of Astronautics, 2012, 33(6): 705–712. (in Chinese)
Li, J. R., Li, H. Y., Tang, G. J., Luo, Y. Z. Research on the strategy of angles-only relative navigation for autonomous rendezvous. Science China Technological Sciences, 2011, 54(7): 1865–1872.
Hou, B., Wang, D. Y., Wang, J. Q., Ge, D. M., Zhou, H. Y., Zhou, X. Y. Optimal maneuvering for autonomous relative navigation using monocular camera sequential images. Journal of Guidance, Control, and Dynamics, 2021, 44(11): 1947–1960.
Luo, J. J., Gong, B. C., Yuan, J. P., Zhang, Z. F. Angles-only relative navigation and closed-loop guidance for spacecraft proximity operations. Acta Astronautica, 2016, 128: 91–106.
Franquiz, F. J., Muñoz, J. D., Udrea, B., Balas, M. J. Optimal range observability maneuvers of a spacecraft formation using angles-only navigation. Acta Astronautica, 2018, 153: 337–348.
Zhang, Y. Z., Huang, P. F., Song, K. H., Meng, Z. J. An angles-only navigation and control scheme for noncooperative rendezvous operations. IEEE Transactions on Industrial Electronics, 2019, 66(11): 8618–8627.
Zhang, Y. Z., Huang, P. F., Meng, Z. J., Liu Z. X. Precise angles-only navigation for noncooperative proximity operation with application to tethered space robot. IEEE Transactions on Control Systems Technology, 2019, 27(3): 1139–1150.
Fujimoto, K., Scheeres, D. J. Correlation of optical observations of earth-orbiting objects and initial orbit determination. Journal of Guidance, Control, and Dynamics, 2012, 35(1): 208–221.
Liu, C. Q., Jia, Y. H., Xu, S. J. Comparison of four different Kalman filters for relative navigation based on line-of-sight-only measurement. Aerospace Control and Application, 2014, 40(1): 52–57. (in Chinese)
D'Onofrio, F., Bucchioni, G., Innocenti, M. Bearings-only guidance in cis-lunar rendezvous. Journal of Guidance, Control, and Dynamics, 2021, 44(10): 1862–1874.
Greaves, J. A., Scheeres, D. J. Observation and maneuver detection for cislunar vehicles using optical measurements and the optimal control based estimator. The Journal of the Astronautical Sciences, 2021, 68: 826–854.
Hu, R. H., Huang, X. Y., Xu, C. Integrated visual navigation based on angles-only measurements for asteroid final landing phase. Astrodynamics, 2023, 7(1): 69–82.
D'Amico, S., Ardaens, J. S., Gaias, G., Benninghoff, H., Schlepp, B., Jørgensen, J. L. Noncooperative rendezvous using angles-only optical navigation: System design and flight results. Journal of Guidance, Control, and Dynamics, 2013, 36(6): 1576–1595.
Gaias, G., Ardaens, J. Flight demonstration of autonomous noncooperative rendezvous in low earth orbit. Journal of Guidance, Control, and Dynamics, 2017, 41(6): 1337–1354.
Ardaens, J., Gaias, G. Angles-only relative orbit determination in low earth orbit. Advances in Space Research, 2018, 61(11): 2740–2760.
Gaias, G., Ardaens, J. In-orbit experience and lessons learned from the AVANTI experiment. Acta Astronautica, 2018, 153: 383–393.