{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T15:02:17Z","timestamp":1776956537694,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T00:00:00Z","timestamp":1641772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Airborne angle-only sensors can be used to track stationary or mobile ground targets. In order to make the problem observable in 3-dimensions (3-D), the height of the target (i.e., the height of the terrain) from the sea-level is needed to be known. In most of the existing works, the terrain height is assumed to be known accurately. However, the terrain height is usually obtained from Digital Terrain Elevation Data (DTED), which has different resolution levels. Ignoring the terrain height uncertainty in a tracking algorithm will lead to a bias in the estimated states. In addition to the terrain uncertainty, another common source of uncertainty in angle-only sensors is the sensor biases. Both these uncertainties must be handled properly to obtain better tracking accuracy. In this paper, we propose algorithms to estimate the sensor biases with the target(s) of opportunity and algorithms to track targets with terrain and sensor bias uncertainties. Sensor bias uncertainties can be reduced by estimating the biases using the measurements from the target(s) of opportunity with known horizontal positions. This step can be an optional step in an angle-only tracking problem. In this work, we have proposed algorithms to pick optimal targets of opportunity to obtain better bias estimation and algorithms to estimate the biases with the selected target(s) of opportunity. Finally, we provide a filtering framework to track the targets with terrain and bias uncertainties. The Posterior Cramer\u2013Rao Lower Bound (PCRLB), which provides the lower bound on achievable estimation error, is derived for the single target filtering with an angle-only sensor with terrain uncertainty and measurement biases. The effectiveness of the proposed algorithms is verified by Monte Carlo simulations. The simulation results show that sensor biases can be estimated accurately using the target(s) of opportunity and the tracking accuracies of the targets can be improved significantly using the proposed algorithms when the terrain and bias uncertainties are present.<\/jats:p>","DOI":"10.3390\/s22020509","type":"journal-article","created":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T22:03:13Z","timestamp":1641852193000},"page":"509","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Ground Target Tracking Using an Airborne Angle-Only Sensor with Terrain Uncertainty and Sensor Biases"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7947-0878","authenticated-orcid":false,"given":"Dipayan","family":"Mitra","sequence":"first","affiliation":[{"name":"Department of Electrical & Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aranee","family":"Balachandran","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ratnasingham","family":"Tharmarasa","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Oliveira, T., and Encarna\u00e7ao, P. (2010, January 2\u20135). Ground target tracking for unmanned aerial vehicles. Proceedings of the AIAA Guidance, Navigation, and Control Conference, Toronto, ON, Canada.","DOI":"10.2514\/6.2010-8082"},{"key":"ref_2","unstructured":"Mallick, M., Arulampalam, S., Mihaylova, L., and Yan, Y. (2011, January 5\u20138). Angle-only filtering in 3D using modified spherical and log spherical coordinates. Proceedings of the 14th International Conference on Information Fusion, Chicago, IL, USA."},{"key":"ref_3","unstructured":"Datta Gupta, S., Yu, J.Y., Mallick, M., Coates, M., and Morelande, M. (2015, January 6\u20139). Comparison of angle-only filtering algorithms in 3D using EKF, UKF, PF, PFF, and ensemble KF. Proceedings of the 18th International Conference on Information Fusion (Fusion), Washington, DC, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/JSTARS.2015.2418173","article-title":"An Airborne Radar Sensor for Maritime and Ground Surveillance and Reconnaissance\u2014Algorithmic Issues and Exemplary Results","volume":"9","author":"Kirscht","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1109\/MGRS.2019.2957600","article-title":"Along-Track Interferometric SAR Systems for Ground-Moving Target Indication: Achievements, Potentials, and Outlook","volume":"8","author":"Budillon","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1109\/TGRS.2016.2622712","article-title":"Image-Based Target Detection and Radial Velocity Estimation Methods for Multichannel SAR-GMTI","volume":"55","author":"Suwa","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3476","DOI":"10.1109\/TAES.2020.2973866","article-title":"Airborne Maritime Surveillance Using Magnetic Anomaly Detection Signature","volume":"56","author":"Sithiravel","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1109\/LRA.2015.2511444","article-title":"Active Magnetic Anomaly Detection Using Multiple Micro Aerial Vehicles","volume":"1","author":"Dames","year":"2016","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_9","unstructured":"Liu, J., Han, C., and Vadakkepat, P. (2010, January 26\u201329). Process noise identification based particle filter: An efficient method to track highly maneuvering target. Proceedings of the 13th International Conference on Information Fusion, Edinburgh, UK."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mallick, M., Chang, K.C., Arulampalam, S., Yan, Y., and La Scala, B. (2019, January 2\u20135). Heterogeneous Track-to-Track Fusion in 2D Using Sonar and Radar Sensors. Proceedings of the 22th International Conference on Information Fusion (FUSION), Ottawa, ON, Canada.","DOI":"10.23919\/FUSION43075.2019.9011399"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Mallick, M., Sinha, A., and Liu, J. (2017, January 10\u201313). Enhancements to bearing-only filtering. Proceedings of the 20th International Conference on Information Fusion (Fusion), Xi\u2019an, China.","DOI":"10.23919\/ICIF.2017.8009822"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2036","DOI":"10.1109\/TAES.2018.2881352","article-title":"Globally Valid Posterior Cram\u00e9r\u2013Rao Bound for Three-Dimensional Bearings-Only Filtering","volume":"55","author":"Schmitt","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1109\/LGRS.2015.2438394","article-title":"Accuracy of Digital Elevation Models Derived From Terrestrial Laser Scanning Data","volume":"12","author":"Fan","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, Z., Hovakimyan, N., Dobrokhodov, V., and Kaminer, I. (2010, January 15\u201317). Vision-based target tracking and motion estimation using a small UAV. Proceedings of the 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA.","DOI":"10.1109\/CDC.2010.5718149"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1947","DOI":"10.1109\/TAES.2017.2677746","article-title":"A Scalable Multitarget Tracking System for Cooperative Unmanned Aerial Vehicles","volume":"53","author":"Farmani","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Tyagi, P., Kumar, Y., and Sujit, P. (2021, January 15\u201318). NMPC-based UAV 3D Target Tracking In The Presence Of Obstacles and Visibility Constraints. Proceedings of the 2021 International Conference on Unmanned Aircraft Systems (ICUAS), Athens, Greece.","DOI":"10.1109\/ICUAS51884.2021.9476710"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.1109\/TAES.2019.2895709","article-title":"Single Space Based Sensor Bias Estimation Using a Single Target of Opportunity","volume":"56","author":"Belfadel","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2837","DOI":"10.1109\/TAES.2018.2831118","article-title":"Source Localization Based on Acoustic Single Direction Measurements","volume":"54","author":"Reis","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1049\/iet-spr.2015.0068","article-title":"Joint estimation of state and system biases in non-linear system","volume":"11","author":"Zhou","year":"2017","journal-title":"IET Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1109\/TAES.2019.2929973","article-title":"Sensor Bias Estimation Based on Ridge Least Trimmed Squares","volume":"56","author":"Tian","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","unstructured":"Van Trees, H.L. (1968). Detection, Estimation, and Modulation Theory, Part I, Wiley."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bacharach, L., Fritsche, C., Orguner, U., and Chaumette, E. (2019, January 12\u201317). A Tighter Bayesian Cram\u00c9R-rao Bound. Proceedings of the ICASSP 2019\u20142019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK.","DOI":"10.1109\/ICASSP.2019.8683614"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1109\/78.533723","article-title":"Exploring estimator bias-variance tradeoffs using the uniform CR bound","volume":"44","author":"Hero","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1109\/TSP.2004.828929","article-title":"Minimum variance in biased estimation: Bounds and asymptotically optimal estimators","volume":"52","author":"Eldar","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","unstructured":"Duan, Z., and Li, X.R. (2013, January 9\u201312). Constrained target motion modeling\u2013Part I: Straight line track. Proceedings of the 16th International Conference on Information Fusion, Istanbul, Turkey."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1109\/TSP.2015.2493985","article-title":"The Accurate Continuous-Discrete Extended Kalman Filter for Radar Tracking","volume":"64","author":"Kulikov","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4977","DOI":"10.1109\/TSP.2010.2056923","article-title":"Cubature Kalman Filtering for Continuous-Discrete Systems: Theory and Simulations","volume":"58","author":"Arasaratnam","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1109\/TAC.2015.2404511","article-title":"A Systematization of the Unscented Kalman Filter Theory","volume":"60","author":"Menegaz","year":"2015","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1109\/TAC.2013.2258825","article-title":"Feedback Particle Filter","volume":"58","author":"Yang","year":"2013","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_30","unstructured":"Wan, E., and Van Der Merwe, R. (2000, January 4). The unscented Kalman filter for nonlinear estimation. Proceedings of the IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium, Lake Louise, AB, Canada."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1016\/j.jprocont.2007.11.004","article-title":"Applying the unscented Kalman filter for nonlinear state estimation","volume":"18","author":"Kandepu","year":"2008","journal-title":"J. Process Control"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/78.668800","article-title":"Posterior Cramer-Rao bounds for discrete-time nonlinear filtering","volume":"46","author":"Tichavsky","year":"1998","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/TAES.2013.6404131","article-title":"Track Initialization: Prior Target Velocity and Acceleration Moments","volume":"49","author":"Musicki","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/509\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:14:47Z","timestamp":1760364887000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/509"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,10]]},"references-count":33,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["s22020509"],"URL":"https:\/\/doi.org\/10.3390\/s22020509","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,10]]}}}