{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T12:33:02Z","timestamp":1771504382649,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Natural Science Foundation of China","award":["62471471"],"award-info":[{"award-number":["62471471"]}]},{"name":"The National Natural Science Foundation of China","award":["62201589"],"award-info":[{"award-number":["62201589"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In the realm of bearings-only target tracking, the pseudo-linear Kalman filter (PLKF) has garnered significant interest, due to its low computational demands and robust stability. However, the interrelation between the measurement matrix and noise introduces bias into the PLKF\u2019s target state estimation. To address this issue, we introduce a fusion unbiased PLKF (FUBKF) algorithm. This algorithm initiates with a global pseudo-linear treatment of the measurement equation, subsequently isolating the noise within the measurement matrix. By employing the unscented Kalman filter (UKF), the algorithm achieves precise estimation of the measurement matrix, thereby mitigating the estimation error stemming from the correlation between the measurement matrix and noise. Simulation outcomes demonstrate that the proposed algorithm substantially enhances tracking accuracy and sustains high stability in both 2D and 3D bearings-only target tracking scenarios, encompassing both non-maneuvering and maneuvering conditions.<\/jats:p>","DOI":"10.3390\/rs16234536","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T11:48:56Z","timestamp":1733226536000},"page":"4536","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fusion Unbiased Pseudo-Linear Kalman Filter-Based Bearings-Only Target Tracking"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-5190-7147","authenticated-orcid":false,"given":"Zhihao","family":"Cai","sequence":"first","affiliation":[{"name":"State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Shiqi","family":"Xing","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Weize","family":"Meng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Junpeng","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Xinyuan","family":"Su","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6908-1975","authenticated-orcid":false,"given":"Sinong","family":"Quan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4149","DOI":"10.1109\/TSMC.2019.2932449","article-title":"Optimization-Based Control for Bearing-Only Target Search with a Mobile Vehicle","volume":"51","author":"Li","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1109\/TAES.2020.3034023","article-title":"Bearings-Only Filtering Using Uncorrelated Conversion Based Filters","volume":"57","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6681","DOI":"10.1109\/TSP.2020.3035289","article-title":"A Closed-Form Estimator for Bearings-Only Fusion of Heterogeneous Passive Sensors","volume":"68","author":"Arulampalam","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4672","DOI":"10.1109\/TSP.2020.3012004","article-title":"An Algebraic Closed-Form Solution for Bearings-Only Maneuvering Target Motion Analysis from a Nonmaneuvering Platform","volume":"68","author":"Badriasl","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Urooj, A., Chaulya, S., and Radhakrishnan, R. (2023). Numerically Stable Centered Error Entropy and Mixture Minimum Error Entropy Es-timators for Bearings-Only Target Tracking Problem. IEEE Sens. Lett., 7.","DOI":"10.1109\/LSENS.2023.3335122"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Das, S., Kumar, K., and Bhaumik, S. (2023, January 4\u20138). Bearings-Only Tracking with Speed and Range Constraints. Proceedings of the 2023 31st European Signal Processing Conference (EUSIPCO), Helsinki, Finland.","DOI":"10.23919\/EUSIPCO58844.2023.10289720"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Song, S., Dai, Y., Sun, S., and Jin, T. (2024). Efficient Image Reconstruction Methods Based on Structured Sparsity for Short-Range Radar. IEEE Trans. Geosci. Remote Sens., 62.","DOI":"10.1109\/TGRS.2024.3404626"},{"key":"ref_8","unstructured":"Wang, J., Quan, S., Xing, S., Li, Y., Wang, H., and Meng, W. (2024). PSO-based Fine Polarimetric Decomposition for Ship Scattering Characterization. ISPRS J. Photogramm. Remote Sens., 1\u201316."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"P\u00e9rez, A.C., and Jauffret, C. (2023, January 27\u201330). Observability of Bias of Measurements in Bearings-Only Target Motion Analysis. Proceedings of the 2023 26th International Conference on Information Fusion (FUSION), Charleston, SC, USA.","DOI":"10.23919\/FUSION52260.2023.10224118"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Liu, Z., Di, X., Shen, X., and Wang, L. (2023, January 28\u201330). Bearings only passive location for UAV in formation flight. Proceedings of the 2023 IEEE International Conference on Control, Electronics and Computer Technology (ICCECT), Jilin, China.","DOI":"10.1109\/ICCECT57938.2023.10140876"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1109\/TCST.2018.2890370","article-title":"Bearings-Only Tracking Using Augmented Ensemble Kalman Filter","volume":"28","author":"Sun","year":"2020","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, X., Zheng, J., Han, T., and Hu, Q. (2023, January 24\u201326). Aircrafts Scheduling Based Target Cooperative Tracking with Bearings-Only Measurements. Proceedings of the 2023 42nd Chinese Control Conference (CCC), Tianjin, China.","DOI":"10.23919\/CCC58697.2023.10240156"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xing, S., Song, S., Quan, S., Sun, D., Wang, J., and Li, Y. (2022). Near-Field 3D Sparse SAR Direct Imaging with Irregular Samples. Remote Sens., 14.","DOI":"10.3390\/rs14246321"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6488","DOI":"10.1109\/TSP.2021.3129599","article-title":"Analysis of Propagation Delay Effects on Bearings-Only Fusion of Heterogeneous Sensors","volume":"69","author":"Arulampalam","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1109\/TSMC.2020.3012485","article-title":"Observability Metrics for Single-Target Tracking with Bearings-Only Measurements","volume":"52","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"19524","DOI":"10.1109\/JSEN.2023.3283863","article-title":"A Pseudolinear Maximum Correntropy Kalman Filter Framework for Bearings-Only Target Tracking","volume":"23","author":"Zhong","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4899","DOI":"10.1109\/TAES.2020.3003703","article-title":"Underwater Target Tracking in Uncertain Multipath Ocean Environments","volume":"56","author":"Liu","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2486","DOI":"10.1109\/LAWP.2024.3397881","article-title":"An Effective Image Reconstruction Enhancement Method with Convolutional Reweighting for Near-Field SAR","volume":"23","author":"Song","year":"2024","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Rao, S.K., and Divya, G.N. (2021, January 17\u201318). Underwater State Estimation using Bearings only Measurements with an Emphasis on Sonar. Proceedings of the 2021 3rd International Conference on Advances in Computing, Communication Control and Networking (ICAC3N), Greater Noida, India.","DOI":"10.1109\/ICAC3N53548.2021.9725459"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Turner, J.D., McMahon, J., and Zavlanos, M.M. (2022, January 23\u201327). Receding Horizon Tracking of an Unknown Number of Mobile Targets using a Bear-ings-Only Sensor. Proceedings of the 2022 International Conference on Robotics and Automation (ICRA), Philadelphia, PA, USA.","DOI":"10.1109\/ICRA46639.2022.9811882"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"8504","DOI":"10.1109\/JSEN.2023.3243039","article-title":"Event-Triggered Distributed Bias-Compensated Pseudolinear Information Filter for Bearings-Only Tracking Under Measurement Uncertainty","volume":"8","author":"Jiang","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, X., Liang, J., Huang, G., Ma, S., and Li, H. (2024). Adaptive Invariant Extended Kalman Filter-Based Tightly-Coupled SINS\/RTK-Integrated Positioning for Rotor Unmanned Aerial Vehicle. IEEE Trans. Instrum. Meas., 73.","DOI":"10.1109\/TIM.2024.3449937"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1109\/LCSYS.2024.3410889","article-title":"Extended Kalman Filter\u2013Koopman Operator for Tractable Stochastic Optimal Control","volume":"8","author":"Ramadan","year":"2024","journal-title":"IEEE Control Syst. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Li, H., Chang, S., Yao, Q., Wan, C., Zou, G.J., and Zhang, D.L. (2024). Robust Heading and Attitude Estimation of MEMS IMU in Magnetic Anomaly Field Using a Partially Adaptive Decoupled Extended Kalman Filter and LSTM Algorithm. IEEE Trans. Instrum. Meas., 73.","DOI":"10.1109\/TIM.2024.3381659"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6973","DOI":"10.1109\/JSEN.2015.2469105","article-title":"Cubature + Extended Hybrid Kalman Filtering Method and Its Application in PPP\/IMU Tightly Coupled Navigation Systems","volume":"15","author":"Zhao","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1109\/LSP.2023.3285118","article-title":"Outlier-Robust Iterative Extended Kalman Filtering","volume":"30","author":"Tao","year":"2023","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1109\/LCSYS.2024.3432349","article-title":"Unilateral Constrained Extended Kalman Filter","volume":"8","author":"Herrera","year":"2024","journal-title":"IEEE Control Syst. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"15140","DOI":"10.1109\/TIE.2024.3366214","article-title":"A Differential Signal and Extended-Kalman-Filter-Based Anti-Interference Magnetic Tracking Method for Surgical Scenes","volume":"71","author":"Lv","year":"2024","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"7143","DOI":"10.1109\/TASE.2023.3338744","article-title":"APFC: Adaptive Particle Filter for Change Point Detection of Profile Data in Manufacturing Systems","volume":"21","author":"Xie","year":"2024","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhou, N., Liu, Q., Yang, Y., Wu, D., Gao, G., and Lei, S. (2024). An Indoor Positioning Algorithm Based on Particle Filter and Neigh-bor-Guided Particle Optimization for Wireless Sensor Networks. IEEE Trans. Instrum. Meas., 73.","DOI":"10.1109\/TIM.2023.3329158"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6972","DOI":"10.1109\/TAES.2024.3409644","article-title":"Rao\u2013Blackwellized Particle Filter Using Noise Adaptive Kalman Filter for Fully Mixing State-Space Models","volume":"60","author":"Badar","year":"2024","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"35845","DOI":"10.1109\/JSEN.2024.3439540","article-title":"Particle Filter-Based Enhanced Transition Model in Signal for Unsupervised Localization","volume":"24","author":"Chen","year":"2024","journal-title":"IEEE Sens. J."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"He, M., and Chan, S.C. (2024, January 24\u201327). A New Adaptive Fading Instrumental Variable Pseudolinear Kalman Filter for 3D AOA Target Tracking. Proceedings of the 2024 IEEE 99th Vehicular Technology Conference (VTC2024-Spring), Singapore.","DOI":"10.1109\/VTC2024-Spring62846.2024.10682824"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Hao, H., and Duan, Z. (2024, January 4\u20137). Bias-compensated Pseudolinear Kalman Filter for Acoustic Sensor Tracking with Colored Measurement Noise. Proceedings of the 2024 IEEE International Conference on Mechatronics and Automation (ICMA), Tianjin, China.","DOI":"10.1109\/ICMA61710.2024.10633190"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Liang, R., Xu, S., Zhang, L., Zhang, Y., and Xiao, D. (2021, January 15\u201319). A One-step Pseudolinear Kalman Filter for Invasive Target Tracking in Three-dimensional Space. Proceedings of the 2021 IEEE International Conference on Real-time Computing and Robotics (RCAR), Xining, China.","DOI":"10.1109\/RCAR52367.2021.9517641"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, J., and Guo, G. (2021). A Recursive Estimator for Pseudolinear Target Motion Analysis Using Multiple Hybrid Sensors. IEEE Transac-Tions Instrum. Meas., 70.","DOI":"10.1109\/TIM.2021.3097400"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3385","DOI":"10.1109\/TSP.2020.2998896","article-title":"AOA Pseudolinear Target Motion Analysis in the Presence of Sensor Location Errors","volume":"68","author":"Pang","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"6119","DOI":"10.1109\/TSP.2017.2749207","article-title":"Improved pseudolinear kalman filter algorithms for bearings-only target tracking","volume":"65","author":"Nguyen","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1109\/LSP.2019.2945677","article-title":"Bias-compensated diffusion pseudolinear kalman filter algorithm for censored bearings-only target tracking","volume":"26","author":"Wang","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1109\/LSP.2018.2869108","article-title":"Instrumental Variable Based Kalman Filter Algorithm for Three-Dimensional AOA Target Tracking","volume":"25","author":"Nguyen","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Huang, Z., Chen, S., Hao, C., and Orlando, D. (2021). Bearings-Only Target Tracking with an Unbiased Pseudolinear Kalman Filter. Remote Sens., 13.","DOI":"10.3390\/rs13152915"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Zhang, S., Wang, E., Zhu, Z., Yi, J., Wang, Y., and Kuai, E. (2024). UKF-FNN-RIC: A Highly Accurate UWB Localization Algorithm for TOA Scenario. IEEE Trans. Instrum. Meas., 73.","DOI":"10.1109\/TIM.2024.3476531"},{"key":"ref_43","unstructured":"Martin, B., Michael Ernesto, L., and Edmund F\u00f8rland, B. (2023, January 27\u201330). Extended target PMBM tracker with a Gaussian Process target model on LiDAR data. Proceedings of the 2023 26th International Conference on Information Fusion (FUSION), Charleston, SC, USA."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"6449","DOI":"10.1109\/TIT.2020.3013991","article-title":"A Cram\u00e9r-Rao Lower Bound Derivation for Passive Sonar Track-Before-Detect Algorithms","volume":"66","author":"Northardt","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2036","DOI":"10.1109\/TAES.2018.2881352","article-title":"Globally Valid Posterior Cramer-Rao Bound for Three-Dimensional Bearings-Only Filtering","volume":"55","author":"Schmitt","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/TSP.2018.2883915","article-title":"Cramer-Rao Bound for Constrained Parameter Estimation Using Lehmann-Unbiasedness","volume":"67","author":"Nitzan","year":"2019","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/23\/4536\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:46:15Z","timestamp":1760114775000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/23\/4536"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,3]]},"references-count":46,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["rs16234536"],"URL":"https:\/\/doi.org\/10.3390\/rs16234536","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,3]]}}}