{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T13:21:41Z","timestamp":1770988901421,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T00:00:00Z","timestamp":1628726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671181"],"award-info":[{"award-number":["61671181"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In bearings-only tracking systems, the pseudolinear Kalman filter (PLKF) has advantages in stability and computational complexity, but suffers from correlation problems. Existing solutions require bias compensation to reduce the correlation between the pseudomeasurement matrix and pseudolinear noise, but incomplete compensation may cause a loss of estimation accuracy. In this paper, a new pseudolinear filter is proposed under the minimum mean square error (MMSE) framework without requirement of bias compensation. The pseudolinear state-space model of bearings-only tracking is first developed. The correlation between the pseudomeasurement matrix and pseudolinear noise is thoroughly analyzed. By splitting the bearing noise term from the pseudomeasurement matrix and performing some algebraic manipulations, their cross-covariance can be calculated and incorporated into the filtering process to account for their effects on estimation. The target state estimation and its associated covariance can then be updated according to the MMSE update equation. The new pseudolinear filter has a stable performance and low computational complexity and handles the correlation problem implicitly under a unified MMSE framework, thus avoiding the severe bias problem of the PLKF. The posterior Cramer\u2013Rao Lower Bound (PCRLB) for target state estimation is presented. Simulations are conducted to demonstrate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s21165444","type":"journal-article","created":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T10:54:41Z","timestamp":1628765681000},"page":"5444","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A New Pseudolinear Filter for Bearings-Only Tracking without Requirement of Bias Compensation"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5149-9460","authenticated-orcid":false,"given":"Shizhe","family":"Bu","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiqiang","family":"Meng","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1530-9321","authenticated-orcid":false,"given":"Gongjian","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bar-Shalom, Y., Li, X.R., and Kirubarajan, T. (2001). Estimation with Applications to Tracking and Navigation, Wiley.","DOI":"10.1002\/0471221279"},{"key":"ref_2","unstructured":"He, Y., Xiu, J.J., and Guan, X. (2016). Radar Data Processing with Applications, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bai, J., Li, S., Zhang, H., Huang, L.B., and Wang, P. (2021). Robust Target Detection and Tracking Algorithm Based on Roadside Radar and Camera. Sensors, 21.","DOI":"10.3390\/s21041116"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Luo, J.H., Wang, Z.Y., Chen, Y.P., Wu, M., and Yang, Y. (2020). An Improved Unscented Particle Filter Approach for Multi-Sensor Fusion Target Tracking. Sensors, 20.","DOI":"10.3390\/s20236842"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Shi, Y.F., Qayyum, S., Memon, S.A., Khan, U., Imtiaz, J., Ullah, I., Dancey, D., and Nawaz, R. (2020). A Modified Bayesian Framework for Multi-Sensor Target Tracking with Out-of-Sequence-Measurements. Sensors, 20.","DOI":"10.3390\/s20143821"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1109\/48.557551","article-title":"A Closed-Form Solution to Bearings-Only Target Motion Analysis","volume":"22","author":"Nardone","year":"1997","journal-title":"IEEE Trans. Ocean. Enfin."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1654","DOI":"10.1109\/TAES.2016.150471","article-title":"Multisensor-Multitarget Bearing-Only Sensor Registration","volume":"52","author":"Taghavi","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5523","DOI":"10.1109\/TSP.2010.2064770","article-title":"Bearings-Only Target Motion Analysis via Instrumental Variable Estimation","volume":"58","author":"Zhang","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Shi, Y.F., Choi, J.W., Xu, L., Kim, J., Ullah, I., and Khan, U. (2020). Distributed Target Tracking in Challenging Environments Using Multiple Asynchronous Bearing-Only Sensors. Sensors, 20.","DOI":"10.3390\/s20092671"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Borisov, A., Bosov, A., Miller, B., and Miller, G. (2020). Passive Underwater Target Tracking: Conditionally Minimax Nonlinear Filtering with Bearing-Doppler Observations. Sensors, 20.","DOI":"10.3390\/s20082257"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"29802","DOI":"10.3390\/s151229768","article-title":"UAV Control on the Basis of 3D Landmark Bearing-Only Observations","volume":"15","author":"Karpenko","year":"2015","journal-title":"Sensors"},{"key":"ref_12","unstructured":"Aidala, V.J. Kalman Filter Behavior in Bearings-Only Tracking Applications, IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","unstructured":"Aidala, V., and Hammel, S. Utilization of modified polar coordinates for bearings-only tracking, IEEE Trans. Autom. Control."},{"key":"ref_14","unstructured":"Yang, R., Ng, G.W., and Bar-Shalom, Y. (2015, January 6\u20139). Bearings-only tracking with fusion from heterogenous passive sensors: ESM\/EO and acoustic. Proceedings of the 18th International Conference on Information Fusion, Washington, DC, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1049\/ip-rsn:20045073","article-title":"Recursive Bayesian estimation: bearing-only applications","volume":"152","author":"Karlsson","year":"2005","journal-title":"IEE Proc. Radar Sonar Navig."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1109\/JSYST.2013.2260641","article-title":"Bearing-only maneuvering mobile tracking with nonlinear filtering algorithms in wireless sensor networks","volume":"8","author":"Chang","year":"2014","journal-title":"IEEE Syst. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1163\/156939308784160857","article-title":"Novel roughening algorithm and hardware architecture for bearings-only tracking using particle filter","volume":"22","author":"Hong","year":"2008","journal-title":"J. Electromagn. Waves Appl."},{"key":"ref_18","unstructured":"Lingren, A., and Gong, K. Position and Velocity Estimation Via Bearing Observations, IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","unstructured":"Miller, B.M., Stepanyan, K.V., Miller, A.B., Andreev, K.V., and Khoroshenkikh, S.N. (2013, January 1\u20136). Optimal filter selection for UAV trajectory control problems. Proceedings of the Conference Information Technology and System, Kaliningrad, Russia."},{"key":"ref_20","first-page":"240","article-title":"Comparison of EKF, pseudomeasurement, and particle filters for a bearing-only target tracking problem","volume":"4728","author":"Lin","year":"2007","journal-title":"Proc. SPIE Int. Soc. Opt. Eng."},{"key":"ref_21","unstructured":"Aidala, V.J., and Nardone, S.C. Biased Estimation Properties of the Pseudolinear Tracking Filter, IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1109\/48.219533","article-title":"A nearly unbiased inherently stable bearings-only tracker","volume":"18","author":"Holtsberg","year":"1993","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_23","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_24","unstructured":"Lindgren, A.G. (1980, January 7\u20139). Properties of a nonlinear estimator for determining position and velocity from angle-of-arrival measurements. Processdings of the 14th Asilomar Conference on Circuits, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1109\/TAC.1984.1103664","article-title":"Fundamental properties and performance of conventional bearings-only target motion analysis","volume":"29","author":"Nardone","year":"1984","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.1109\/7.165369","article-title":"Bearings-only and Doppler-bearing tracking using instrumental variables","volume":"28","author":"Chen","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1109\/7.784053","article-title":"On the convergence of iterative methods for bearings-only tracking","volume":"35","author":"Cadre","year":"1999","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/TSP.2005.861088","article-title":"Bias compensation for the bearings-only pseudolinear target track estimator","volume":"54","author":"Dogancay","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.sigpro.2004.10.014","article-title":"On the efficiency of a bearings-only instrumental variable estimator for target motion analysis","volume":"85","year":"2005","journal-title":"Signal Proc."},{"key":"ref_30","unstructured":"Dogancay, K., and Arablouei, R. (September, January 31). Selective angle measurements for a 3D-AOA instrumental variable TMA algorithm. Proceedings of the 23rd European Signal Processing Conference, Nice, France."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1570","DOI":"10.1109\/TSP.2015.2399869","article-title":"3D Pseudolinear Target Motion Analysis From Angle Measurements","volume":"63","author":"Dogancay","year":"2015","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_32","unstructured":"Zhou, G., Yu, C., and Quan, T. (2012, January 9\u201312). A sequential tracking filter without requirement of measurement decorrelation. Proceedings of the 2012 International Conference on Information Fusion, Singapore."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/JSEE.2015.00123","article-title":"Sequential nonlinear tracking filter without requirement of measurement decorrelation","volume":"26","author":"Zhou","year":"2015","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/78.668800","article-title":"Posterior Cramer\u2014Rao Bounds for Discrete-Time Nonlinear Filtering","volume":"46","author":"Tichavsky","year":"1998","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"11618","DOI":"10.3390\/s101211618","article-title":"Performance Bound for Extended Target Tracking Using High Resolution Sensors","volume":"10","author":"Zhong","year":"2010","journal-title":"Sensors"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1109\/7.220948","article-title":"Tracking with debiased consistent converted measurements versus EKF","volume":"29","author":"Lerro","year":"1993","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_37","unstructured":"Ristic, B., Zollo, S., and Arulampalam, S. (2001, January 7\u201310). Performance Bounds for Manoeuvring Target Tracking Using Asynchronous Multi-Platform Angle-Only Measurements. Proceedings of the 4th International Conference on Information Fusion, Montr\u00e9al, QC, Canada."},{"key":"ref_38","unstructured":"Bar-Shalom, Y., and Fortmann, T.E. (1998). Tracking and Data Association, Academic."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5444\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:44:50Z","timestamp":1760165090000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,12]]},"references-count":38,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["s21165444"],"URL":"https:\/\/doi.org\/10.3390\/s21165444","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,12]]}}}