{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:32:06Z","timestamp":1760236326491,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,16]],"date-time":"2021-11-16T00:00:00Z","timestamp":1637020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>As a new-style filter, the smooth variable structure filter (SVSF) has attracted significant interest. Based on the predictor-corrector method and sliding mode concept, the SVSF is more robust in the face of modeling errors and uncertainties compared to the Kalman filter. Since the estimation performance is usually insufficient in real cases where the measurement vector is of fewer dimensions than the state vector, an improved SVSF (ISVSF) is proposed by combining the existing SVSF with Bayesian theory. The ISVSF contains two steps: firstly, a preliminary estimation is performed by SVSF. Secondly, Bayesian formulas are adopted to improve the estimation for higher accuracy. The ISVSF shows high robustness in dealing with modeling uncertainties and noise. It is noticeable that ISVSF could deliver satisfying performance even if the state of the system is undergoing a sudden change. According to the simulation results of target tracking, the proposed ISVSF performance can be better than that obtained with existing filters.<\/jats:p>","DOI":"10.3390\/rs13224612","type":"journal-article","created":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T02:42:28Z","timestamp":1637116948000},"page":"4612","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Improved Smooth Variable Structure Filter for Robust Target Tracking"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1604-1221","authenticated-orcid":false,"given":"Yu","family":"Chen","sequence":"first","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710126, China"}]},{"given":"Luping","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710126, China"}]},{"given":"Guangmin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710126, China"}]},{"given":"Bo","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710126, China"},{"name":"Department of Electrical, Electronic, and Information Engineering, University of Bologna, 47521 Cesena (FC), Italy"}]},{"given":"Jingrong","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710126, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1109\/TAES.2005.1561886","article-title":"Survey of maneuvering target tracking. Part V. Multiple-model methods","volume":"41","author":"Li","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1016\/j.conengprac.2012.04.003","article-title":"Nonlinear Bayesian state estimation: A review of recent developments","volume":"20","author":"Patwardhan","year":"2012","journal-title":"Control. Eng. Pr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A New Approach to Linear Filtering and Prediction Problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5078","DOI":"10.1109\/TSP.2019.2935868","article-title":"Iterated Extended Kalman Smoother-Based Variable Splitting for L1-Regularized State Estimation","volume":"67","author":"Gao","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1049\/iet-rsn.2020.0258","article-title":"Robust extended Kalman filtering for non-linear systems with unknown input: A UBB model approach","volume":"14","author":"Asgari","year":"2020","journal-title":"IET Radar Sonar Navig."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1109\/TAC.2012.2204830","article-title":"Transformed Unscented Kalman Filter","volume":"58","author":"Chang","year":"2013","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.sigpro.2013.08.015","article-title":"Combined cubature Kalman and smooth variable structure filtering: A robust nonlinear estimation strategy","volume":"96","author":"Gadsden","year":"2014","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.isatra.2018.10.015","article-title":"Fault detection and diagnosis based on particle filters combined with interactive multiple-model estimation in dynamic process systems","volume":"85","author":"Zhang","year":"2019","journal-title":"ISA Trans."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1049\/iet-rsn.2018.5587","article-title":"GNSS multipath estimation and mitigation based on particle filter","volume":"13","author":"Qin","year":"2019","journal-title":"IET Radar Sonar Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.adhoc.2018.09.017","article-title":"GRNN and KF framework based real time target tracking using PSOC BLE and smartphone","volume":"84","author":"Jondhale","year":"2019","journal-title":"Ad Hoc Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/JSEN.2018.2873357","article-title":"Kalman Filtering Framework-Based Real Time Target Tracking in Wireless Sensor Networks Using Generalized Regression Neural Networks","volume":"19","author":"Jondhale","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1109\/9.489270","article-title":"Multiple-model estimation with variable structure","volume":"41","author":"Li","year":"1996","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"118472","DOI":"10.1109\/ACCESS.2020.3004871","article-title":"A Novel Nonlinear Algorithm for Non-Gaussian Noises and Measurement Information Loss in Underwater Navigation","volume":"8","author":"Huang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"70162","DOI":"10.1109\/ACCESS.2020.2986022","article-title":"Maximum Correntropy Square-Root Cubature Kalman Filter for Non-Gaussian Measurement Noise","volume":"8","author":"He","year":"2020","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3606","DOI":"10.1109\/TSP.2019.2916755","article-title":"A Novel Robust Gaussian\u2013Student\u2019s t Mixture Distribution Based Kalman Filter","volume":"67","author":"Huang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1109\/JPROC.2007.893255","article-title":"The Smooth Variable Structure Filter","volume":"95","author":"Habibi","year":"2007","journal-title":"Proc. IEEE"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1109\/TAES.2014.110768","article-title":"Kalman and smooth variable structure filters for robust estimation","volume":"50","author":"Gadsden","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gadsden, S.A., and Habibi, S.R. (2010, January 15\u201317). A new form of the smooth variable structure filter with a covariance derivation. Proceedings of the 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA.","DOI":"10.1109\/CDC.2010.5717397"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"014503","DOI":"10.1115\/1.4006628","article-title":"A New Robust Filtering Strategy for Linear Systems","volume":"135","author":"Gadsden","year":"2013","journal-title":"J. Dyn. Syst. Meas. Control."},{"key":"ref_20","first-page":"102912","article-title":"The smooth variable structure filter: A comprehensive review","volume":"110","author":"Ma","year":"2020","journal-title":"Digit. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1016\/j.sigpro.2012.07.036","article-title":"Kalman filtering strategies utilizing the chattering effects of the smooth variable structure filter","volume":"93","author":"AlShabi","year":"2013","journal-title":"Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.sigpro.2018.05.025","article-title":"The uncertainty learning filter: A revised smooth variable structure filter","volume":"152","author":"Spiller","year":"2018","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.sigpro.2018.09.036","article-title":"A nonlinear second-order filtering strategy for state estimation of uncertain systems","volume":"155","author":"Afshari","year":"2019","journal-title":"Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1109\/TITS.2019.2899051","article-title":"Online Multiple Maneuvering Vehicle Tracking System Based on Multi-Model Smooth Variable Structure Filter","volume":"21","author":"Luo","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"148989","DOI":"10.1109\/ACCESS.2019.2946609","article-title":"Combined Quaternion-Based Error State Kalman Filtering and Smooth Variable Structure Filtering for Robust Attitude Estimation","volume":"7","author":"Youn","year":"2019","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/TAES.2017.2649138","article-title":"Target Tracking Formulation of the SVSF With Data Association Techniques","volume":"53","author":"Attari","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1109\/TITS.2015.2504331","article-title":"An SVSF-Based Generalized Robust Strategy for Target Tracking in Clutter","volume":"17","author":"Attari","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.ifacol.2019.08.051","article-title":"SLAM based on Adaptive SVSF for Cooperative Unmanned Vehicles in Dynamic environment","volume":"52","author":"Demim","year":"2019","journal-title":"IFAC PapersOnLine"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1049\/iet-smt.2017.0529","article-title":"Adaptive state estimation for tracking of civilian aircraft","volume":"12","author":"Patra","year":"2018","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1080\/00051144.2017.1372123","article-title":"Cooperative SLAM for multiple UGVs navigation using SVSF filter","volume":"58","author":"Demim","year":"2017","journal-title":"Automatika"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1109\/TAES.2017.2671118","article-title":"Predictive Smooth Variable Structure Filter for Attitude Synchronization Estimation During Satellite Formation Flying","volume":"53","author":"Cao","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1109\/TMECH.2013.2253616","article-title":"Novel Model-Based Estimators for the Purposes of Fault Detection and Diagnosis","volume":"18","author":"Gadsden","year":"2013","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TVT.2014.2317736","article-title":"Automotive Internal-Combustion-Engine Fault Detection and Classification Using Artificial Neural Network Techniques","volume":"64","author":"Ahmed","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1109\/JESTPE.2014.2331062","article-title":"Reduced-Order Electrochemical Model Parameters Identification and State of Charge Estimation for Healthy and Aged Li-Ion Batteries\u2014Part II: Aged Battery Model and State of Charge Estimation","volume":"2","author":"Ahmed","year":"2014","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/JSYST.2019.2919792","article-title":"Recursive Smooth Variable Structure Filter for Estimation Processes in Direct Power Control Scheme Under Balanced and Unbalanced Power Grid","volume":"14","author":"Alshabi","year":"2020","journal-title":"IEEE Syst. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1080\/15435075.2019.1671423","article-title":"A hybrid observer for SOC estimation of lithium-ion battery based on a coupled electrochemical-thermal model","volume":"16","author":"Xu","year":"2019","journal-title":"Int. J. Green Energy"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.conengprac.2018.04.015","article-title":"Reliable state of charge and state of health estimation using the smooth variable structure filter","volume":"77","author":"Afshari","year":"2018","journal-title":"Control. Eng. Pr."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.neunet.2018.09.012","article-title":"Estimation theory and Neural Networks revisited: REKF and RSVSF as optimization techniques for Deep-Learning","volume":"108","author":"Ismail","year":"2018","journal-title":"Neural Netw."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s00521-015-1875-2","article-title":"Artificial neural network training utilizing the smooth variable structure filter estimation strategy","volume":"27","author":"Ahmed","year":"2016","journal-title":"Neural Comput. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","article-title":"Cubature kalman filters","volume":"54","author":"Arasaratnam","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Chen, Y., Xu, L., Yan, B., and Li, C. (2020). A Novel Smooth Variable Structure Smoother for Robust Estimation. Sensors, 20.","DOI":"10.3390\/s20061781"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1115\/1.1590682","article-title":"The Variable Structure Filter","volume":"125","author":"Habibi","year":"2003","journal-title":"J. Dyn. Syst. Meas. Control."},{"key":"ref_43","first-page":"632","article-title":"Robust nonlinear control and estimation of a prrr robot system","volume":"34","author":"Hatamleh","year":"2019","journal-title":"Int. J. Robot. Autom."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"8744","DOI":"10.1109\/TIM.2020.2999165","article-title":"A Hybrid Estimation-Based Technique for Partial Discharge Localization","volume":"69","author":"Avzayesh","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_45","unstructured":"Grewal, M., and Andrews, A. (2015). Kalman Filtering: Theory and Practice with MATLAB, John Wiley & Sons. [4th ed.]."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/22\/4612\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:31:13Z","timestamp":1760167873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/22\/4612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,16]]},"references-count":45,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["rs13224612"],"URL":"https:\/\/doi.org\/10.3390\/rs13224612","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,11,16]]}}}