{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T04:43:52Z","timestamp":1780634632519,"version":"3.54.1"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T00:00:00Z","timestamp":1552953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2017YFC0821102"],"award-info":[{"award-number":["2017YFC0821102"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2016YFB0502004"],"award-info":[{"award-number":["2016YFB0502004"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The unscented Kalman filter (UKF) is widely used to address the nonlinear problems in target tracking. However, this standard UKF shows unstable performance whenever the noise covariance mismatches. Furthermore, in consideration of the deficiencies of the current adaptive UKF algorithm, this paper proposes a new adaptive UKF scheme for the time-varying noise covariance problems. First of all, the cross-correlation between the innovation and residual sequences is given and proven. On this basis, a linear matrix equation deduced from the innovation and residual sequences is applied to resolve the process noise covariance in real time. Using the redundant measurements, an improved measurement-based adaptive Kalman filtering algorithm is applied to estimate the measurement noise covariance, which is entirely immune to the state estimation. The results of the simulation indicate that under the condition of time-varying noise covariances, the proposed adaptive UKF outperforms the standard UKF and the current adaptive UKF algorithm, hence improving tracking accuracy and stability.<\/jats:p>","DOI":"10.3390\/s19061371","type":"journal-article","created":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T12:12:25Z","timestamp":1552997545000},"page":"1371","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Adaptive Unscented Kalman Filter for Target Tracking with Unknown Time-Varying Noise Covariance"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7570-3948","authenticated-orcid":false,"given":"Baoshuang","family":"Ge","sequence":"first","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hai","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"},{"name":"Science and Technology on Aircraft Control Laboratory, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liuyang","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maaz Mohammed","family":"Butt","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhou, H., Huang, H., Zhao, H., Zhao, X., and Yin, X. (2017). Adaptive Unscented Kalman Filter for Target Tracking in the Presence of Nonlinear Systems Involving Model Mismatches. Remote Sens., 9.","DOI":"10.3390\/rs9070657"},{"key":"ref_2","first-page":"4","article-title":"WSN based robust ground target tracking for precision guided missiles","volume":"3","author":"Chatterjee","year":"2013","journal-title":"Int. J. Res. Comput. Appl. Manag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Sreeja, S., and Hablani, H. (2016, January 4\u20138). Precision munition guidance and estimation of target position in 2-D. Proceedings of the AIAA Guidance, Navigation, and Control Conference, San Diego, CA, USA.","DOI":"10.2514\/6.2016-2113"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cao, Y., Wang, G., Yan, D., and Zhao, Z. (2016). Two Algorithms for the Detection and Tracking of Moving Vehicle Targets in Aerial Infrared Image Sequences. Remote Sens., 8.","DOI":"10.3390\/rs8010028"},{"key":"ref_5","unstructured":"Zhao, M., Zhang, X., and Yang, Q. (2016). Modified Multi-Mode Target Tracker for High-Frequency Surface Wave Radar. Remote Sens., 8."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Benfold, B., and Reid, I. (2011, January 20\u201325). Stable multi-target tracking in real-time surveillance video. Proceedings of the Computer Vision and Pattern Recognition, Colorado Springs, CO, USA.","DOI":"10.1109\/CVPR.2011.5995667"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TSMCB.2003.810953","article-title":"Tracking a maneuvering target using neural fuzzy network","volume":"34","author":"Duh","year":"2004","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_8","first-page":"755","article-title":"Adaptive UKF Method with Applications to Target Tracking","volume":"37","author":"Shi","year":"2011","journal-title":"Acta Autom. Sin."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problem","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_10","first-page":"584","article-title":"The unscented particle filter","volume":"96","author":"Doucet","year":"2001","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"012071","DOI":"10.1088\/1742-6596\/974\/1\/012071","article-title":"Estimation of three-dimensional radar tracking using modified extended kalman filter","volume":"897","author":"Aditya","year":"2018","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kumar, G., Prasad, D., and Singh, R.P. (2017, January 17\u201319). Target tracking using adaptive Kalman Filter. Proceedings of the 2017 International Conference on Smart grids, Power and Advanced Control Engineering, Bangalore, India.","DOI":"10.1109\/ICSPACE.2017.8343461"},{"key":"ref_13","unstructured":"Lippiello, V., Siciliano, B., and Villani, L. (2005, January 3\u20138). Visual motion tracking with full adaptive extended Kalman filter: An experimental study. Proceedings of the 16th IFAC World Congress, Prague, Czech Republic."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"144","DOI":"10.3390\/s7010144","article-title":"An Improved Particle Filter for Target Tracking in Sensor Systems","volume":"7","author":"Wang","year":"2007","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Okuma, K., Taleghani, A., De Freitas, N., Little, J., and Lowe, D. (2004, January 11\u201314). A Boosted Particle Filter: Multitarget Detection and Tracking. Proceedings of the 8th European Conference on Computer Vision, Prague, Czech Republic.","DOI":"10.1007\/978-3-540-24670-1_3"},{"key":"ref_16","unstructured":"Julier, S., and Uhlmann, J.K. (2018, September 26). A General Method for Approximating Nonlinear Transformations of Probability Distributions. Available online: http:\/\/citeseerx.ist.psu.edu\/viewdoc\/summary?doi=10.1.1.46.6718."},{"key":"ref_17","first-page":"779","article-title":"A comparison of estimation accuracy by the use of KF, EKF & UKF filters","volume":"46","author":"Konatowski","year":"2007","journal-title":"Wit Trans. Model. Simul."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"111","DOI":"10.3390\/rs70100111","article-title":"High-Precision Attitude Post-Processing and Initial Verification for the ZY-3 Satellite","volume":"7","author":"Tang","year":"2014","journal-title":"Remote Sens."},{"key":"ref_19","unstructured":"Wan, E.A., and Van der Merwe, R. (2000, January 4). The unscented Kalman filter for nonlinear estimation. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium, Lake Louise, AB, Canada."},{"key":"ref_20","unstructured":"Blair, W.D., Watson, G.A., and Rice, T.R. (1991, January 10\u201312). Tracking maneuvering targets with an interacting multiple model filter containing exponentially-correlated acceleration models. Proceedings of the Twenty-Third Southeastern Symposium on System Theory, Columbia, SC, USA."},{"key":"ref_21","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_22","unstructured":"Farina, A., Immediata, S., and Timmoneri, L. (2006, January 4\u20136). Impact of ballistic target model uncertainty on IMM-UKF and IMM-EKF tracking accuracies. Proceedings of the 2006 14th European Signal Processing Conference, Florence, Italy."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Xu, Q., Li, X., and Chan, C.Y. (2017). A Cost-Effective Vehicle Localization Solution Using an Interacting Multiple Model-Unscented Kalman Filters (IMM-UKF) Algorithm and Grey Neural Network. Sensors, 17.","DOI":"10.3390\/s17061431"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, S. (2009, January 19\u201320). An Adaptive Unscented Kalman Filter for Dead Reckoning Systems. Proceedings of the 2009 International Conference on Information Engineering and Computer Science, Wuhan, China.","DOI":"10.1109\/ICIECS.2009.5365064"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1061\/(ASCE)AS.1943-5525.0000178","article-title":"Adaptive Fading UKF with Q-Adaptation: Application to Picosatellite Attitude Estimation","volume":"26","author":"Soken","year":"2013","journal-title":"J. Aerosp. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Li, L., Hua, C., and Yang, H. (2014, January 3\u20135). A new adaptive unscented Kalman filter based on covariance matching technique. Proceedings of the 2014 International Conference on Mechatronics and Control, Jinzhou, China.","DOI":"10.1109\/ICMC.2014.7231764"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.actaastro.2015.12.014","article-title":"Covariance matching based adaptive unscented Kalman filter for direct filtering in INS\/GNSS integration","volume":"120","author":"Meng","year":"2016","journal-title":"Acta Astronaut."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Akhlaghi, S., Zhou, N., and Huang, Z. (2017, January 16\u201320). Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation. Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA.","DOI":"10.1109\/PESGM.2017.8273755"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/TCST.2014.2317781","article-title":"An adaptive unscented Kalman filtering approach for online estimation of model parameters and state-of-charge of lithium-ion batteries for autonomous mobile robots","volume":"23","author":"Partovibakhsh","year":"2015","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_30","first-page":"35","article-title":"Adaptive Filtering Algorithm of Multi-Sensor Information Fusion for Individual Navigation","volume":"5","author":"Zhang","year":"2018","journal-title":"Navig. Position. Timing"},{"key":"ref_31","first-page":"696","article-title":"Measurement-based adaptive Kalman filtering algorithm for GPS\/INS integrated navigation system","volume":"18","author":"Zhang","year":"2010","journal-title":"J. Chin. Inert. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"23953","DOI":"10.3390\/s150923953","article-title":"An Adaptive Low-Cost GNSS\/MEMS-IMU Tightly-Coupled Integration System with Aiding Measurement in a GNSS Signal-Challenged Environment","volume":"15","author":"Zhou","year":"2015","journal-title":"Sensors"},{"key":"ref_33","first-page":"1596","article-title":"A Redundant measurement Adaptive Kalman Filter Algorithm","volume":"36","author":"Zhou","year":"2015","journal-title":"Acta Aeronaut. Astronaut. Sin."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Li, Z., Zhang, H., Zhou, Q., and Che, H. (2017). An Adaptive Low-Cost INS\/GNSS Tightly-Coupled Integration Architecture Based on Redundant Measurement Noise Covariance Estimation. Sensors, 17.","DOI":"10.3390\/s17092032"},{"key":"ref_35","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_36","doi-asserted-by":"crossref","unstructured":"Julier, S.J. (2002, January 8\u201310). The Scaled Unscented Transformation. Proceedings of the American Control Conference, Anchorage, AK, USA.","DOI":"10.1109\/ACC.2002.1025369"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/j.measurement.2008.02.009","article-title":"Centralized and decentralized process and sensor fault monitoring using data fusion based on adaptive extended Kalman filter algorithm","volume":"41","author":"Salahshoor","year":"2008","journal-title":"Measurement"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1002\/acs.2393","article-title":"Robust adaptive unscented Kalman filter for attitude estimation of pico satellites","volume":"28","author":"Hajiyev","year":"2014","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/TAC.1976.1101260","article-title":"Adaptive sequential estimation with unknown noise statistics","volume":"21","author":"Myers","year":"1976","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.automatica.2018.11.037","article-title":"Redundant measurement-based second order mutual difference adaptive Kalman filter","volume":"100","author":"Jiang","year":"2019","journal-title":"Automatica"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1371\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:38:57Z","timestamp":1760186337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1371"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,19]]},"references-count":40,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19061371"],"URL":"https:\/\/doi.org\/10.3390\/s19061371","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,19]]}}}