{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T11:49:32Z","timestamp":1784202572303,"version":"3.55.0"},"reference-count":118,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T00:00:00Z","timestamp":1615852800000},"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":["61903009"],"award-info":[{"award-number":["61903009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>State estimation is widely used in various automated systems, including IoT systems, unmanned systems, robots, etc. In traditional state estimation, measurement data are instantaneous and processed in real time. With modern systems\u2019 development, sensors can obtain more and more signals and store them. Therefore, how to use these measurement big data to improve the performance of state estimation has become a hot research issue in this field. This paper reviews the development of state estimation and future development trends. First, we review the model-based state estimation methods, including the Kalman filter, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc. Particle filters and Gaussian mixture filters that can handle mixed Gaussian noise are discussed, too. These methods have high requirements for models, while it is not easy to obtain accurate system models in practice. The emergence of robust filters, the interacting multiple model (IMM), and adaptive filters are also mentioned here. Secondly, the current research status of data-driven state estimation methods is introduced based on network learning. Finally, the main research results for hybrid filters obtained in recent years are summarized and discussed, which combine model-based methods and data-driven methods. This paper is based on state estimation research results and provides a more detailed overview of model-driven, data-driven, and hybrid-driven approaches. The main algorithm of each method is provided so that beginners can have a clearer understanding. Additionally, it discusses the future development trends for researchers in state estimation.<\/jats:p>","DOI":"10.3390\/s21062085","type":"journal-article","created":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T21:42:41Z","timestamp":1615930961000},"page":"2085","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":126,"title":["The New Trend of State Estimation: From Model-Driven to Hybrid-Driven Methods"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2230-0077","authenticated-orcid":false,"given":"Xue-Bo","family":"Jin","sequence":"first","affiliation":[{"name":"Artificial Intelligence College, Beijing Technology and Business University, Beijing 100048, China"},{"name":"China Light Industry Key Laboratory of Industrial Internet and Big Data, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruben Jonhson","family":"Robert Jeremiah","sequence":"additional","affiliation":[{"name":"School of Food and Health, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ting-Li","family":"Su","sequence":"additional","affiliation":[{"name":"Artificial Intelligence College, Beijing Technology and Business University, Beijing 100048, China"},{"name":"China Light Industry Key Laboratory of Industrial Internet and Big Data, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8047-1010","authenticated-orcid":false,"given":"Yu-Ting","family":"Bai","sequence":"additional","affiliation":[{"name":"Artificial Intelligence College, Beijing Technology and Business University, Beijing 100048, China"},{"name":"China Light Industry Key Laboratory of Industrial Internet and Big Data, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0074-3467","authenticated-orcid":false,"given":"Jian-Lei","family":"Kong","sequence":"additional","affiliation":[{"name":"Artificial Intelligence College, Beijing Technology and Business University, Beijing 100048, China"},{"name":"China Light Industry Key Laboratory of Industrial Internet and Big Data, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"172988141983959","DOI":"10.1177\/1729881419839596","article-title":"A review of mobile robots: Concepts, methods, theoretical framework, and applications","volume":"16","author":"Rubio","year":"2019","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_2","first-page":"47","article-title":"Multi-UAV Cooperative Target Tracking Control Based on Nonlinear Guidance","volume":"10","author":"Xin","year":"2019","journal-title":"Command. Inf. Syst. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.inffus.2019.06.021","article-title":"A multi-sensor data fusion enabled ensemble approach for medical data from body sensor networks","volume":"53","author":"Muzammal","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_4","first-page":"65","article-title":"State estimation of AC and DC distribution network under three-phase unbalance","volume":"43","author":"Ma","year":"2019","journal-title":"Autom. Electr. Power Syst."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhao, Z., Wang, Z., and Wang, X. (2021). Fault Detection and Identification Method for Quadcopter Based on Airframe Vibration Signals. Sensors, 21.","DOI":"10.3390\/s21020581"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1007\/s11071-020-06041-3","article-title":"A health performance evaluation method of multirotors under wind turbulence","volume":"102","author":"Zhao","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_7","unstructured":"Sorenson, H.W. (1985). Kalman Filtering: Theory and Application, IEEE Press."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wiener, N. (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series, John Wiley & Sons.","DOI":"10.7551\/mitpress\/2946.001.0001"},{"key":"ref_9","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":"Trans. ASME J. Basic Eng."},{"key":"ref_10","unstructured":"Qin, Y.Y., Zhang, H.Y., and Wang, S.H. (1998). Principles of Kalman Filtering and Integrated Navigation, Northwestern Polytechnical University Press."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2902","DOI":"10.1109\/TAC.2016.2601879","article-title":"Robust Kalman Filtering Under Model Perturbations","volume":"62","author":"Zorzi","year":"2017","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_12","unstructured":"Fu, M., Deng, Z.H., and Zhang, J.W. (2010). Kalman Filtering Theory and Its Application in Navigation System, Science Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1002\/rnc.4779","article-title":"Robust distributed H\u221e filtering over an uncertain sensor network with multiple fading measurements and varying sensor delays","volume":"30","author":"Hedayati","year":"2020","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_14","unstructured":"Julier, S.J., and Uhlmann, J.K. (1995, January 21\u201323). A new approach for filtering nonlinear system. Proceedings of the 1995 American Control Conference, Seattle, WA, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/9.847726","article-title":"A new method for the nonlinear transformation of means and covariances in filters and estimators","volume":"45","author":"Julier","year":"2000","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1016\/S0005-1098(00)00089-3","article-title":"New developments in state estimation for nonlinear systems","volume":"36","author":"Norgarrd","year":"2000","journal-title":"Automatica"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Julier, S.J., and Uhlmann, J. (2002, January 8\u201310). Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations. Proceedings of the American Control Conference, Anchorage, AK, USA.","DOI":"10.1109\/ACC.2002.1023128"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.1016\/j.automatica.2011.08.005","article-title":"Cubature Kalman smoothers","volume":"47","author":"Arasaratnam","year":"2011","journal-title":"Automatica"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3701","DOI":"10.1109\/TAES.2020.2977790","article-title":"Parameter Estimation of Generalized Gamma Distribution Toward SAR Image Processing","volume":"56","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105962","DOI":"10.1016\/j.ijepes.2020.105962","article-title":"A hybrid robust forecasting-aided state estimator considering bimodal Gaussian mixture measurement errors","volume":"120","author":"Jin","year":"2020","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1007\/s10044-019-00847-7","article-title":"Robust object tracking with crow search optimized multi-cue particle filter","volume":"23","author":"Walia","year":"2020","journal-title":"Pattern Anal. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Sun, S.L., Wei, H., and Yang, F.B. (2018). Advances in multi-sensor information fusion: Theory and applications 2017. Sensors, 18.","DOI":"10.3390\/s18041162"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3788","DOI":"10.3390\/ijerph16203788","article-title":"Spatio-temporal prediction for the monitoring-blind area of industrial atmosphere based on the fusion network","volume":"16","author":"Bai","year":"2019","journal-title":"Int. J. Environ. Res. Public Health"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.biosystemseng.2018.09.005","article-title":"An approach of improved multivariate timing-random deep belief net modelling for algal bloom prediction","volume":"177","author":"Wang","year":"2019","journal-title":"Biosyst. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Hong, J., Laflamme, S., Dodson, J., and Joyce, B. (2018). Introduction to State Estimation of High-Rate System Dynamics. Sensors, 18.","DOI":"10.3390\/s18010217"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2312","DOI":"10.1109\/TSG.2018.2870600","article-title":"A Survey on State Estimation Techniques and Challenges in Smart Distribution Systems","volume":"10","author":"Dehghanpour","year":"2018","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jin, X., Yin, G., and Chen, N. (2019). Advanced Estimation Techniques for Vehicle System Dynamic State: A Survey. Sensors, 19.","DOI":"10.3390\/s19194289"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Su, T.L., Kong, J.L., Bai, Y.T., Miao, B.B., and Dou, C. (2018). State-of-the-art mobile intelligence: Enabling robots to move like humans by estimating mobility with artificial intelligence. Appl. Sci., 8.","DOI":"10.3390\/app8030379"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.trb.2004.03.003","article-title":"Real-time freeway traffic state estimation based on extended Kalman filter: A general approach","volume":"39","author":"Wang","year":"2005","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yang, Y., Liu, X., Zhang, W., Liu, X., and Guo, Y. (2020). A Nonlinear Double Model for Multisensor-Integrated Navigation Using the Federated EKF Algorithm for Small UAVs. Sensors, 20.","DOI":"10.3390\/s20102974"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Du, H., Wang, W., Xu, C., Xiao, R., and Sun, C. (2020). Real-Time Onboard 3D State Estimation of an Unmanned Aerial Vehicle in Multi-Environments Using Multi-Sensor Data Fusion. Sensors, 20.","DOI":"10.3390\/s20030919"},{"key":"ref_32","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_33","doi-asserted-by":"crossref","first-page":"1768","DOI":"10.1002\/asjc.1954","article-title":"Indoor tracking by RFID fusion with IMU data","volume":"21","author":"Wang","year":"2019","journal-title":"Asian J. Control"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Dou, C., Su, T.L., Lian, X.F., and Shi, Y. (2016). Parallel Irregular Fusion Estimation Based on Nonlinear Filter for Indoor RFID Tracking System. Int. J. Distrib. Sens. Netw.","DOI":"10.1155\/2016\/1472930"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Luo, Z., Fu, Z., and Xu, Q. (2020). An Adaptive Multi-Dimensional Vehicle Driving State Observer Based on Modified Sage-Husa UKF Algorithm. Sensors, 20.","DOI":"10.3390\/s20236889"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, J., Wang, P., Zha, F., Guo, W., Jiang, Z., and Sun, L. (2020). A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot. Sensors, 20.","DOI":"10.3390\/s20082251"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhang, X., and Shen, Y. (2020). Distributed Kalman Filtering Based on the Non-Repeated Diffusion Strategy. Sensors, 20.","DOI":"10.3390\/s20236923"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Zhang, J., Hu, G., and Zhong, Y. (2020). Set-Membership Based Hybrid Kalman Filter for Nonlinear State Estimation under Systematic Uncertainty. Sensors, 20.","DOI":"10.3390\/s20030627"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Nan, D., Wang, W., Wang, K., Mahfoud, R.J., Alhelou, H.H., and Siano, P. (2019). Dynamic State Estimation for Synchronous Machines Based on Adaptive Ensemble Square Root Kalman Filter. Appl. Sci., 9.","DOI":"10.3390\/app9235200"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Santos, N.P., Lobo, V., and Bernardino, A. (2019, January 16\u201319). Unmanned Aerial Vehicle Tracking Using a Particle Filter Based Approach. Proceedings of the IEEE International Underwater Technology Symposium, UT 2019\u2014Proceedings, Kaohsiung, Taiwan.","DOI":"10.1109\/UT.2019.8734465"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.cja.2018.12.006","article-title":"Reliable flight performance assessment of multirotor based on interacting multiple model particle filter and health degree","volume":"32","author":"Zhao","year":"2019","journal-title":"Chin. J. Aeronaut."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/78.978374","article-title":"A tutorial on particle filters for online nonlinear\/non-Gaussian Bayesian tracking","volume":"50","author":"Arulampalam","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2335","DOI":"10.1002\/qj.3551","article-title":"Particle filters for high-dimensional geoscience applications: A review","volume":"145","author":"Leeuwen","year":"2019","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_44","first-page":"555","article-title":"Non Linear Filtering: Interacting Particle Solution","volume":"2","year":"1996","journal-title":"Markov Process. Relat. Fields"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s10596-010-9207-1","article-title":"Bridging the ensemble Kalman filter and particle filters: The adaptive Gaussian mixture filter","volume":"15","author":"Stordal","year":"2011","journal-title":"Comput. Geosci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2676","DOI":"10.1109\/TIP.2017.2781304","article-title":"Correlation Particle Filter for Visual Tracking","volume":"27","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Jing, Y., and Chen, Y. (2020, January 16\u201318). Distributed Color-Based Particle Filter for Target Tracking in Camera Network. Proceedings of the International Conference on Collaborative Computing: Networking, Applications and Worksharing, Shanghai, China.","DOI":"10.1007\/978-3-030-67540-0_24"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1109\/TAES.2010.5417160","article-title":"Maneuvering Target Tracking in the Presence of Glint using the Nonlinear Gaussian Mixture Kalman Filter","volume":"46","author":"Bilik","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1109\/TSP.2017.2749211","article-title":"Joint Sensor and Relay Power Control in Tracking Gaussian Mixture Targets by Wireless Sensor Networks","volume":"66","author":"Bengua","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.dsp.2016.11.010","article-title":"Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering","volume":"62","author":"Ding","year":"2017","journal-title":"Digit. Signal Process"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2506","DOI":"10.1049\/iet-cta.2016.0202","article-title":"Performance analysis of the generalised projection identification for time-varying systems","volume":"10","author":"Ding","year":"2016","journal-title":"IET Control Theory Appl."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"112575","DOI":"10.1016\/j.cam.2019.112575","article-title":"Gradient estimation algorithms for the parameter identification of bilinear systems using the auxiliary model","volume":"369","author":"Ding","year":"2020","journal-title":"J. Comput. Appl. Math."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1687814017730003","DOI":"10.1177\/1687814017730003","article-title":"The parameter estimation algorithms based on the dynamical response measurement data","volume":"9","author":"Xu","year":"2017","journal-title":"Adv. Mech. Eng."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1007\/s12555-016-0081-z","article-title":"A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems","volume":"15","author":"Pan","year":"2017","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1049\/iet-cta.2019.0413","article-title":"Recursive parameter estimation and its convergence for bilinear systems","volume":"14","author":"Zhang","year":"2020","journal-title":"IET Control Theory Appl."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.sigpro.2018.01.012","article-title":"The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique","volume":"147","author":"Li","year":"2018","journal-title":"Signal Process"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1016\/j.jfranklin.2019.11.003","article-title":"Recursive identification of bilinear time-delay systems through the redundant rule","volume":"257","author":"Zhang","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.automatica.2016.04.050","article-title":"Robust H\u221e filter design with past output measurements for uncertain discrete-time systems","volume":"71","author":"Frezzatto","year":"2016","journal-title":"Automatica"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1109\/TSP.2017.2656845","article-title":"Intrinsically Bayesian Robust Kalman Filter: An Innovation Process Approach","volume":"65","author":"Dehghannasiri","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1002\/acs.2770","article-title":"Robust guaranteed cost state estimation for discrete-time systems with random delays and random uncertainties","volume":"31","author":"Nishanthi","year":"2017","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Roy, S., Berry, D.W., Petersen, I.R., and Huntington, E.H. (2017). Robust guaranteed-cost adaptive quantum phase estimation. Phys. Rev. A, 95.","DOI":"10.1103\/PhysRevA.95.052322"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1016\/j.automatica.2012.05.070","article-title":"Distributed H-infinity state estimation with stochastic parameters and nonlinearities through sensor networks: The finite-horizon case","volume":"48","author":"Ding","year":"2012","journal-title":"Automatica"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.isatra.2018.09.006","article-title":"Robust H\u221e control for networked control systems with randomly occurring uncertainties: Observer-based case","volume":"83","author":"Li","year":"2018","journal-title":"ISA Trans."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1109\/59.852144","article-title":"A linear matrix inequality approach to robust damping control design in power systems with superconducting magnetic energy storage device","volume":"15","author":"Pal","year":"2000","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Liu, Y., Fu, Y., Lin, H., Liu, J., Gao, M., and He, Z. (2020). A New Constrained State Estimation Method Based on Unscented H\u221e Filtering. Appl. Sci., 10.","DOI":"10.3390\/app10238484"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1109\/7.705913","article-title":"IMM tracking of maneuvering targets in the presence of glint","volume":"34","author":"Daeipour","year":"1998","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/TAES.2015.140423","article-title":"Hybrid grid multiple-model estimation with application to maneuvering target tracking","volume":"52","author":"Xu","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_68","first-page":"315908","article-title":"Closed-Loop Estimation for Randomly Sampled Measurements in Target Tracking System","volume":"2014","author":"Jin","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1109\/TAES.2020.3011998","article-title":"INS\/Odometer Land Navigation by Accurate Measurement Modeling and Multiple-Model Adaptive Estimation","volume":"57","author":"Ouyang","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1016\/j.isatra.2020.01.030","article-title":"Adaptive filtering for MEMS gyroscope with dynamic noise model","volume":"101","author":"Bai","year":"2020","journal-title":"ISA Trans."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/00207721.2018.1544303","article-title":"Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses","volume":"50","author":"Xu","year":"2019","journal-title":"Int. J. Syst. Sci."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"3046","DOI":"10.1007\/s00034-017-0705-4","article-title":"Iterative parameter estimation for signal models based on measured data","volume":"37","author":"Xu","year":"2018","journal-title":"Circuits Syst. Signal Process"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1016\/j.jfranklin.2018.08.030","article-title":"State space model identification of multirate processes with time-delay using the expectation maximization","volume":"356","author":"Gu","year":"2019","journal-title":"J. Frankl. Inst."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1007\/s12555-017-0482-7","article-title":"Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data","volume":"16","author":"Xu","year":"2018","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1049\/iet-cta.2019.0731","article-title":"Hierarchical multi-innovation generalised extended stochastic gradient methods for multivariable equation-error autoregressive moving average systems","volume":"14","author":"Xu","year":"2020","journal-title":"IET Control Theory Appl."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1049\/iet-spr.2019.0481","article-title":"Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises","volume":"14","author":"Pan","year":"2020","journal-title":"IET Signal Process"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1002\/acs.3113","article-title":"Separable multi-innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems","volume":"34","author":"Xu","year":"2020","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"2415","DOI":"10.1007\/s11071-017-3594-y","article-title":"Recursive parameter identification of the dynamical models for bilinear state space systems","volume":"89","author":"Zhang","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"3079","DOI":"10.1016\/j.jfranklin.2018.01.011","article-title":"Combined state and parameter estimation for a bilinear state space system with moving average noise","volume":"355","author":"Zhang","year":"2018","journal-title":"J. Frankl. Inst."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"2176","DOI":"10.1049\/iet-cta.2020.0104","article-title":"Bias compensation-based parameter and state estimation for a class of time-delay non-linear state-space models","volume":"14","author":"Gu","year":"2020","journal-title":"IET Control Theory Appl."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"219","DOI":"10.5772\/54471","article-title":"Target Tracking of a Linear Time Invariant System under Irregular Sampling","volume":"9","author":"Jin","year":"2012","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1049\/iet-cta.2018.0156","article-title":"State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle","volume":"12","author":"Zhang","year":"2018","journal-title":"IET Control Theory Appl."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"10102","DOI":"10.1016\/j.jfranklin.2019.06.032","article-title":"Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise","volume":"356","author":"Wang","year":"2019","journal-title":"J. Frankl. Inst."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-Term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Yang, N.X., Wang, X.Y., Bai, Y.T., Su, T.L., and Kong, J.L. (2019). Integrated predictor based on decomposition mechanism for PM2.5 long-term prediction. Appl. Sci., 9.","DOI":"10.3390\/app9214533"},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Zheng, W.Z., Kong, J.L., Wang, X.Y., Bai, Y.L., Su, T.L., and Lin, S. (2021). Deep-Learning Forecasting Method for Electric Power Load via Attention-Based Encoder-Decoder with Bayesian Optimization. Energies, 14.","DOI":"10.3390\/en14061596"},{"key":"ref_87","first-page":"3104","article-title":"Sequence to Sequence Learning with Neural Networks","volume":"27","author":"Sutskever","year":"2014","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_88","first-page":"577","article-title":"Attention-based models for speech recognition","volume":"28","author":"Chorowski","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_89","doi-asserted-by":"crossref","unstructured":"Pham Luong, M.T., and Manning, C.H. (2015). Effective Approaches to Attention-based Neural Machine Translation. arXiv.","DOI":"10.18653\/v1\/D15-1166"},{"key":"ref_90","first-page":"157","article-title":"Multivariate Time Series Prediction Based on Optimized Temporal Convolutional Networks with Stacked Auto-encoders","volume":"2019","author":"Wang","year":"2019","journal-title":"Mach. Learn."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"4346803","DOI":"10.1155\/2020\/4346803","article-title":"Deep-Learning Prediction Model with Serial Two-Level Decomposition Based on Bayesian Optimization","volume":"2020","author":"Jin","year":"2020","journal-title":"Complexity"},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Yang, N.X., Wang, X., Bai, Y., Su, T.L., and Kong, J. (2020). Deep Hybrid Model Based on EMD with Classification by Frequency Characteristics for Long-Term Air Quality Prediction. Mathematics, 8.","DOI":"10.3390\/math8020214"},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Yu, X.H., Wang, X.Y., Bai, Y.T., Su, T.L., and Kong, J.L. (2020). Deep Learning Predictor for Sustainable Precision Agriculture Based on Internet of Things System. Sustainability, 12.","DOI":"10.3390\/su12041433"},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Niu, X., Li, J., and Sun, J. (2019, January 18\u201321). Dynamic Detection of False Data Injection Attack in Smart Grid using Deep Learning. Proceedings of the 2019 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Washington, DC, USA.","DOI":"10.1109\/ISGT.2019.8791598"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1109\/JSAC.2019.2904363","article-title":"Deep Transfer Learning for Intelligent Cellular Traffic Prediction Based on Cross-Domain Big Data","volume":"37","author":"Zhang","year":"2019","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1109\/JAS.2020.1003474","article-title":"A Sensorless State Estimation for A Safety-Oriented Cyber-Physical System in Urban Driving: Deep Learning Approach","volume":"8","author":"Murdoch","year":"2021","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_97","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Yang, N.X., Wang, X.Y., Bai, Y.T., Su, T.L., and Kong, J.L. (2020). Hybrid Deep Learning Predictor for Smart Agriculture Sensing Based on Empirical Mode Decomposition and Gated Recurrent Unit Group Model. Sensors, 20.","DOI":"10.3390\/s20051334"},{"key":"ref_98","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Yu, X.H., Su, T.L., Yang, D.N., Bai, Y.T., Kong, J.L., and Wang, L. (2021). Distributed Deep Fusion Predictor for a Multi-Sensor System Based on Causality Entropy. Entropy, 23.","DOI":"10.3390\/e23020219"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.neucom.2018.10.097","article-title":"A deep learning based multitask model for network-wide traffic speed predication","volume":"396","author":"Zhang","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"4910","DOI":"10.1109\/TPWRS.2019.2919157","article-title":"Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning","volume":"34","author":"Mestav","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_101","doi-asserted-by":"crossref","unstructured":"Mestav, K.R., and Tong, L. (2019, January 24\u201327). Learning the Unobservable: High-Resolution State Estimation via Deep Learning. Proceedings of the 2019 57th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA.","DOI":"10.1109\/ALLERTON.2019.8919782"},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s00521-018-3790-9","article-title":"An approach of recursive timing deep belief network for algal bloom forecasting","volume":"32","author":"Wang","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1007\/s13042-018-0847-0","article-title":"Deep Boltzmann machine for nonlinear system modelling","volume":"10","author":"Yu","year":"2018","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"106523","DOI":"10.1016\/j.knosys.2020.106523","article-title":"Parallel deep prediction with covariance intersection fusion on non-stationary time series","volume":"2021","author":"Shi","year":"2021","journal-title":"Knowl. Based Syst."},{"key":"ref_105","doi-asserted-by":"crossref","unstructured":"Bai, Y., Jin, X., Wang, X., Wang, X., and Xu, J. (2020). Dynamic correlation analysis method of air pollutants in spatio-temporal analysis. Int. J. Environ. Res. Public Health, 17.","DOI":"10.3390\/ijerph17010360"},{"key":"ref_106","first-page":"2546","article-title":"Algorithms for hyper-parameter optimization","volume":"24","author":"Bergstra","year":"2011","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"4796","DOI":"10.1109\/TPWRS.2019.2909150","article-title":"Data-Driven Learning-Based Optimization for Distribution System State Estimation","volume":"34","author":"Zamzam","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.automatica.2015.02.019","article-title":"Data-driven power control for state estimation: A Bayesian inference approach","volume":"54","author":"Wu","year":"2015","journal-title":"Automatica"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.inffus.2019.06.012","article-title":"DeepMTT: A deep learning maneuvering target-tracking algorithm based on bidirectional LSTM network","volume":"53","author":"Liu","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_110","doi-asserted-by":"crossref","unstructured":"Shaukat, N., Ali, A., Iqbal, M.J., Moinuddin, M., and Otero, P. (2021). Multi-Sensor Fusion for Underwater Vehicle Localization by Augmentation of RBF Neural Network and Error-State Kalman Filter. Sensors, 21.","DOI":"10.3390\/s21041149"},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"e3671","DOI":"10.1002\/ett.3671","article-title":"An efficient Deep reinforcement learning with extended Kalman filter for device-to-device communication underlaying cellular network","volume":"30","author":"Khuntia","year":"2019","journal-title":"Trans. Emerg. Telecommun. Technol."},{"key":"ref_112","doi-asserted-by":"crossref","unstructured":"Zhang, L., Mao, D., Niu, J., Wu, Q.M., and Ji, Y. (2020). Continuous tracking of targets for stereoscopic HFSWR based on IMM filtering combined with ELM. Remote Sens., 12.","DOI":"10.3390\/rs12020272"},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"103234","DOI":"10.1016\/j.robot.2019.07.004","article-title":"Learning Kalman Network: A deep monocular visual odometry for on-road driving","volume":"121","author":"Zhao","year":"2019","journal-title":"Robot. Auton. Syst."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"04019014","DOI":"10.1061\/(ASCE)CP.1943-5487.0000835","article-title":"Evolutionary Deep Learning with Extended Kalman Filter for Effective Prediction Modeling and Efficient Data Assimilation","volume":"33","author":"Li","year":"2019","journal-title":"J. Comput. Civ. Eng."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.ins.2019.06.039","article-title":"Long short-term memory-based deep recurrent neural networks for target tracking","volume":"502","author":"Gao","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_116","doi-asserted-by":"crossref","unstructured":"Bai, Y., Wang, X., Jin, X., Zhao, Z., and Zhang, B. (2020). A neuron-based Kalman filter with nonlinear auto-regressive model. Sensors, 20.","DOI":"10.3390\/s20010299"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/TIM.2019.2895495","article-title":"Deep Learning-Based Neural Network Training for State Estimation Enhancement: Application to Attitude Estimation","volume":"69","author":"Sharman","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_118","doi-asserted-by":"crossref","unstructured":"Yu, Y., Liu, Q., Chambon, S., and Hamzah, M. (2019, January 26\u201328). Using deep Kalman filter to predict drilling time series. Proceedings of the International Petroleum Technology Conference, Beijing, China.","DOI":"10.2523\/19207-MS"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/6\/2085\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:36:42Z","timestamp":1760161002000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/6\/2085"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,16]]},"references-count":118,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["s21062085"],"URL":"https:\/\/doi.org\/10.3390\/s21062085","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,16]]}}}