{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T09:39:00Z","timestamp":1786527540913,"version":"build-2736575974"},"reference-count":47,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T00:00:00Z","timestamp":1786492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Reliable navigation in GPS-denied environments remains a critical challenge for autonomous vehicles (AVs), particularly in complex indoor and urban settings. GPS-based localization systems often fail under these conditions, highlighting the need for resilient multimodal solutions. In this article, we present a radar-assisted tracking system that integrates LiDAR and inertial measurements within a sensor-fusion architecture to achieve robust navigation. The principal methodological contribution is a unified tracking and prediction framework that combines Bayesian state estimation with learning-based temporal prediction, enabling accurate tracking while continuously forecasting the slave robot\u2019s short-term future state from mapping observations generated by the master robot, with a typical end-to-end perception-to-action latency of 20\u201360 ms. The communication and prediction forecasting module operates with an update interval below 35 ms, enabling real-time cooperative robotic operation. Sensor data are fused through a pipeline incorporating Gaussian Mixture Models (GMMs) for post-processing, which helps mitigate the limitations associated with individual sensors during edge processing. Moreover, Kalman filtering is employed to mitigate sensor noise and drift, thereby improving state estimation accuracy through trajectory smoothing. The fused spatiotemporal information is subsequently exploited by a Convolutional Recurrent Neural Network (CRNN) coupled with a Nonlinear Autoregressive model with eXogenous Inputs (NARX) to model the robot\u2019s motion dynamics and provide short-horizon state prediction. Through simulations and real-world indoor experiments conducted in GPS-denied environments, we validate the system\u2019s ability to provide accurate and continuous pose estimation with low localization errors. Experimental results show that the proposed framework achieves root-mean-square errors of 0.12 m, 0.15 m, and 0.28 m along the X, Y, and Z axes, respectively, while maintaining sub-meter maximum position deviations throughout the evaluated trajectories. These results confirm that the proposed framework provides reliable localization and predictive state estimation for cooperative robotic navigation in indoor GPS-denied environments. Future work will investigate outdoor validation and extend the framework to additional data-driven decision-making models for future robotic services.<\/jats:p>","DOI":"10.3390\/e28080903","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T09:11:36Z","timestamp":1786525896000},"page":"903","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Master Mix Localization Algorithm for Autonomous Systems in Indoor Environments"],"prefix":"10.3390","volume":"28","author":[{"given":"Zakaryae","family":"Ezzouine","sequence":"first","affiliation":[{"name":"Research Modeling and Multiphysics Engineering Laboratory (LMIMP), National School of Arts and Crafts, University Moulay Ismail, B.P. 15290 ENSAM, Mekn\u00e8s 50500, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2142-8623","authenticated-orcid":false,"given":"Adil","family":"Salbi","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Systems Analysis Information Processing and Integrated Management Laboratory (LASTIMI), High School of Technology, Mohammed V University of Rabat, Avenue Le Prince H\u00e9ritier, B.P. 227, Sal\u00e9 11000, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1652-5904","authenticated-orcid":false,"given":"Mohamed","family":"Abouzahir","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Systems Analysis Information Processing and Integrated Management Laboratory (LASTIMI), High School of Technology, Mohammed V University of Rabat, Avenue Le Prince H\u00e9ritier, B.P. 227, Sal\u00e9 11000, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6179-3919","authenticated-orcid":false,"given":"Ilham","family":"Elmourabit","sequence":"additional","affiliation":[{"name":"Engineering Sciences and Biosciences Laboratory (LSIB), Department of Engineering Sciences and Biosciences, Faculty of Sciences and Techniques, Hassan II University of Casablanca, B.P. 9154 Rue Tarik Ibnou Ziad, Casablanca 20360, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3429-0558","authenticated-orcid":false,"given":"Adil","family":"Brouri","sequence":"additional","affiliation":[{"name":"Research Modeling and Multiphysics Engineering Laboratory (LMIMP), National School of Arts and Crafts, University Moulay Ismail, B.P. 15290 ENSAM, Mekn\u00e8s 50500, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1262-9485","authenticated-orcid":false,"given":"S\u00e9bastien","family":"Roy","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Sherbrooke University, Sherbrooke, QC J1N 3C6, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.1109\/TAES.2012.6324666","article-title":"How Many GNSS Satellites Are Too Many?","volume":"48","author":"Gao","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Broumandan, A., and Lachapelle, G. (2018). GNSS Spoofing Detection. Sensors, 18.","DOI":"10.3390\/s18051305"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"23895","DOI":"10.1038\/s41598-024-74773-y","article-title":"Design a novel algorithm for enhancing UWB positioning accuracy in GPS-denied environments","volume":"14","author":"Huang","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Aziz, T., and Koo, I. (2025). A Comprehensive Review of Indoor Localization Techniques and Applications in Various Sectors. Appl. Sci., 15.","DOI":"10.3390\/app15031544"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Liu, J., Yang, Z., Zlatanova, S., Li, S., and Yu, B. (2025). Indoor Localization Methods for Smartphones with Multi-Source Sensors Fusion: Tasks, Challenges, Strategies, and Perspectives. Sensors, 25.","DOI":"10.3390\/s25061806"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Sandamini, C., Maduranga, M.W.P., Tilwari, V., Yahaya, J., Qamar, F., Nguyen, Q.N., and Ibrahim, S.R.A. (2023). A Review of Indoor Positioning Systems for UAV Localization with Machine Learning Algorithms. Electronics, 12.","DOI":"10.3390\/electronics12071533"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2094","DOI":"10.1109\/TIV.2023.3307157","article-title":"Radar-Camera Fusion for Object Detection and Semantic Segmentation in Autonomous Driving: A Comprehensive Review","volume":"9","author":"Yao","year":"2024","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"180093","DOI":"10.1109\/ACCESS.2024.3508271","article-title":"A Comprehensive Review on Deep Learning-Based Data Fusion","volume":"12","author":"Hussain","year":"2024","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1515\/mms-2015-0037","article-title":"Application of Kalman Filter in Navigation Process of Automated Guided Vehicles","volume":"22","year":"2015","journal-title":"Metrol. Meas. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Xu, H., Geng, D., Fan, Z., Wu, D., and Chen, M. (2024). An Automatic Vehicle Navigation System Based on Filters Integrating Inertial Navigation and Global Positioning Systems. Machines, 12.","DOI":"10.3390\/machines12090663"},{"key":"ref_11","unstructured":"Carpenter, J.R., and D\u2019Souza, C.N. (2025). Navigation Filter Best Practices, No. 20180003657."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Schieber, H., Duerr, F., Schoen, T., and Beyerer, J. (2022, January 4\u20139). Deep Sensor Fusion with Pyramid Fusion Networks for 3D Semantic Segmentation. Proceedings of the 2022 IEEE Intelligent Vehicles Symposium (IV), Aachen, Germany.","DOI":"10.1109\/IV51971.2022.9827113"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"17494","DOI":"10.1038\/s41598-026-43381-3","article-title":"FusionLSTM-CNF: A Confidence-Calibrated Multi-Modal Late Fusion Framework for Robust Stock Movement Prediction under Uncertainty","volume":"16","author":"Wang","year":"2026","journal-title":"Sci. Rep."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Singh, S. (2014, January 12\u201316). LOAM: Lidar Odometry and Mapping in Real-Time. Proceedings of the Robotics: Science and Systems Conference (RSS), Berkeley, CA, USA.","DOI":"10.15607\/RSS.2014.X.007"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ye, H., Chen, Y., and Liu, M. (2019, January 20\u201324). Tightly Coupled 3D Lidar Inertial Odometry and Mapping. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8793511"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Shan, T., Englot, B., Meyers, D., Wang, W., Ratti, C., and Rus, D. (2020, January 24). LIO-SAM: Tightly-Coupled Lidar Inertial Odometry via Smoothing and Mapping. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA.","DOI":"10.1109\/IROS45743.2020.9341176"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3317","DOI":"10.1109\/LRA.2021.3064227","article-title":"FAST-LIO: A Fast, Robust LiDAR-Inertial Odometry Package by Tightly-Coupled Iterated Kalman Filter","volume":"6","author":"Xu","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TRO.2022.3141876","article-title":"FAST-LIO2: Fast Direct LiDAR-Inertial Odometry","volume":"38","author":"Xu","year":"2022","journal-title":"IEEE Trans. Robot."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.1109\/TRO.2021.3075644","article-title":"ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM","volume":"37","author":"Campos","year":"2021","journal-title":"IEEE Trans. Robot."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1109\/TRO.2016.2624754","article-title":"Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age","volume":"32","author":"Cadena","year":"2016","journal-title":"IEEE Trans. Robot."},{"key":"ref_21","unstructured":"Zhang, J., Zhuge, H., Wu, Z., Peng, G., Wen, M., Liu, Y., and Wang, D. (June, January 29). 4DRadarSLAM: A 4D Imaging Radar SLAM System for Large-Scale Environments Based on Pose Graph Optimization. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), London, UK."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2550","DOI":"10.1109\/JSAC.2024.3413995","article-title":"Millimeter-Wave Radio SLAM: End-to-End Processing Methods and Experimental Validation","volume":"42","author":"Kaltiokallio","year":"2024","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5299","DOI":"10.1109\/LRA.2023.3293354","article-title":"UWB Radar SLAM: An Anchorless Approach in Vision-Denied Indoor Environments","volume":"8","author":"Premachandra","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, T., Su, Y., Shao, S.L., Yao, C., and Wang, Z. (October, January 27). GR-Fusion: Multi-Sensor Fusion SLAM for Ground Robots with High Robustness and Low Drift. Proceedings of the 2021 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech Republic.","DOI":"10.1109\/IROS51168.2021.9636232"},{"key":"ref_25","first-page":"2835","article-title":"Camera, LiDAR, and IMU Based Multi-Sensor Fusion SLAM: A Survey","volume":"16","author":"Zhang","year":"2024","journal-title":"Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1109\/COMST.2024.3372153","article-title":"Visible Light Positioning as a Next-Generation Indoor Positioning Technology: A Tutorial","volume":"26","author":"Bastiaens","year":"2024","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_27","first-page":"2104","article-title":"A Survey on Visible Light Positioning for Next-Generation Indoor Localization","volume":"26","author":"Kim","year":"2024","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1109\/TCSVT.2016.2542699","article-title":"Multi-Tracker Partition Fusion","volume":"27","author":"Khalid","year":"2017","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2947","DOI":"10.1109\/TIP.2019.2955239","article-title":"Notice of Violation of IEEE Publication Principles: Recent Advances in 3D Object Detection in the Era of Deep Neural Networks: A Survey","volume":"29","author":"Rahman","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_30","unstructured":"Shekhar, S., and Xiong, H. (2016). Indoor Localization. Encyclopedia of GIS, Springer."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bar-Shalom, Y., Kirubarajan, T., and Li, X. (2001). Estimation with Applications to Tracking and Navigation, Wiley-Interscience.","DOI":"10.1002\/0471221279"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Billings, S.A. (2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains, Wiley.","DOI":"10.1002\/9781118535561"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TIM.2007.908635","article-title":"Analysis and Modeling of Inertial Sensors Using Allan Variance","volume":"57","author":"Hou","year":"2008","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_34","unstructured":"Brown, R.G., and Hwang, P.Y.C. (1992). Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons, Inc."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"8195","DOI":"10.1038\/s41598-025-90492-4","article-title":"Application of multi-sensor fusion localization algorithm based on recurrent neural networks","volume":"15","author":"Huang","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_36","unstructured":"Siegwart, R., Nourbakhsh, I.R., and Scaramuzza, D. (2021). Introduction to Autonomous Robots: Mechanisms, Sensors, and Algorithms, MIT Press. [2nd ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Huang, S., Zhang, H., Xu, K., Lv, X., and Ma, X. (2025, January 19\u201323). M3DSS: A Multi-Platform, Multi-Sensor, and Multi-Scenario Dataset for SLAM System. Proceedings of the 2025 IEEE International Conference on Robotics and Automation (ICRA), Atlanta, GA, USA.","DOI":"10.1109\/ICRA55743.2025.11128631"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/34.88573","article-title":"Least-Squares Estimation of Transformation Parameters Between Two Point Patterns","volume":"13","author":"Umeyama","year":"1991","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Sturm, J., Engelhard, N., Endres, F., Burgard, W., and Cremers, D. (2012, January 7\u201312). A Benchmark for the Evaluation of RGB-D SLAM Systems. Proceedings of the 2012 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vilamoura-Algarve, Portugal.","DOI":"10.1109\/IROS.2012.6385773"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/s10514-009-9155-6","article-title":"On Measuring the Accuracy of SLAM Algorithms","volume":"27","author":"Grisetti","year":"2009","journal-title":"Auton. Robot."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/JPROC.2003.823141","article-title":"Unscented Filtering and Nonlinear Estimation","volume":"92","author":"Julier","year":"2004","journal-title":"Proc. IEEE"},{"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","unstructured":"Dosovitskiy, A., Ros, G., Codevilla, F., Lopez, A., and Koltun, V. (2017). CARLA: An Open Urban Driving Simulator. Proceedings of the 1st Annual Conference on Robot Learning, PMLR."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/MCOM.2017.1600238CM","article-title":"UAV-Enabled Intelligent Transportation Systems for the Smart City: Applications and Challenges","volume":"55","author":"Menouar","year":"2017","journal-title":"IEEE Commun. Mag."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.tra.2020.09.018","article-title":"Applications of Unmanned Aerial Vehicle (UAV) in Road Safety, Traffic and Highway Infrastructure Management: Recent Advances and Challenges","volume":"141","author":"Outay","year":"2020","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s10796-020-10044-1","article-title":"Security, Privacy and Risks Within Smart Cities: Literature Review and Development of a Smart City Interaction Framework","volume":"24","author":"Ismagilova","year":"2022","journal-title":"Inf. Syst. Front."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1007\/s10311-023-01604-3","article-title":"Artificial Intelligence for Waste Management in Smart Cities: A Review","volume":"21","author":"Fang","year":"2023","journal-title":"Environ. Chem. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/8\/903\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T09:14:03Z","timestamp":1786526043000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/8\/903"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,12]]},"references-count":47,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["e28080903"],"URL":"https:\/\/doi.org\/10.3390\/e28080903","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,12]]}}}