{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T21:10:36Z","timestamp":1777151436226,"version":"3.51.4"},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["ECCS-1845833"],"award-info":[{"award-number":["ECCS-1845833"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Signal acquisition is a crucial step in Global Navigation Satellite System (GNSS) receivers, which is typically solved by maximizing the so-called Cross-Ambiguity Function (CAF) as a hypothesis testing problem. This article proposes to use deep learning models to perform such acquisition, whereby the CAF is fed to a data-driven classifier that outputs binary class posteriors. The class posteriors are used to compute a Bayesian hypothesis test to statistically decide the presence or absence of a GNSS signal. The versatility and computational affordability of the proposed method are addressed by splitting the CAF into smaller overlapping sections, which are fed to a bank of parallel classifiers whose probabilistic results are optimally fused to provide a so-called probability ratio map from which acquisition is decided. Additionally, the article shows how noncoherent integration schemes are enabled through optimal data fusion, with the goal of increasing the resulting classifier accuracy. The article provides simulation results showing that the proposed data-driven method outperforms current CAF maximization strategies, enabling enhanced acquisition at medium-to-high carrier-to-noise density ratios.<\/jats:p>","DOI":"10.3390\/s23031566","type":"journal-article","created":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T01:36:59Z","timestamp":1675215419000},"page":"1566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Deep Learning of GNSS Acquisition"],"prefix":"10.3390","volume":"23","author":[{"given":"Parisa","family":"Borhani-Darian","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6953-755X","authenticated-orcid":false,"given":"Haoqing","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5960-6600","authenticated-orcid":false,"given":"Pau","family":"Closas","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,1]]},"reference":[{"key":"ref_1","unstructured":"Dardari, D., Falletti, E., and Luise, M. (2011). Satellite and Terrestrial Radio Positioning Techniques: A Signal Processing Perspective, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Morton, Y.J., van Diggelen, F., Spilker, J.J., Parkinson, B.W., Lo, S., and Gao, G. (2021). Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, John Wiley & Sons.","DOI":"10.1002\/9781119458449"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1109\/TVT.2015.2403868","article-title":"Indoor tracking: Theory, methods, and technologies","volume":"64","author":"Dardari","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Williams, N., Darian, P.B., Wu, G., Closas, P., and Barth, M. (2022). Impact of Positioning Uncertainty on Connected and Automated Vehicle Applications. SAE Int. J. Connect. Autom. Veh., 6.","DOI":"10.4271\/12-06-02-0010"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1109\/JPROC.2016.2550638","article-title":"Vulnerabilities, threats, and authentication in satellite-based navigation systems [scanning the issue]","volume":"104","author":"Amin","year":"2016","journal-title":"Proc. IEEE"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/MAES.2019.2906971","article-title":"Navigation systems panel report navigation systems for autonomous and semi-autonomous vehicles: Current trends and future challenges","volume":"34","author":"Kassas","year":"2019","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_7","unstructured":"Kaplan, E., and Hegarty, C. (2005). Understanding GPS: Principles and Applications, Artech House."},{"key":"ref_8","unstructured":"Misra, P., and Enge, P. (2006). Global Positioning System: Signals, Measurements and Performance, Ganga-Jamuna Press. [2nd ed.]."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tsui, J.B. (2005). Fundamentals of Global Positioning System Receivers: A Software Approach, John Wiley & Sons.","DOI":"10.1002\/0471712582"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Borio, D. (2008). A Statistical Theory for GNSS Signal Acquisition. [Ph.D. Thesis, Polytecnico di Torino].","DOI":"10.1155\/2008\/356267"},{"key":"ref_11","first-page":"1","article-title":"An analytic way to optimize the detector of a post-correlation FFT acquisition algorithm","volume":"1000","author":"Mathis","year":"2003","journal-title":"Quadrature"},{"key":"ref_12","unstructured":"Whalen, A. (2013). Detection of Signals in Noise, Academic Press."},{"key":"ref_13","unstructured":"Lehner, A., and Steingass, A. (2005, January 13\u201316). A novel channel model for land mobile satellite navigation. Proceedings of the Institute of Navigation Conference ION GNSS, Long Beach, CA, USA."},{"key":"ref_14","first-page":"54","article-title":"A fresh look at GNSS anti-jamming","volume":"12","author":"Borio","year":"2017","journal-title":"Inside GNSS"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Borio, D. (2017, January 9\u201312). Robust signal processing for GNSS. Proceedings of the 2017 European Navigation Conference (ENC), Lausanne, Switzerland.","DOI":"10.1109\/EURONAV.2017.7954204"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1049\/iet-rsn.2016.0610","article-title":"Myriad Non-Linearity for GNSS Robust Signal Processing","volume":"11","author":"Borio","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Borio, D., and Closas, P. (2018). Complex Signum Non-Linearity for Robust GNSS Signal Mitigation. IET Radar Sonar Navig., 12.","DOI":"10.1049\/iet-rsn.2017.0552"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Borio, D., Li, H., and Closas, P. (2018). Huber\u2019s Non-Linearity for GNSS Interference Mitigation. Sensors, 18.","DOI":"10.3390\/s18072217"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Borio, D., and Closas, P. (2019). Robust Transform Domain Signal Processing for GNSS. Navigation.","DOI":"10.1002\/navi.300"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Li, H., Borio, D., and Closas, P. (2019, January 16\u201320). Dual-Domain Robust GNSS Interference Mitigation. Proceedings of the International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2019), Miami, FL, USA.","DOI":"10.33012\/2019.16991"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1002\/navi.391","article-title":"GNSS interference mitigation: A measurement and position domain assessment","volume":"68","author":"Borio","year":"2021","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Borhani-Darian, P., and Closas, P. (2020, January 20\u201323). Deep Neural Network Approach to GNSS Signal Acquisition. Proceedings of the 2020 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Portland, OR, USA.","DOI":"10.1109\/PLANS46316.2020.9110205"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109367","DOI":"10.1016\/j.comnet.2022.109367","article-title":"Automated deep learning-based wide-band receiver","volume":"218","author":"Azari","year":"2022","journal-title":"Comput. Netw."},{"key":"ref_24","first-page":"62","article-title":"More than we ever dreamed possible: Processor technology for GNSS software receivers in the year 2015","volume":"10","author":"Dampf","year":"2015","journal-title":"Inside GNSS"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Siemuri, A., Kuusniemi, H., Elmusrati, M., V\u00e4lisuo, P., and Shamsuzzoha, A. (2021, January 1\u20133). Machine Learning Utilization in GNSS\u2014Use Cases, Challenges and Future Applications. Proceedings of the 2021 International Conference on Localization and GNSS (ICL-GNSS), Tampere, Finland.","DOI":"10.1109\/ICL-GNSS51451.2021.9452295"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Abdallah, A.A., and Kassas, Z.M. (2020, January 20\u201323). Deep learning-aided spatial discrimination for multipath mitigation. Proceedings of the 2020 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Portland, OR, USA.","DOI":"10.1109\/PLANS46316.2020.9109935"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"20563","DOI":"10.1109\/JSEN.2021.3098006","article-title":"Prediction on the Urban GNSS Measurement Uncertainty Based on Deep Learning Networks With Long Short-Term Memory","volume":"21","author":"Zhang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-018-0776-0","article-title":"Satellite selection with an end-to-end deep learning network","volume":"22","author":"Huang","year":"2018","journal-title":"GPS Solut."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Li, H., Borhani-Darian, P., Wu, P., and Closas, P. (2020, January 21\u201325). Deep Learning of GNSS Signal Correlation. Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020), St. Louis, MO, USA.","DOI":"10.33012\/2020.17598"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Savas, C., and Dovis, F. (2019, January 16\u201320). Multipath Detection based on K-means Clustering. Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, FL, USA.","DOI":"10.33012\/2019.17028"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Suzuki, T., Kusama, K., and Amano, Y. (2020, January 21\u201325). NLOS Multipath Detection using Convolutional Neural Network. Proceedings of the 33rd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2020), St. Louis, MO, USA.","DOI":"10.33012\/2020.17663"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Munin, E., Blais, A., and Couellan, N. (2020, January 3\u20134). Convolutional neural network for multipath detection in GNSS receivers. Proceedings of the 2020 International Conference on Artificial Intelligence and Data Analytics for Air Transportation (AIDA-AT), Singapore.","DOI":"10.1109\/AIDA-AT48540.2020.9049188"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Caparra, G., Zoccarato, P., and Melman, F. (2021, January 20\u201324). Machine Learning Correction for Improved PVT Accuracy. Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, MO, USA.","DOI":"10.33012\/2021.17974"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Manesh, M.R., Kenney, J., Hu, W.C., Devabhaktuni, V.K., and Kaabouch, N. (2019, January 11\u201314). Detection of GPS spoofing attacks on unmanned aerial systems. Proceedings of the 2019 16th IEEE Annual Consumer Communications & Networking Conference (CCNC), Las Vegas, NV, USA.","DOI":"10.1109\/CCNC.2019.8651804"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Borhani-Darian, P., Li, H., Wu, P., and Closas, P. (2020, January 20\u201323). Deep Neural Network Approach to Detect GNSS Spoofing Attacks. Proceedings of the 33rd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2020), Portland, OR, USA.","DOI":"10.33012\/2020.17537"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Tohidi, S., and Mosavi, M.R. (2020, January 1\u20132). Effective detection of GNSS spoofing attack Using A multi-layer perceptron neural network classifier trained by PSO. Proceedings of the 2020 25th International Computer Conference, Computer Society of Iran (CSICC), Tehran, Iran.","DOI":"10.1109\/CSICC49403.2020.9050078"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Calvo-Palomino, R., Bhattacharya, A., Bovet, G., and Giustiniano, D. (September, January 31). Short: LSTM-based GNSS Spoofing Detection Using Low-cost Spectrum Sensors. Proceedings of the 2020 IEEE 21st International Symposium on \u201cA World of Wireless, Mobile and Multimedia Networks\u201d (WoWMoM), Cork, Ireland.","DOI":"10.1109\/WoWMoM49955.2020.00055"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Semanjski, S., Muls, A., Semanjski, I., and De Wilde, W. (2019, January 4\u20136). Use and validation of supervised machine learning approach for detection of GNSS signal spoofing. Proceedings of the 2019 International Conference on Localization and GNSS (ICL-GNSS), Nuremberg, Germany.","DOI":"10.1109\/ICL-GNSS.2019.8752775"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Morales Ferre, R., de la Fuente, A., and Lohan, E.S. (2019). Jammer classification in GNSS bands via machine learning algorithms. Sensors, 19.","DOI":"10.3390\/s19224841"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Louis, A., and Raimondi, M. (2020, January 21\u201325). Neural Network based Evil WaveForms Detection. Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020), St. Louis, MO, USA.","DOI":"10.33012\/2020.17651"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Brum, D., Veronez, M.R., de Souza, E.M., Koch, I.\u00c9., Gonzaga, L., Klein, I., Matsuoka, M.T., Rofatto, V.F., Junior, A.M., and dos Reis Racolte, G.E. (August, January 28). A Proposed Earthquake Warning System Based on Ionospheric Anomalies Derived From GNSS Measurements and Artificial Neural Networks. Proceedings of the IGARSS 2019\u20142019 IEEE International Geoscience and Remote Sensing Symposium, Yokohama, Japan.","DOI":"10.1109\/IGARSS.2019.8900197"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Alshaye, M., Alawwad, F., and Elshafiey, I. (2020, January 19\u201321). Hurricane tracking using Multi-GNSS-R and deep learning. Proceedings of the 2020 3rd International Conference on Computer Applications & Information Security (ICCAIS), Riyadh, Saudi Arabia.","DOI":"10.1109\/ICCAIS48893.2020.9096717"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.1109\/LGRS.2018.2852143","article-title":"Sea ice sensing from GNSS-R data using convolutional neural networks","volume":"15","author":"Yan","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1109\/TAES.2018.2850385","article-title":"Detection of GNSS ionospheric scintillations based on machine learning decision tree","volume":"55","author":"Linty","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Liu, Y., Morton, Y., and Jiao, Y. (2018, January 23\u201326). Application of Machine Learning to Characterization of GPS L1 Ionospheric Amplitude Scintillation. Proceedings of the 2018 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Monterey, CA, USA.","DOI":"10.1109\/PLANS.2018.8373500"},{"key":"ref_46","first-page":"967","article-title":"Prediction of tropospheric wet delay by an artificial neural network model based on meteorological and GNSS data","volume":"23","author":"Selbesoglu","year":"2020","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1002\/navi.379","article-title":"Survey on signal processing for GNSS under ionospheric scintillation: Detection, monitoring, and mitigation","volume":"67","author":"Linty","year":"2020","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Imbiriba, T., Demirkaya, A., Dun\u00edk, J., Straka, O., Erdo\u011fmu\u015f, D., and Closas, P. (2022, January 4\u20137). Hybrid Neural Network Augmented Physics-based Models for Nonlinear Filtering. Proceedings of the FUSION Conference, Link\u00f6ping, Sweden.","DOI":"10.23919\/FUSION49751.2022.9841291"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1109\/JSTSP.2018.2797022","article-title":"Over-the-air deep learning based radio signal classification","volume":"12","author":"Roy","year":"2018","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"3789","DOI":"10.1109\/JSTARS.2017.2689009","article-title":"Neural networks based sea ice detection and concentration retrieval from GNSS-R delay-Doppler maps","volume":"10","author":"Yan","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_51","unstructured":"White, C., Neiswanger, W., and Savani, Y. (March, January 22). BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search. Proceedings of the AAAI Conference on Artificial Intelligence, Virtually."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Liu, S., and Deng, W. (2015, January 3\u20136). Very deep convolutional neural network based image classification using small training sample size. Proceedings of the 2015 3rd IAPR Asian Conference on Pattern Recognition (ACPR), Kuala Lumpur, Malaysia.","DOI":"10.1109\/ACPR.2015.7486599"},{"key":"ref_53","unstructured":"Simonyan, K., and Zisserman, A. (2014). Very deep convolutional networks for large-scale image recognition. arXiv."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/LRA.2020.3038377","article-title":"Bayesian and Neural Inference on LSTM-Based Object Recognition from Tactile and Kinesthetic Information","volume":"6","author":"Pastor","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_55","unstructured":"Mathworks (2023, January 26). Create Simple Deep Learning Network for Classification. Available online: https:\/\/www.mathworks.com\/help\/deeplearning\/examples\/create-simple-deep-learning-network-for-classification.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/3\/1566\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:20:30Z","timestamp":1760120430000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/3\/1566"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,1]]},"references-count":55,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["s23031566"],"URL":"https:\/\/doi.org\/10.3390\/s23031566","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,1]]}}}