{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:22:40Z","timestamp":1747196560196,"version":"3.40.5"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"DOI":"10.1186\/s13634-025-01215-w","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T19:23:36Z","timestamp":1747164216000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Measurement noise covariance estimation in Gaussian filters: an online Bayesian solution"],"prefix":"10.1186","volume":"2025","author":[{"given":"Gerald","family":"LaMountain","sequence":"first","affiliation":[]},{"given":"Jordi","family":"Vil\u00e0-Valls","sequence":"additional","affiliation":[]},{"given":"Pau","family":"Closas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"1215_CR1","unstructured":"S. Haykin, Kalman Filtering and Neural Networks vol. 47. John Wiley & Sons, (2004)"},{"issue":"4","key":"1215_CR2","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.1109\/TVT.2015.2403868","volume":"64","author":"D Dardari","year":"2015","unstructured":"D. Dardari, P. Closas, P.M. Djuric, Indoor tracking: Theory, methods, and technologies. IEEE Trans. Vehic. Technol. 64(4), 1263\u20131278 (2015)","journal-title":"IEEE Trans. Vehic. Technol."},{"issue":"7","key":"1215_CR3","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/MAES.2017.150260","volume":"32","author":"J Vila-Valls","year":"2017","unstructured":"J. Vila-Valls, P. Closas, M. Navarro, C. Fernandez-Prades, Are PLLs dead? A tutorial on Kalman filter-based techniques for digital carrier synchronization. IEEE Aerospace Electr Syst Magaz 32(7), 28\u201345 (2017)","journal-title":"IEEE Aerospace Electr Syst Magaz"},{"issue":"2","key":"1215_CR4","doi-asserted-by":"publisher","first-page":"2312","DOI":"10.1109\/TSG.2018.2870600","volume":"10","author":"K Dehghanpour","year":"2018","unstructured":"K. Dehghanpour, Z. Wang, J. Wang, Y. Yuan, F. Bu, A survey on state estimation techniques and challenges in smart distribution systems. IEEE Trans. Smart Grid 10(2), 2312\u20132322 (2018)","journal-title":"IEEE Trans. Smart Grid"},{"issue":"2","key":"1215_CR5","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1109\/JAS.2017.7510811","volume":"5","author":"H Guo","year":"2018","unstructured":"H. Guo, D. Cao, H. Chen, C. Lv, H. Wang, S. Yang, Vehicle dynamic state estimation: State of the art schemes and perspectives. IEEE\/CAA J. Automatica Sinica 5(2), 418\u2013431 (2018)","journal-title":"IEEE\/CAA J. Automatica Sinica"},{"issue":"12","key":"1215_CR6","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1109\/MAES.2020.3002001","volume":"35","author":"J Dun\u00edk","year":"2020","unstructured":"J. Dun\u00edk, S.K. Biswas, A.G. Dempster, T. Pany, P. Closas, State estimation methods in navigation: Overview and application. IEEE Aerospace Electr. Syst. Magaz. 35(12), 16\u201331 (2020)","journal-title":"IEEE Aerospace Electr. Syst. Magaz."},{"issue":"5","key":"1215_CR7","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1109\/9.855552","volume":"45","author":"K Ito","year":"2000","unstructured":"K. Ito, K. Xiong, Gaussian filters for nonlinear filtering problems. IEEE Trans. Autom. Control 45(5), 910\u2013927 (2000)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"1215_CR8","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1109\/9.847726","volume":"45","author":"SJ Julier","year":"2000","unstructured":"S.J. Julier, J.K. Ulhmann, H.F. Durrant-Whyte, A new method for nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. Autom. Control 45(3), 472\u2013482 (2000)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1215_CR9","unstructured":"R.V. der Merwe, Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. PhD thesis, OHSU, Portland, Oregon, USA (2004)"},{"issue":"5","key":"1215_CR10","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1109\/JPROC.2007.894705","volume":"95","author":"I Arasaratnam","year":"2007","unstructured":"I. Arasaratnam, S. Haykin, R.J. Elliot, Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature. Proc. IEEE 95(5), 953\u2013977 (2007)","journal-title":"Proc. IEEE"},{"issue":"6","key":"1215_CR11","doi-asserted-by":"publisher","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","volume":"54","author":"I Arasaratnam","year":"2009","unstructured":"I. Arasaratnam, S. Haykin, Cubature Kalman filters. IEEE Trans. Autom. Control 54(6), 1254\u20131269 (2009)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"10","key":"1215_CR12","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1109\/TAC.1972.1100100","volume":"17","author":"R Mehra","year":"1972","unstructured":"R. Mehra, Approaches to adaptive filtering. IEEE Trans. Autom. Control 17(10), 693\u2013698 (1972)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1215_CR13","doi-asserted-by":"crossref","unstructured":"J. Dun\u00edk, O. Straka, O. Kost, J. Havl\u00edk, Noise covariance matrices in state-space models: A survey and comparison of estimation methods-Part I (Int. J. Adapt, Control Signal Process), (2017)","DOI":"10.1002\/acs.2783"},{"issue":"2","key":"1215_CR14","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.automatica.2005.09.006","volume":"42","author":"BJ Odelson","year":"2006","unstructured":"B.J. Odelson, M.R. Rajamani, J.B. Rawlings, A new autocovariance least-square method for estimating noise covariances. Automatica 42(2), 303\u2013308 (2006)","journal-title":"Automatica"},{"issue":"2","key":"1215_CR15","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1109\/TAC.2016.2571899","volume":"62","author":"J Dun\u00edk","year":"2017","unstructured":"J. Dun\u00edk, O. Straka, M. Simandl, On autocovariance least-squares method for noise covariance matrices estimation. IEEE Trans. Autom. Control 62(2), 967\u2013972 (2017)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"8","key":"1215_CR16","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1109\/TAC.1976.1101260","volume":"21","author":"KA Myers","year":"1976","unstructured":"K.A. Myers, B.D. Tapley, Adaptive sequential estimation with unknown noise statistics. IEEE Trans. Autom. Control 21(8), 520\u2013523 (1976)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"1215_CR17","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1109\/TAC.1981.1102696","volume":"26","author":"J Leathrum","year":"1981","unstructured":"J. Leathrum, On the sequential estimation of state noise variances. IEEE Trans. Autom. Control 26(3), 745\u2013746 (1981)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1215_CR18","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316870","volume-title":"Bayesian Theory","author":"JM Bernardo","year":"1994","unstructured":"J.M. Bernardo, A.F.M. Smith, Bayesian Theory (Wiley Series in Probability and Statistics. John Wiley & Sons, Chichester, 1994)"},{"key":"1215_CR19","doi-asserted-by":"crossref","unstructured":"S. S\u00e4rkk\u00e4, Bayesian Filtering and Smoothing. Institute of Mathematical Statistics Textbooks, vol. 3. Cambridge University Press, Cambridge (2013)","DOI":"10.1017\/CBO9781139344203"},{"key":"1215_CR20","doi-asserted-by":"crossref","unstructured":"G. LaMountain, J. Vil\u00e0-Valls, P. Closas, Bayesian covariance estimation for kalman filter based digital carrier synchronization. In: Proc. of the 21st International Technical Meeting of the Satellite Division of the Institute of Navigation ION GNSS, Miami, Florida, pp. 3575\u20133586 (2018)","DOI":"10.33012\/2018.15911"},{"issue":"6","key":"1215_CR21","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1109\/TAC.1968.1099025","volume":"13","author":"T Kailath","year":"1968","unstructured":"T. Kailath, An innovations approach to least-squares estimation-Part I: Linear filtering in additive white noise. IEEE Trans. Autom. Control 13(6), 646\u2013655 (1968). https:\/\/doi.org\/10.1109\/TAC.1968.1099025","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"1215_CR22","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1109\/TAC.1970.1099422","volume":"15","author":"R Mehra","year":"1970","unstructured":"R. Mehra, On the identification of variances and adaptive filtering. IEEE Trans. Autom. Control 15(2), 175\u2013184 (1970)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"1215_CR23","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1109\/TAC.1971.1099704","volume":"16","author":"PA Frost","year":"1971","unstructured":"P.A. Frost, T. Kailath, An innovations approach to least-squares estimation-Part III: Nonlinear estimation in white Gaussian noise. IEEE Trans. Autom. Control 16(3), 217\u2013226 (1971)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1215_CR24","unstructured":"I. Arasaratnam, Cubature kalman filtering: Theory & applications. PhD thesis, McMaster University, Hamilton, Ontario, Canada (2009)"},{"issue":"2","key":"1215_CR25","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.automatica.2011.08.057","volume":"48","author":"B Jia","year":"2012","unstructured":"B. Jia, M. Xin, Y. Cheng, Sparse-grid quadrature nonlinear filtering. Automatica 48(2), 327\u2013341 (2012)","journal-title":"Automatica"},{"key":"1215_CR26","doi-asserted-by":"crossref","unstructured":"P. Closas, J. Vil\u00e0-Valls, C. Fern\u00e1ndez-Prades Computational complexity reduction techniques for quadrature Kalman filters. In: Proc. CAMSAP\u201915, Cancun, Mexico (2015)","DOI":"10.1109\/CAMSAP.2015.7383842"},{"issue":"4","key":"1215_CR27","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1093\/comjnl\/7.4.308","volume":"7","author":"JA Nelder","year":"1965","unstructured":"J.A. Nelder, R. Mead, A simplex method for function minimization. Computer J. 7(4), 308\u2013313 (1965). https:\/\/doi.org\/10.1093\/comjnl\/7.4.308","journal-title":"Computer J."},{"key":"1215_CR28","volume-title":"Estimation with Applications to Tracking and Navigation","author":"Y Bar-Shalom","year":"2001","unstructured":"Y. Bar-Shalom, X. Rong Li, T. Kirubarajan, Estimation with Applications to Tracking and Navigation, 1st edn. (A Wiley-Interscience publication. John Wiley & Sons, Nashville, TN, 2001)","edition":"1"},{"issue":"1","key":"1215_CR29","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1093\/mnras\/225.1.155","volume":"225","author":"G Fasano","year":"1987","unstructured":"G. Fasano, A. Franceschini, A multidimensional version of the Kolmogorov-Smirnov test. Monthly Notices Royal Astronom. Soc. 225(1), 155\u2013170 (1987). https:\/\/doi.org\/10.1093\/mnras\/225.1.155","journal-title":"Monthly Notices Royal Astronom. Soc."}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-025-01215-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13634-025-01215-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-025-01215-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T19:23:43Z","timestamp":1747164223000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/s13634-025-01215-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,13]]},"references-count":29,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["1215"],"URL":"https:\/\/doi.org\/10.1186\/s13634-025-01215-w","relation":{},"ISSN":["1687-6180"],"issn-type":[{"value":"1687-6180","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,13]]},"assertion":[{"value":"7 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"14"}}