{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T03:26:21Z","timestamp":1768447581139,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2013,4,8]],"date-time":"2013-04-08T00:00:00Z","timestamp":1365379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Real-time estimation of crop progress stages is critical to the US agricultural economy and decision making. In this paper, a Hidden Markov Model (HMM) based method combining multisource features has been presented. The multisource features include mean Normalized Difference Vegetation Index (NDVI), fractal dimension, and Accumulated Growing Degree Days (AGDDs). In our case, these features are global variable, and measured in the state-level. Moreover, global feature in each Day of Year (DOY) would be impacted by multiple progress stages. Therefore, a mixture model is employed to model the observation probability distribution with all possible stage components. Then, a filtering based algorithm is utilized to estimate the proportion of each progress stage in the real-time. Experiments are conducted in the states of Iowa, Illinois and Nebraska in the USA, and our results are assessed and validated by the Crop Progress Reports (CPRs) of the National Agricultural Statistics Service (NASS). Finally, a quantitative comparison and analysis between our method and spectral pixel-wise based methods is presented. The results demonstrate the feasibility of the proposed method for the estimation of corn progress stages. The proposed method could be used as a supplementary tool in aid of field survey. Moreover, it also can be used to establish the progress stage estimation model for different types of crops.<\/jats:p>","DOI":"10.3390\/rs5041734","type":"journal-article","created":{"date-parts":[[2013,4,8]],"date-time":"2013-04-08T12:01:31Z","timestamp":1365422491000},"page":"1734-1753","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Hidden Markov Models for Real-Time Estimation of Corn Progress Stages Using MODIS and Meteorological Data"],"prefix":"10.3390","volume":"5","author":[{"given":"Yonglin","family":"Shen","sequence":"first","affiliation":[{"name":"Key Laboratory of Environment Change & Natural Disaster of MOE, Beijing Normal University, Beijing 100875, China"},{"name":"Center for Spatial Information Science and Systems (CSISS), George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lixin","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Environment Change & Natural Disaster of MOE, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Di","sequence":"additional","affiliation":[{"name":"Center for Spatial Information Science and Systems (CSISS), George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Genong","family":"Yu","sequence":"additional","affiliation":[{"name":"Center for Spatial Information Science and Systems (CSISS), George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Tang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Environment Change & Natural Disaster of MOE, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoxian","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, South China University of Technology,  Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanzheng","family":"Shao","sequence":"additional","affiliation":[{"name":"Center for Spatial Information Science and Systems (CSISS), George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,4,8]]},"reference":[{"key":"ref_1","unstructured":"Available online: http:\/\/www.usda.gov\/oce\/weather\/pubs\/Weekly\/Wwcb\/index.htm."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/S0034-4257(02)00135-9","article-title":"Monitoring vegetation phenology using MODIS","volume":"84","author":"Zhang","year":"2003","journal-title":"Remote Sens. Environ"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.rse.2008.09.003","article-title":"Noise reduction of NDVI time series: An empirical comparison of selected techniques","volume":"113","author":"Hird","year":"2009","journal-title":"Remote Sens. Environ"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.rse.2012.04.001","article-title":"Inter-comparison of four models for smoothing satellite sensor time-series data to estimate vegetation phenology","volume":"123","author":"Atkinson","year":"2012","journal-title":"Remote Sens. Environ"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"117","DOI":"10.2307\/1478925","article-title":"The remote sensing approach in broad-scale phenological studies","volume":"3","author":"Ricotta","year":"2000","journal-title":"Appl. Veg. Sci"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Sasaoka, K., Chiba, S., and Saino, T (2011). Climatic forcing and phytoplankton phenology over the subarctic north pacific from 1998 to 2006, as observed from ocean color data. Geophys. Res. Lett.","DOI":"10.1029\/2011GL048299"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2335","DOI":"10.1111\/j.1365-2486.2009.01910.x","article-title":"Intercomparison, interpretation, and assessment of spring phenology in north america estimated from remote sensing for 1982\u20132006","volume":"15","author":"White","year":"2009","journal-title":"Glob. Chang. Biol"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1111\/j.1475-2743.1989.tb00755.x","article-title":"WOFOST: A simulation model of crop production","volume":"5","author":"Diepen","year":"1989","journal-title":"Soil Use Manage"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/S1161-0301(02)00109-0","article-title":"Cropsyst, a cropping systems simulation model","volume":"18","author":"Donatelli","year":"2003","journal-title":"Eur. J. Agron"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Tsuji, G.Y., Hoogenboom, G., and Thornton, P. (1998). Understanding Options for Agricultural Production, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-017-3624-4"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0168-1923(92)90060-H","article-title":"Climatic impacts on dryland winter wheat by daily soil water and crop stress simulations","volume":"58","author":"Saxton","year":"1992","journal-title":"Agr. For. Meteorol"},{"key":"ref_12","unstructured":"Kroes, J.G., Dam, J.C.V., Groenendijk, P., Hendriks, R.F.A., and Jacobs, C.M.J. (2008). SWAP Version 3.2: Theory Description and User Manual, Alterra. Alterra Report."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hudson, I.L., and Keatley, M.R. (2010). Phenological Research: Methods for Environmental and Climate Change Analysis, Springer-Verlag.","DOI":"10.1007\/978-90-481-3335-2"},{"key":"ref_14","unstructured":"Toukiloglou, P (2007). Comparison of AVHRR, MODIS and VEGETATION for Land Cover Mapping and Drought Monitoring at 1 km Spatial Resolution. Ph.D. Thesis, Cranfield University, Bedford, UK."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"703","DOI":"10.2307\/3235884","article-title":"Measuring phenological variability from satellite imagery","volume":"5","author":"Reed","year":"1994","journal-title":"J. Veg. Sci"},{"key":"ref_16","first-page":"403","article-title":"Regional yield estimation for winter wheat with MODIS-NDVI data in Shandong, China","volume":"10","author":"Ren","year":"2008","journal-title":"Int. J. Appl. Earth Obs. Geoinf"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"949","DOI":"10.3390\/rs5020949","article-title":"Advances in remote sensing of agriculture: Context description, existing operational monitoring systems and major information needs","volume":"5","author":"Atzberger","year":"2013","journal-title":"Remote Sens"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1109\/JSTARS.2009.2021959","article-title":"The impact of phenological variation on texture measures of remotely sensed imagery","volume":"2","author":"Culbert","year":"2009","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ"},{"key":"ref_19","first-page":"1","article-title":"Correlation between corn progress stages and fractal dimension from MODIS-NDVI time series","volume":"10","author":"Shen","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett"},{"key":"ref_20","unstructured":"Available online: http:\/\/www.nass.usda.gov\/Publications\/NationalCropProgress\/TermsandDefinitions\/index.asp."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1002\/rnc.1727","article-title":"An HMM approach for optimal investment of an insurer","volume":"22","author":"Elliott","year":"2012","journal-title":"Int. J. Robust Nonlinear Contr"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/5.18626","article-title":"A tutorial on hidden Markov models and selected applications in speech recognition","volume":"77","author":"Rabiner","year":"1989","journal-title":"Proc. IEEE"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1006\/jmbi.1994.1104","article-title":"Hidden Markov models in computational biology: Applications to protein modeling","volume":"235","author":"Krogh","year":"1994","journal-title":"J. Mol. Biol"},{"key":"ref_24","unstructured":"Aurdal, L., Bang, H.R., Eikvil, L., Solberg, R., Vikhamar, D., and Solberg, A (2005, January 16\u201318). Hidden Markov Models Applied to Vegetation Dynamics Analysis Using Satellite Remote Sensing. Biloxi, MS, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.patrec.2010.02.008","article-title":"Hidden Markov models for crop recognition in remote sensing image sequences","volume":"32","author":"Leite","year":"2011","journal-title":"Pattern Recognition Lett"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1109\/36.298019","article-title":"Hidden Markov models applied to vegetation dynamics analysis using satellite remote sensing","volume":"32","author":"Viovy","year":"1994","journal-title":"IEEE Trans. Geosci. Remote Sens"},{"key":"ref_27","unstructured":"Available online: http:\/\/cdiac.ornl.gov\/epubs\/ndp\/ushcn\/ushcn.html."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1080\/01431168608948945","article-title":"Characteristics of maximum-value composite images from temporal AVHRR data","volume":"7","author":"Holben","year":"1986","journal-title":"Int. J. Remote Sens"},{"key":"ref_29","unstructured":"Wiebold, B (2002). Growing Degree Days and Corn Maturity, University of Missouri. Technical Report."},{"key":"ref_30","first-page":"1082","article-title":"Precipitation averages for large areas","volume":"39","author":"Thiessen","year":"1911","journal-title":"Mon. Wea. Rev"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1744-7348.2005.04088.x","article-title":"Thermal time-concepts and utility","volume":"146","author":"Trudgill","year":"2005","journal-title":"Ann. Appl. Biol"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0168-1923(97)00027-0","article-title":"Growing degree-days: One equation, two interpretations","volume":"87","author":"McMaster","year":"1997","journal-title":"Agr. Forest Meteorol"},{"key":"ref_33","unstructured":"Jaakkola, T.S. Available online: http:\/\/ocw.mit.edu\/courses\/electrical-engineering-and-computer-science\/6-867-machine-learning-fall-2006\/lecture-notes\/lec19.pdf."},{"key":"ref_34","unstructured":"Srihari, S.N. Available online: http:\/\/www.cedar.buffalo.edu\/srihari\/CSE574\/index.html."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Schader, M., Gaul, W., and Vichi, M. (2003). Between Data Science and Applied Data Analysis, Springer.","DOI":"10.1007\/978-3-642-18991-3"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1093\/bioinformatics\/btr199","article-title":"Exploiting prior knowledge and gene distances in the analysis of tumor expression profiles with extended Hidden Markov Models","volume":"27","author":"Seifert","year":"2011","journal-title":"Bioinformatics"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1016\/j.agrformet.2011.02.010","article-title":"Crop management and phenology trends in the U.S. corn belt: Impacts on yields, evapotranspiration and energy balance","volume":"151","author":"Sacks","year":"2011","journal-title":"Agr. Forest Meteorol"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":"J. Roy. Stat. Soc. B"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Heij, C., de Boer, P., Franses, P.H., Kloek, T., and van Dijk, H.K. (2004). Econometric Methods with Applications in Business and Economics, Oxford University Press Inc.","DOI":"10.1093\/oso\/9780199268016.001.0001"},{"key":"ref_40","unstructured":"Yu, G., Di, L., Yang, Z., Shen, Y., Zhang, B., and Chen, Z (2012, January 2\u20134). Corn Growth Stage Estimation Using Time Series Vegetation Index. Shanghai, China."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1109\/TGRS.2010.2095462","article-title":"Detecting spatiotemporal changes of corn developmental stages in the U.S. corn belt using MODIS WDRVI data","volume":"49","author":"Sakamoto","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens"},{"key":"ref_42","first-page":"1919","article-title":"High-order hidden Markov model and application to continuous mandarin digit recognition","volume":"27","author":"Lee","year":"2011","journal-title":"J. Inf. Sci. Eng"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/89.554265","article-title":"Automatic word recognition based on second-order hidden Markov models","volume":"5","author":"Mari","year":"1997","journal-title":"IEEE Trans. Speech Audio Proc"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Seifert, M., Cortijo, S., Colom\u00e9-Tatch\u00e9, M., Johannes, Frank, Roudier, F., and Colot, V. (2012). MeDIP-HMM: Genome-wide identification of distinct DNA methylation states from high-density tiling arrays. Bioinformatics.","DOI":"10.1093\/bioinformatics\/bts562"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1002286","article-title":"Parsimonious higher-order hidden Markov models for improved array-CGH analysis with applications to Arabidopsis thaliana","volume":"8","author":"Seifert","year":"2012","journal-title":"PLoS Comp. Biol"},{"key":"ref_46","unstructured":"Derrode, S., Carincotte, C., and Bourennane, S (2004, January 17\u201321). Unsupervised Image Segmentation Based on High-Order Hidden MARKOV Chains. Marseille, France."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/5\/4\/1734\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:45:59Z","timestamp":1760219159000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/5\/4\/1734"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,8]]},"references-count":46,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,4]]}},"alternative-id":["rs5041734"],"URL":"https:\/\/doi.org\/10.3390\/rs5041734","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,8]]}}}