{"title":"最小二乘法的理论","authors":"E. H. Thompson","doi":"10.1111/J.1477-9730.1962.TB00326.X","DOIUrl":null,"url":null,"abstract":"This paper gives derivations of some of the more important results in the method of least squares in terms of matrix algebra. The following topics are covered: derivation of normal equations and their solution; residuals; estimation of standard errors; dependent unknowns; probability distribution of least-square estimates of unknowns.","PeriodicalId":56094,"journal":{"name":"Photogrammetric Record","volume":"4 1","pages":"53-65"},"PeriodicalIF":2.1000,"publicationDate":"2006-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/J.1477-9730.1962.TB00326.X","citationCount":"6","resultStr":"{\"title\":\"THE THEORY OF THE METHOD OF LEAST SQUARES\",\"authors\":\"E. H. Thompson\",\"doi\":\"10.1111/J.1477-9730.1962.TB00326.X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper gives derivations of some of the more important results in the method of least squares in terms of matrix algebra. The following topics are covered: derivation of normal equations and their solution; residuals; estimation of standard errors; dependent unknowns; probability distribution of least-square estimates of unknowns.\",\"PeriodicalId\":56094,\"journal\":{\"name\":\"Photogrammetric Record\",\"volume\":\"4 1\",\"pages\":\"53-65\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2006-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1111/J.1477-9730.1962.TB00326.X\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Photogrammetric Record\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://doi.org/10.1111/J.1477-9730.1962.TB00326.X\",\"RegionNum\":3,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"GEOGRAPHY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Photogrammetric Record","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1111/J.1477-9730.1962.TB00326.X","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"GEOGRAPHY, PHYSICAL","Score":null,"Total":0}
This paper gives derivations of some of the more important results in the method of least squares in terms of matrix algebra. The following topics are covered: derivation of normal equations and their solution; residuals; estimation of standard errors; dependent unknowns; probability distribution of least-square estimates of unknowns.
期刊介绍：
The Photogrammetric Record is an international journal containing original, independently and rapidly refereed articles that reflect modern advancements in photogrammetry, 3D imaging, computer vision, and other related non-contact fields. All aspects of the measurement workflow are relevant, from sensor characterisation and modelling, data acquisition, processing algorithms and product generation, to novel applications. The journal provides a record of new research which will contribute both to the advancement of photogrammetric knowledge and to the application of techniques in novel ways. It also seeks to stimulate debate though correspondence, and carries reviews of recent literature from the wider geomatics discipline.
Relevant topics include, but are not restricted to:
- Photogrammetric sensor calibration and characterisation
- Laser scanning (lidar)
- Image and 3D sensor technology (e.g. range cameras, natural user interface systems)
- Photogrammetric aspects of image processing (e.g. radiometric methods, feature extraction, image matching and scene classification)
- Mobile mapping and unmanned vehicular systems (UVS; UAVs)
- Registration and orientation
- Data fusion and integration of 3D and 2D datasets
- Point cloud processing
- 3D modelling and reconstruction
- Algorithms and novel software
- Visualisation and virtual reality
- Terrain/object modelling and photogrammetric product generation
- Geometric sensor models
- Databases and structures for imaging and 3D modelling
- Standards and best practice for data acquisition and storage
- Change detection and monitoring, and sequence analysis
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