16th ISPRS Congress: 16th ISPRS Congress

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Multivolume work

Persistent identifier:: 1019357673

Author:: Legendre, Adrien Marie

Title:: Traité des fonctions elliptiques et des intégrales Euleriennes avec des tables pour en faciliter le calcul numérique

Year of publication:: 1825

Place of publication:: Paris

Publisher of the original:: Imprimerie de Huzard-Courcier

Identifier (digital):: 1019357673

Language:: French

Additional Notes:: Tome 1. (1825) Théorie des fonctions elliptiques et son application à différens problèmes de géométrie et de mécanique.--Tome 2. (1826) Méthodes pour construire les tables elliptiques. Recueil des tables elliptiques. Traité des intégrales eulériennes. Appendice.--Tome 3. (1828) Supplémens

Document type:: Multivolume work

Volume

Persistent identifier:: 1019359196

Author:: Legendre, Adrien Marie

Title:: Contenant divers supplèmens à la théorie des fonctions elliptiques

Scope:: 1 Online-Ressource (VII, 359 Seiten, 1 ungezähltes gefaltetes Blatt mit Bildtafeln)

Year of publication:: 1828

Place of publication:: Paris

Publisher of the original:: Imprimerie de Huzard-Courcier

Identifier (digital):: 1019359196

Language:: French

Usage licence:: Public Domain Mark 1.0

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2018

Document type:: Volume

Collection:: Mathematics

Chapter

Title:: TROISIÈME SUPPLÉMENT.

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: § XII. De la transcendante [...]x = [...].

Document type:: Multivolume work

Structure type:: Chapter

7 Inferred Accuracy The level of measured error is determined by three things: the accuracy of the models, the accuracy of the reference ground truth, and the accuracy of marking features in the imagery. These errors can be expected to be independent and so combine in an RMS way. That is, _ 2 2 2 Ermensured = Fidel X Preference + E enini Of these error sources, the model error is of the most interest and if the other two dominate, as we shall show is the case, the magnitude of the first can only be inferred. For the TM data, the USGS maps conformed to the NMAS which state that 90% of the features are accurate to within 1/50 inch. This corresponds to an MSE of 8.0 m. We estimated the marking error to be about 0.25 pixels or 7.5 m. The combined map and marking error come to 11.0 m. This is greater than the lowest measured error and so does not tell us much about the best accuracy that can be achieved. More.revealing is the multitemporal accuracy. If we make the reasonable assumptions that errors in the two scenes are independent, have mean zero and the same magnitude, then we deduce that AA - RA/vV2 7.1 m/ V2 = 5.0 m (inferred) For SPOT, the map errors were estimated in the following way. Fifteen GCPs with a location accuracy of better than 1 m were available in a small region of the scene. Their locations were compared with the positions on the maps leading to an estimate of 4.9 m RMS for the map error. The marking accuracy was estimated by having different operators mark the same points and measuring the difference in the marked coordinates. This led to an estimate of 3.0 m RMS. The combined map and marking error is thus 5.7 m. For the best accuracies measured (6.4 m) this suggests a model error of AA = 6.42 57 =29m (inferred) Alternatively, we can use the accuracy of the height determinations from the stereo pair to infer a planimetric accuracy. It can be shown that an across track error of E leads to a height error of E enit tan 0, -- tan 0, where 0, and 6, are the incidence angles of the two scenes. If we assume that the along- track error has the same magnitude as the across-track error and that the errors in the two models are independent, then we can infer that AA = PFreignt(tan 0, + tan 0;) 348

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