Multivariate total least - squares adjustment for empirical affine transformations

B. Schaffrin, Y. A. Felus

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

21 اقتباسات (Scopus)

ملخص

In Geodetic Science it occurs frequently that, for a given set of points, their coordinates have been measured in two (or more) different systems, and empirical transformation parameters need to be determined by some sort of adjustment for a defined class of transformations. In the linear case, these parameters appear in a matrix that relates one set of coordinates with the other, after correcting them for random errors and centering them around their mid-points (to avoid shift parameters). In the standard approach, a structured version of the Errors-in-Variables (EIV) model would be obtained which would require elaborate modifications of the regular Total Least-Squares Solution (TLSS). In this contribution, a multivariate (but unstructured) EIV model is proposed for which an algorithm has been developed using the nonlinear Euler-Lagrange conditions. The new algorithm is used to estimate the TLSS of the affine transformation parameters. Other types of linear transformations (such as the similarity transformation, e.g.) may require additional constraints.

اللغة الأصليةالإنجليزيّة
عنوان منشور المضيفVI Hotine-Marussi Symposium on Theoretical and Computational Geodesy - IAG Symposium
الصفحات238-242
عدد الصفحات5
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 2008
منشور خارجيًانعم
الحدثIAG Symposium - 6th Hotine-Marussi Symposium on Theoretical and Computational Geodesy - Wuhan, الصين
المدة: ٢٩ مايو ٢٠٠٦٢ يونيو ٢٠٠٦

سلسلة المنشورات

الاسمInternational Association of Geodesy Symposia
مستوى الصوت132
رقم المعيار الدولي للدوريات (المطبوع)0939-9585

!!Conference

!!ConferenceIAG Symposium - 6th Hotine-Marussi Symposium on Theoretical and Computational Geodesy
الدولة/الإقليمالصين
المدينةWuhan
المدة٢٩/٠٥/٠٦٢/٠٦/٠٦

بصمة

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