Experimental Design Approach For Coordinate Transformation

Abstract

The coordinate transformation is realized to use together points coordinate which have different datum. 2D similarity, 2D affine and 3D similarity coordinate transformation is often applied in geodesy. The geometrical relationship between two coordinate systems is established by the common points which their coordinates are known in two coordinate system. In this process, the common points coordinates are used as measurements. The coordinate transformation parameters are determined with more measurement than required number according to adjustment calculus. The coordinate transformation is an experimental process which the combining of several factors are evaluated. The experimental design The effect on response variable of different factors can be investigated using experimental design methods. One of these methods is Full Factorial Design. The aim of this study is to analyze the factors effects of 2D coordinate transformation on the response variable using 23 factorial design. The common point number (10-20), transformation method (similarity-affine) and adjustment method (the least square-the least absolute value) are taken as experimental factors in the coordinate transformation between ED50-ITRF96 datums. The result of experiment are evaluated by Minitab16 statistical software to determine the significance of the factors and the levels of factors and the regression equation is obtained between the factors and response variable. Keywords : Coordinate Transformation, Experimental Design, Common Point, Transformation Methods, Adjustment Method.

Keywords

• Coordinate Transformation, Experimental Design, Common Point, Transformation Methods

Koordinat Dönüşümünde Deney Tasarımı Yaklaşımı

Öz

Farklı datumlarda koordinatı belirlenmiş noktaların bir arada kullanılabilmesi için koordinat dönüşümü yapılır. 2boyutlu Benzerlik ve Afin ile 3 boyutlu Benzerlik dönüşümleri jeodezik uygulamalarda çok sıklıkla kullanılır. Koordinat dönüşümü işleminde her iki koordinat sisteminde de koordinatı bilinen ortak noktalar kullanılarak iki koordinat sistemi arasındaki geometrik ilişki kurulur. Ortak nokta koordinatları, koordinat dönüşüm parametrelerinin belirlenmesi sürecinde ölçü olarak kullanılır. Gereğinden fazla sayıda ortak nokta kullanılarak, koordinat dönüşüm parametreleri dengeleme hesabı ile elde edilir. Koordinat dönüşümü işlemi birkaç faktörün bir arada değerlendirilmesiyle oluşan deneysel bir süreçtir. Farklı parametrelerin sonuç değişkeni üzerindeki etkileri deneysel tasarım yöntemleri ile irdelenebilir, bu yöntemlerden birisi Full Faktöriyel Dizayndır. Bu çalışmanın amacı 23 faktöriyel tasarım kullanarak deneysel faktörlerinin koordinat dönüşümündeki etkilerini analiz etmektir. ED50-ITRF96 datumları arasındaki dönüşümde, deneysel faktörler olarak; ortak nokta sayısı (10-20) dönüşüm yöntemi (benzerlik-afin) ve dengeleme yöntemi (En Küçük Mutlak Toplam ve En Küçük Kareler) belirlenmiştir. Deneysel faktörlerin ve seviyelerinin öneminin belirlenmesi için deney sonuçları Minitab16 istatistiksel yazılımıyla değerlendirilmiş ve bir regresyon modeli önerilmiştir. Anahtar Kelimeler: Koordinat dönüşümü, Deney tasarımı, Ortak Nokta, Dönüşüm Yöntemi, Dengeleme Yöntemi.

Anahtar Kelimeler

• Koordinat dönüşümü, Deney tasarımı, Ortak Nokta, Dönüşüm Yöntemi, Dengeleme Yöntemi

Kaynakça

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