Nokta Konum Doğruluğunun İki Ve Üç Boyutlu Koordinat Dönüşümüne Etkisi

Abstract

Geçmişten günümüze süregelen insan-toprak ilişkisi ve bu ilişkinin sürdürülebilir ve toplumsal bir seviyede oluşturulabilmesi ayrıca insan yaşamını kolaylaştırmak, düzenlemek, sosyal bir çevrede yaşamasını sağlamak için yapılan çok sayıda mühendislik projelerinin amacına uygun olması, kullanılması, diğer projeler ile bağlantılı olması için temelde yeryüzündeki konumunun belirlenmesi gereklidir. Bu nedenle yapılan ve yaşadığımız dünyanın her bölgesinde yapılan çalışmalarda kullanılmak üzere tek anlamlı farklı koordinat sistemleri tanımlanmıştır. Bu tanımlanan koordinat sistemleri ile farklı koordinat sistemlerine dayalı oluşturulan, insan-toprak ilişkisine bağlı bir bilgi sistemi olsun ya da mühendislik projesi olsun birbirleri ile ilişkilendirilmesi gerekmektedir. Bu gereklilik çalışmanın amacına göre farklı koordinat sistemlerine geçişte farklı doğruluk derecesinde bir yaklaşım içerebilir. Koordinat sistemleri tanımlanırken bir başka koordinat sistemi ile arasındaki dönüşüm parametreleri belirlenmelidir. Farklı jeodezik sistemlerin kullanılması, bir sistemden diğerine geçişte koordinat dönüşümleri jeodezide en çok kullanılan işlemlerden birisidir. Dönüşüm için gerekli olan dönüşüm parametreleri olarak adlandırılan bilinmeyenlerin çözümü için her iki koordinat sisteminde de ortak olan jeodezik noktalara ihtiyaç duyulmaktadır. Bilinmeyenlerin çözümü için genel olarak en küçük kareler (Least Squares, LS) dengelemesi yöntemi kullanılmaktadır. Bu yöntem ile çözüme ulaşımda her iki sistemdeki koordinatların doğru olarak kabul edildiği düşünülür. Ancak biliyoruz ki her ölçü kendi içerisinde rastlantısal nitelikte bir takım hatalar barındırmaktadır. Başlangıç koordinat sisteminde olsun veya hedef koordinat sisteminde olsun nokta koordinatları hatalar içermektedir. LS yaklaşımında koordinat doğruluklarını içeren veriler kullanılamamaktadır. Bu yöntemin yerine dizayn matrisleri oluşturulurken nokta konum doğruluklarını kullanabilmek için toplam en küçük kareler (total least squares, TLS) yaklaşımı kullanılmaktadır. Böylece bilinmeyenlerin kestiriminde daha gerçekçi değerler elde edilebilir. Bu çalışmada klasik yaklaşım LS ile TLS, ayrıca bu yöntem için iki farklı yaklaşım üzerinde durulacak ve her üç yöntemle elde edilen parametreler ve sonuçlar karşılaştırılacaktır.

From past to this day ongoing human-earth relationship to ensure properly and in a realistic way this relationship sustainable social level can be created, also in order to facilitate human life, to organize a social environment to be lived, large number of engineering projects to be linked with other projects as intended use to be made that it is necessary to first determine its position on earth. Every region of the world we live in different coordinate systems to be used are defined univocally.Either geographic information systems or engineering projects based on produce to be defined different coordinate systems, it is neccessary to get associated with each other. According to these requirements, the feasibility in the transition between two different coordinate systems may have differences in sensitivity. In recent years, the least squares method of adjusting spatial data has been rapidly gaining popularity as the method used for analyzing and adjusting surveying data. This should not be surprising, because the method is the most rigorous adjustment procedure available. It is soundly based on the mathematical theory of probability; it allows for appropriate weighting of all observations in accordance with their expected precisions; and it enables complete statistical analyses to be made following adjustments so that the expected precisions of adjusted quantities can be determined. The method of least squares is a standard approach to the approximate solution of overdetermined systems, sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. The most important application is in data fitting. The best fit in the least-squares sense minimizes the sum of squared residuals, a residual being the difference between an observed value and the fitted value provided by a model. When the problem has substantial uncertainties in the independent variable (the 'x' variable), then simple regression and least squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares. The most compelling of all reasons for the recent increased interest in least squares adjustment is that new accuracy standards for surveys are being developed that are based on quantities obtained from least squares adjustments. Thus, surveyors of the future will not be able to test their observations for compliance with these standards unless they adjust their data using least squares. Clearly modern surveyors must be able to apply the method of least squares to adjust their observed data, and they must also be able to perform a statistical evaluation of the results after making the adjustments. In geodesy measuring and calculating horizontal and vertical control networks are different and those two control networks are independently Counting geodetic measurements technology and developing methods, depending on the GPS technique used by a conventional method results compared products differ in raises. Threedimensional coordinates obtained by GPS while the horizontal and vertical systems by conventional methods are discussed separately. GPS technique in the direction of the axis corresponds to the spatial scale is not the same horizontal and vertical trials leads to differences in the scale. In our country, the measurement methods were used as well as specific horizontal and vertical control network except using the locally produced and used systems also are often used. Given the reasons mentioned above geodetic coordinate transformations has an important place in studies. Transformation parameters in the mathematical model of the system is known, unless the transition from one system to another system is possible with these parameters. Generally known parameters in both systems because of commonalities with known coordinates transformation parameters is performed by calculating the coordinate transformation between the systems. Transformation parameters between two different coordinate systems must be determined. The use of different geodetic systems , the transition from one system to another coordinate system is one of the most widely used process in geodetic science. Transformation parameters are calculated from the identical points' coordinates of which are known in both coordinate system. General idea of solution of transformation parameters is the least squares (LS) estimation. LS estimation is the classical approach in adjustment calculations. This method considers that the source coordinates are error-free.. However, we know that every measurement in itself contains a number of random errors . Either source coordinates or the target coordinates contains errors. LS approach take this into account during the solution of the transformation problem where both system coordinates are assumed to be stochastic. Total least squares estimation allows for us to use these errors for adjustment calculation. Thus, a more realistic estimation of transformation parameters' values can be obtained. This study will focus on the use of classical approach LS and TLS, also same technique different approach and the parameters obtained from these methods will be compared. The results are compared to the classical LS solution. TLS is able to handle the uncertainty and the results are more realistic than the classical approach.