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Journals / Harita Dergisi / 2005 / Cilt: 72 - Sayı: 134

Comparison of robust M-Estimations in determination of the outlying baseline vectors in GPS networks

Robust M-Kestirimlerin GPS Ağlarındaki uyuşumsuz baz vektörlerini belirlemede karşılaştırılması

Ertan GÖKALP
Yüksel BOZ
Pages
1–17
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It has been observed that in addition to IGGIII M-Estimation,Danish method and Huber's M-Estimation yield more reliable results than the other methods when the critical values of both are obtained by calculation.

📌 3 Key Takeaways

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Objective & Hypothesis:Least Squares (LS) based parameter estimation methods are sensitive to the deviations of the observation errors from the assumed distribution, normal distribution.
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Key Findings & Data:Therefore, LSE is not distributionally robust.
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Conclusion & Impact:It has been observed that in addition to IGGIII M-Estimation,Danish method and Huber's M-Estimation yield more reliable results than the other methods when the critical values of both are obtained by calculation.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Least Squares (LS) based parameter estimation methods are sensitive to the deviations of the observation errors from the assumed distribution, normal distribution. Therefore, LSE is not distributionally robust. Robust estimation was firstly used by Krarup and Kubik in evaluation of surveying data and subsequently has gained wide use in adjustment processes. After each iteration step of an adjustment process, robust methods reduce or make zero the weights of the outlying observations unlike the conventional methods, which determine the outliers by means of the statistical tests and remove them from the observation set. At the end of the robust methods, no observation is removed from the network and all the outliers are obtained in cooperation. Robust methods can be applied to all geodetic networks. In this paper, the behaviors of the frequently used robust methods in the literature such as Danish method, Huber's M-Estimation, Beaton-Tukey's M-Estimation, Andrews's M-Estimation, and also IGG (Institute of Geodesy and Geophysics) M-Estimation and IGGIII M-Estimation, which were defined close to date, are investigated in determination of the outlying baseline vectors in the GPS networks. It has been observed that in addition to IGGIII M-Estimation,Danish method and Huber's M-Estimation yield more reliable results than the other methods when the critical values of both are obtained by calculation.

Özet

En küçük karelere dayalı parametre tahmin yöntemleri, varsayılan hata dağılımı olan normal dağılımdan gösterilecek olası değişimlere duyarlıdırlar. Bu nedenle, en küçük kareler kestirimi istatistiksel olarak robust (sağlam) değildir. Ölçme ile ilgili verilerin işlenmesinde ilk olarak 1967 yılında Krarup ve Kübik tarafından kullanılmış olan robust kestirim, o günden sonra dengeleme işlemlerinde geniş kullanım kazanmıştır. İstatistiksel testler aracılığıyla uyuşumsuz ölçülerin belirlenmesini ve sonrasında ölçü kümesinden çıkarılmasını hedefleyen geleneksel yöntemlerden farklı olarak; robust yöntemler, ölçülerin dengelenmesi işleminde her bir yineleme sonrası olası uyuşumsuz ölçülerin ağırlıklarını azaltmakta veya sıfır yapmaktadır. Sonuçta, ölçü ağından herhangi bir ölçü açmaksızın uyuşumsuz ölçüler toplu olarak görülebilmektedir. Robust yöntemler, jeodezik ağ türlerinin tümüne uygulanabilen yöntemlerdir. Bu çalışmada, literatürde sıkça karşılaşılan robust yöntemlerden, Danimarka Yöntemi, Huber, Beaton-Tukey ve Andrews'm M-Kestirimi ile bu yöntemlere nazaran daha yakın tarihlerde tanımlanan IGG (Institute of Geodesy and Geophysics) ve IGGIII M-Kestirimi'nin bir jeodezik ağ türü olan GPS ağlarındaki uyuşumsuz baz vektörlerini belirlemedeki davranışları incelenmiştir. Sonuçta IGGII M-Kestirimi ile sınır değer parametreleri hesapla bulunan Danimarka Yöntemi ve Huber'in M-Kestirimi'nin diğer yöntemlere göre daha güvenilir sonuçlar verdiği gözlenmiştir.

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Cite This Article

GÖKALP, E., BOZ, Y. (2005). Comparison of robust M-Estimations in determination of the outlying baseline vectors in GPS networks. Harita Dergisi, Cilt: 72 - Sayı: 134, 1–17. https://ajindex.com/articles/202322

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