Robust Prediction Algorithm Based on a General EIV Model for Multiframe Transformation

Lihui Yao,Peng Lin,Jingxiang Gao,Chao Liu

doi:10.1155/2019/5173956

Abstract

In modern geodesy, there are cases in which the target frame is unique and there is more than one source frame. Helmert transformations, which are extensively used to solve transformation parameters, can be separately solved between the target frame and one of the source frames. However, this is not globally optimal, even though each transformation is locally optimal on its own. Additionally, this also generates the problem of multiple solutions in the noncommon station of the target frame. Moreover, least squares solutions can cause estimation value distortion, with a gross error existing in observations. Thus, in this paper, Helmert transformations among three frames, that is, one target frame and two source frames, are studied as an example. A robust prediction algorithm based on the general errors-in-variables prediction algorithm and the robust estimation is derived in detail and is applied to achieve multiframe total transformation. Furthermore, simulation experiments were conducted and the results validated the superiority of the proposed total transformation method over classical separate approaches.

Highlights

The precision and reliability of terrestrial reference frames have improved with the rapid development of the Global Navigation Satellite System (GNSS) [1]
In this paper, Helmert transformations among three frames, that is, one target frame and two source frames, are studied as an example
A robust prediction algorithm based on the general EIV prediction algorithm and robust estimation was derived in detail and was applied to achieve multiframe total transformation

Summary

Introduction

The precision and reliability of terrestrial reference frames have improved with the rapid development of the Global Navigation Satellite System (GNSS) [1]. Fang transformed the EIV model into a nonlinear Gauss–Markov model and proposed the 3D datum transformation algorithm under any rotation angle by taking the coordinates of common points in the source coordinate system as virtual observation values [12]. There is a statistically significant correlation between the common and noncommon stations [16]; for example, the coordinates of common and noncommon stations come from the same control network adjustment results (e.g., GPS baseline network), but the existing model algorithm does not take into consideration the correlation between reference stations, so the estimation results cannot obtain the optimal solution in theory To overcome this problem, Li et al [17, 18] proposed the concept of seamless frame datum transformation, which combines the estimation parameters and coordinate transformation of noncommon stations. We need to consider the random errors of all observations and their correlation to achieve multiframe total transformation based on the generalized EIV model

Extrapolation Estimation Method Based on the Generalized EIV Model

Robust Estimation Method Based on the Standardized Residuals and Median

Robust Prediction Algorithms for Multiframe Transformation

Experimental Analysis

Conclusions