Adaptive Least-Squares Collocation Algorithm Considering Distance Scale Factor for GPS Crustal Velocity Field Fitting and Estimation

Wei Qu,Hailu Chen,Shichuan Liang,Yuan Gao,Qin Zhang,Wu Zhu,Lihua Zhao

doi:10.3390/rs11222692

Abstract

High-precision, high-reliability, and high-density GPS crustal velocity are extremely important requirements for geodynamic analysis. The least-squares collocation algorithm (LSC) has unique advantages over crustal movement models to overcome observation errors in GPS data and the sparseness and poor geometric distribution in GPS observations. However, traditional LSC algorithms often encounter negative covariance statistics, and thus, calculating statistical Gaussian covariance function based on the selected distance interval leads to inaccurate estimation of the correlation between the random signals. An unreliable Gaussian statistical covariance function also leads to inconsistency in observation noise and signal variance. In this study, we present an improved LSC algorithm that takes into account the combination of distance scale factor and adaptive adjustment to overcome these problems. The rationality and practicability of the new algorithm was verified by using GPS observations. Results show that the new algorithm introduces the distance scale factor, which effectively weakens the influence of systematic errors by improving the function model. The new algorithm can better reflect the characteristics of GPS crustal movement, which can provide valuable basic data for use in the analysis of regional tectonic dynamics using GPS observations.

Highlights

GPS velocity field provides the most intuitive representation of regional crustal movement and deformation, and is the basis of geodynamic studies
The least-squares collocation (LSC) algorithm is an optimal estimation algorithm that simultaneously determines the tendency parameters and the signals with randomness [22]: L =AX+U S +n q×1 q×pp×1 q×mm×1 q×1 where L is the observation vector; X is the non-random tendency parameter; A is coefficient matrix, reflecting the contribution of X to L; S is random signal, which includes the signal of observation points and unobserved points in the study area; U is the rectangular matrix, the left q columns of the U matrix is the unit matrix, corresponding to the observation points signal, the right m − q columns of the U matrix is null matrix, corresponding to the estimated points signal; n represents observation noise
To verify the rationality of the new algorithm in real cases, we selected the Sichuan-Yunnan block located in southern China [15] and used long-term GPS velocities to test the ADLSC algorithm

Summary

Introduction

GPS velocity field provides the most intuitive representation of regional crustal movement and deformation, and is the basis of geodynamic studies. The LSC algorithm has been used to estimate crustal movement signals from GPS velocity fields [9,10,11,12,13,14,15] It has been used in various earth science fields to control systematic and anomaly errors in GIS spatial data [16], detect outliers in multibeam bathymetric data [17], solve common point coordinate errors in 3D coordinate transformation [18], improve the accuracy of mobile light detection and ranging (LiDAR) systems in hostile environments [19], improve the results of downward continuation values of airborne gravity data [20], and refine the local covariance model of gravity anomalies [21]

Methods

Results

Conclusion