A robust estimation algorithm for the increasing breakdown point based on quasi-accurate detection and its application to parameter estimation of the GNSS crustal deformation model

Qu, Wei; Chen, Hailu; Zhang, Qin; Gao, Yuan; Wang, Qingliang; Hao, Ming

doi:10.1007/s00190-021-01574-w

Cited by 8 publications

(6 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Assuming that the observation vector is L and the unknown parameter vector is β, the Gauss-Markov model is constructed, and the error equation can be expressed as follows [33].…”

Section: Robust M-estimationmentioning

confidence: 99%

“…Therefore, usually, a ρ function defines the M-estimation; the determination of the ρ function with a set of observations of variance factor σ 0 , obtained through the ρ function, calculates the equivalent weights of observations. Considering the prior measurement, the IGG3 [30,32,33,39] scheme constructs a robust equivalent weight function using the following formula:…”

Section: Robust M-estimationmentioning

confidence: 99%

“…The original outlier detection method mainly uses the hypothesis test theory to construct test statistics between the null hypothesis and the alternative hypothesis, only to make decisions and identify outliers [5]. Robust estimation can effectively detect and eliminate the outliers; at the same time, the equivalent weight function is used to add weak weights for small-and medium-sized outliers, which can more accurately estimate the model parameters [27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Robust Algorithm for Photon Denoising and Bathymetric Estimation Based on ICESat-2 Data

et al. 2023

View full text Add to dashboard Cite

The Ice, Cloud, and Land Elevation Satellite 2 (ICESat-2) is equipped with an Advanced Terrain Laser Altimeter System (ATLAS) with the capability of penetrating water bodies, making it a widely utilized tool for the bathymetry of various aquatic environments. However, the laser sensor often encounters a significant number of noise photons due to various factors such as sunlight, water quality, and after-pulse effect. These noise photons significantly compromise the accuracy of bathymetry measurements. In an effort to address this issue, this study proposes a two-step method for photon denoising by utilizing a method combining the DBSCAN algorithm and a two-dimensional window filter, achieving an F1 score of 0.94. A robust M-estimation method was employed to estimate the water depth of the denoised and refraction-corrected bathymetric photons, achieving an RMSE of 0.30 m. The method proposed in this paper preserves as much information as possible about signal photons, increases the number of bathymetric points, enhances the resistance to gross error, and guarantees the accuracy of bathymetry measurements while outlining the underwater topography. While the method is not fully automated and requires setting parameters, the fixed parameter values allow for efficient batch denoising of underwater photon points in different environments.

show abstract

“…Assuming that the observation vector is L and the unknown parameter vector is β, the Gauss-Markov model is constructed, and the error equation can be expressed as follows [33].…”

Section: Robust M-estimationmentioning

confidence: 99%

Section: Robust M-estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Robust Algorithm for Photon Denoising and Bathymetric Estimation Based on ICESat-2 Data

et al. 2023

View full text Add to dashboard Cite

show abstract

“…Statistics can be constructed through residuals and posterior information, and combined with statistical hypothesis test, outliers can be reasonably weighted only when the number of gross errors is small [26]. Qu et al [27] proposed an automatic selection strategy that combines the K-means clustering algorithm and quasiaccurate detection [14] method to obtain quasi-accurate observations and calculate the true error. They estimated the variance factor and fixed weight according to the true error, which can accurately estimate the model parameters and has a high breakdown point.…”

Section: Introductionmentioning

confidence: 99%

Robust solution of coordinate transformation parameters with a high breakdown point

Liu

et al. 2023

Meas. Sci. Technol.

View full text Add to dashboard Cite

Because the M estimation method may lead to poor robustness or even failure owing to excessive outliers, a robust algorithm with a high breakdown point was proposed and applied to the estimation of coordinate transformation parameters. Firstly, the sampling method was used to calculate multiple sets of model parameters, and some sampling results were sifted according to posterior information. Then, the samples were sorted according to their number in the sampling results, and the F-test was adopted to screen and reserve valid information. Finally, the initial values of the reliable parameters were computed using the valid information, and the final parameters were obtained by the Institute of Geodesy and Geophysics (IGG) III scheme. Monte Carlo method was adopted for the simulation test, and a case analysis was chosen for verification. The results show that the proposed method can identify and process outliers more accurately than those of Rousseeuw [22] and Tao et al. [25]. When the proportion of outliers exceeded 50%, the proposed algorithm maintained a strong robustness and had a high breakdown point.

show abstract

“…To resist the outliers and estimate the unknown parameters better, a lot of robust estimation methods have been studied, including M estimation [17,18], M split-estimation [19], MM estimation [20], R estimation [21], L1-norm estimation [22], S estimation [23], least trimmed squares estimation [24], and the signconstraint robust least-squares estimation [25], etc. These robust estimation methods are widely used in data processing, such as deformation analysis [26], integrity monitoring [27], and Kalman filtering [28]. Among all these methods, the M estimation is a generalized maximum likelihood estimation and is widely used since it is easy to implement and efficient in practical applications.…”

Section: Introductionmentioning

confidence: 99%

An enhanced outlier processing approach based on the resilient mathematical model compensation in GNSS precise positioning and navigation

Zhang,

Li,

Yuan

et al. 2023

Meas. Sci. Technol.

View full text Add to dashboard Cite

The abnormal measurements are widely existent in Global Navigation Satellite System (GNSS) precise positioning and navigation mainly because of the diffraction, reflection, refraction, and even non-line-of-sight reception. However, when multiple outliers exist in GNSS measurements, traditional methods including test procedure or robust estimation usually cannot work well. This study proposed an enhanced outlier processing approach based on the resilient mathematical model compensation. Specifically, first, to avoid excessive deletion, the total number of measurements is considered in the adaptive test procedure with the help of a scale factor. Second, in adaptive robust estimation, the total number of remaining measurements is also considered, thus making it more compatible with the adaptive test procedure. In addition, to overcome the potential inappropriate reweighting operator, different shrinking factors are adopted for code and phase measurements according to their precision, respectively. To verify the effectiveness of the proposed method, one static monitoring experiment and one kinematic vehicle experiment were conducted, where the method without outlier processing, traditional test procedure, traditional robust estimation, and the proposed method were all used. For the static experiment, the ambiguity resolution and positioning solutions of the proposed method perform best. The positioning accuracy of the float and fixed solutions can be improved by approximately 67.4% and 77.6% on average under challenging environments, respectively. For the kinematic experiment, the performance is also the best in terms of positioning availability and accuracy by using the proposed method.

show abstract

A robust estimation algorithm for the increasing breakdown point based on quasi-accurate detection and its application to parameter estimation of the GNSS crustal deformation model

Cited by 8 publications

References 47 publications

A Robust Algorithm for Photon Denoising and Bathymetric Estimation Based on ICESat-2 Data

A Robust Algorithm for Photon Denoising and Bathymetric Estimation Based on ICESat-2 Data

Robust solution of coordinate transformation parameters with a high breakdown point

An enhanced outlier processing approach based on the resilient mathematical model compensation in GNSS precise positioning and navigation

Contact Info

Product

Resources

About