Use of likelihood ratio tests to detect outliers under the variance shift outlier model

Spatial Outlier Accommodation Using a Spatial Variance Shift Outlier Model

Outlier detection has been a long-debated subject among researchers due to its effect on model fitting. Spatial outlier detection has received considerable attention in the recent past. On the other hand, outlier accommodation, particularly in spatial applications, retains vital information about the model. It is pertinent to develop a method that is capable of accommodating detected spatial outliers in a fashion that retains vital information in the spatial models. In this paper, we formulate the variance shift outlier model (SVSOM) in the spatial regression as a robust spatial model using restricted maximum likelihood (REML) and use weights based on the detected outliers in the model. The spatial outliers are accommodated via a revised model for the outlier observations with the help of the SVSOM. Simulation results show that the SVSOM, based on the detected spatial outliers is more efficient than the general spatial model (GSM). The findings of this study also reveal that contamination in the residuals and x variable have little effect on the parameter estimates of the SVSOM, and that outliers in the y variable are always detectable. Asymptotic distribution of the squared spatial prediction residuals are obtained to confirm the outlyingness of an observation. The merit of or proposed SVSOM for the detection and accommodating outliers is also confirmed using artificial and COVID-19 data sets.

A Novel Method of Fault Detection and Identification in a Tightly Coupled, INS/GNSS-Integrated System

Fault detection and identification are vital for guaranteeing the precision and reliability of tightly coupled inertial navigation system (INS)/global navigation satellite system (GNSS)-integrated navigation systems. A variance shift outlier model (VSOM) was employed to detect faults in the raw pseudo-range data in this paper. The measurements were partially excluded or included in the estimation process depending on the size of the associated shift in the variance. As an objective measure, likelihood ratio and score test statistics were used to determine whether the measurements inflated variance and were deemed to be faulty. The VSOM is appealing because the down-weighting of faulty measurements with the proper weighting factors in the analysis automatically becomes part of the estimation procedure instead of deletion. A parametric bootstrap procedure for significance assessment and multiple testing to identify faults in the VSOM is proposed. The results show that VSOM was validated through field tests, and it works well when single or multiple faults exist in GNSS measurements.

Mean Shift versus Variance Inflation Approach for Outlier Detection—A Comparative Study

Outlier detection is one of the most important tasks in the analysis of measured quantities to ensure reliable results. In recent years, a variety of multi-sensor platforms has become available, which allow autonomous and continuous acquisition of large quantities of heterogeneous observations. Because the probability that such data sets contain outliers increases with the quantity of measured values, powerful methods are required to identify contaminated observations. In geodesy, the mean shift model (MS) is one of the most commonly used approaches for outlier detection. In addition to the MS model, there is an alternative approach with the model of variance inflation (VI). In this investigation the VI approach is derived in detail, truly maximizing the likelihood functions and examined for outlier detection of one or multiple outliers. In general, the variance inflation approach is non-linear, even if the null model is linear. Thus, an analytical solution does usually not exist, except in the case of repeated measurements. The test statistic is derived from the likelihood ratio (LR) of the models. The VI approach is compared with the MS model in terms of statistical power, identifiability of actual outliers, and numerical effort. The main purpose of this paper is to examine the performance of both approaches in order to derive recommendations for the practical application of outlier detection.