Outlier Patterns Research Articles

Data-driven evolution of water quality models: An in-depth investigation of innovative outlier detection approaches-A case study of Irish Water Quality Index (IEWQI) model

Recently, there has been a significant advancement in the water quality index (WQI) models utilizing data-driven approaches, especially those integrating machine learning and artificial intelligence (ML/AI) technology. Although, several recent studies have revealed that the data-driven model has produced inconsistent results due to the data outliers, which significantly impact model reliability and accuracy. The present study was carried out to assess the impact of data outliers on a recently developed Irish Water Quality Index (IEWQI) model, which relies on data-driven techniques. To the author's best knowledge, there has been no systematic framework for evaluating the influence of data outliers on such models. For the purposes of assessing the outlier impact of the data outliers on the water quality (WQ) model, this was the first initiative in research to introduce a comprehensive approach that combines machine learning with advanced statistical techniques. The proposed framework was implemented in Cork Harbour, Ireland, to evaluate the IEWQI model's sensitivity to outliers in input indicators to assess the water quality. In order to detect the data outlier, the study utilized two widely used ML techniques, including Isolation Forest (IF) and Kernel Density Estimation (KDE) within the dataset, for predicting WQ with and without these outliers. For validating the ML results, the study used five commonly used statistical measures.The performance metric (R2) indicates that the model performance improved slightly (R2 increased from 0.92 to 0.95) in predicting WQ after removing the data outlier from the input. But the IEWQI scores revealed that there were no statistically significant differences among the actual values, predictions with outliers, and predictions without outliers, with a 95 % confidence interval at p < 0.05. The results of model uncertainty also revealed that the model contributed <1 % uncertainty to the final assessment results for using both datasets (with and without outliers). In addition, all statistical measures indicated that the ML techniques provided reliable results that can be utilized for detecting outliers and their impacts on the IEWQI model. The findings of the research reveal that although the data outliers had no significant impact on the IEWQI model architecture, they had moderate impacts on the rating schemes' of the model. This finding indicated that detecting the data outliers could improve the accuracy of the IEWQI model in rating WQ as well as be helpful in mitigating the model eclipsing problem. In addition, the results of the research provide evidence of how the data outliers influenced the data-driven model in predicting WQ and reliability, particularly since the study confirmed that the IEWQI model's could be effective for accurately rating WQ despite the presence of the data outliers in the input. It could occur due to the spatio-temporal variability inherent in WQ indicators.However, the research assesses the influence of data input outliers on the IEWQI model and underscores important areas for future investigation. These areas include expanding temporal analysis using multi-year data, examining spatial outlier patterns, and evaluating detection methods. Moreover, it is essential to explore the real-world impacts of revised rating categories, involve stakeholders in outlier management, and fine-tune model parameters. Analysing model performance across varying temporal and spatial resolutions and incorporating additional environmental data can significantly enhance the accuracy of WQ assessment. Consequently, this study offers valuable insights to strengthen the IEWQI model's robustness and provides avenues for enhancing its utility in broader WQ assessment applications.Moreover, the study successfully adopted the framework for evaluating how data input outliers affect the data-driven model, such as the IEWQI model. The current study has been carried out in Cork Harbour for only a single year of WQ data. The framework should be tested across various domains for evaluating the response of the IEWQI model's in terms of the spatio-temporal resolution of the domain. Nevertheless, the study recommended that future research should be conducted to adjust or revise the IEWQI model's rating schemes and investigate the practical effects of data outliers on updated rating categories. However, the study provides potential recommendations for enhancing the IEWQI model's adaptability and reveals its effectiveness in expanding its applicability in more general WQ assessment scenarios.

Fisher's Geometric Model as a Tool to Study Speciation.

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

OS-FCM: A semi-supervised clustering approach to investigating consumers’ usage patterns of contactless shopping-delivery (S-D) channel

Investigating the factors that contribute to consumers’ usage patterns of contactless shopping-delivery (S-D) channel is important for e-commerce retailers and logistics operators. However, in the data as collected by a questionnaire survey, distinct usage patterns are not always easily observed due to the existence of outliers, which places a challenge for the investigation. Hence, this study develops a labelling approach, named OS-FCM, to determine the usage patterns. As a semi-supervised clustering approach, OS-FCM integrates One-Class Support Vector Machine and Fuzzy C-Means, which enables it to make a trade-off between subjective judgement and statistical evidence when identifying patterns and to effectively recognize the patterns of outliers. The dataset with the usage patterns is used to train Random Forest, upon which Shapley Additive exPlanations (SHAP) approach is applied to measure the contributions of each factor. The data as collected by a questionnaire survey in Singapore are used for a case study. By using OS-FCM, the participants are clustered into five patterns with each pattern involving three variables, namely, current usage frequency, current behavioral habit, and future continuance intention. The contributions of each potential factor to the patterns are measured by SHAP values. In the case study, two regular patterns and three outlier patterns are identified. It is found that consumers’ past behavior stands out to be the most important factor to the pattern formation from an aggregated perspective. Factors such as fear appeal and behavior maintenance/change motivations exert differentiated impacts on the formation of the five patterns. Besides, as compared to commonly used clustering methods, OS-FCM has better clustering performance and the patterns determined by OS-FCM are more reasonable and rational, which provides a solid basis for better understanding the usage patterns.

DifFormer: Multi-Resolutional Differencing Transformer With Dynamic Ranging for Time Series Analysis.

Time series analysis is essential to many far-reaching applications of data science and statistics including economic and financial forecasting, surveillance, and automated business processing. Though being greatly successful of Transformer in computer vision and natural language processing, the potential of employing it as the general backbone in analyzing the ubiquitous times series data has not been fully released yet. Prior Transformer variants on time series highly rely on task-dependent designs and pre-assumed "pattern biases", revealing its insufficiency in representing nuanced seasonal, cyclic, and outlier patterns which are highly prevalent in time series. As a consequence, they can not generalize well to different time series analysis tasks. To tackle the challenges, we propose DifFormer, an effective and efficient Transformer architecture that can serve as a workhorse for a variety of time-series analysis tasks. DifFormer incorporates a novel multi-resolutional differencing mechanism, which is able to progressively and adaptively make nuanced yet meaningful changes prominent, meanwhile, the periodic or cyclic patterns can be dynamically captured with flexible lagging and dynamic ranging operations. Extensive experiments demonstrate DifFormer significantly outperforms state-of-the-art models on three essential time-series analysis tasks, including classification, regression, and forecasting. In addition to its superior performances, DifFormer also excels in efficiency - a linear time/memory complexity with empirically lower time consumption.

Spatial Pattern and Influencing Factors of Agricultural Leading Enterprises in Heilongjiang Province, China

As one of the major new agricultural business entities, agricultural leading enterprises (ALEs) are responsible for ensuring national food security, leading agricultural and rural modernization, and increasing farmers’ employment prospects and incomes. From the perspective of headquarters and branches, this study used a point pattern analysis, the local Moran’s index, the rank-size rule, and the geographical detector to depict the spatial pattern of ALEs in Heilongjiang Province, detect influencing factors, and reveal the spatial layout mechanism. The main conclusions are as follows. (1) ALE headquarters and branches in Heilongjiang Province had different location requirements, and their layout orientation, clustering areas, and influencing factors were different. (2) The headquarters displayed a pronounced urban and agglomeration orientation, while branches exhibited a significant farm dependence and raw material orientation. (3) Both the headquarters and the branches showed a significant trend towards spatial clustering. The headquarters were mainly in the Harbin municipal district and surrounding counties, including Wuchang, Zhaodong, and Beilin, which showed a high–high cluster pattern. The branches were mainly in the Sanjiang Plain. Tongjiang, Fujin, Hulin, Mishan, Raohe, Baoqing, and Suibin showed a high–high cluster pattern, while the Harbin municipal district and Bei’an showed a high–low outlier pattern. (4) The ALEs’ regional connection network in Heilongjiang Province was radially distributed with the Harbin municipal district as the centre. The agricultural reclamation system deeply influenced it. (5) The number of supporting enterprises, number of permanent residents, gross domestic product, railway mileage, number of people with Bachelor’s degrees or above, and distance from the provincial capital were the main influencing factors of the headquarters spatial pattern in Heilongjiang Province. The number of state farms in Heilongjiang Province, the per capita grain yield, highway mileage, and distance from the provincial capital were the main influencing factors of the branch spatial patterns in Heilongjiang Province. The interaction results indicated that the explanatory power of two-factor interaction was stronger than that of a single factor regardless of headquarters or branches, and most interaction types were bilinear enhancements. This study aims to provide a decision-making reference for the long-term development of ALEs in Heilongjiang Province at the present stage and accelerate the development of agricultural industrialization in major grain-producing areas.

Nested Binary Classifier as an Outlier Detection Method in Human Activity Recognition Systems.

The present article is devoted to outlier detection in phases of human movement. The aim was to find the most efficient machine learning method to detect abnormal segments inside physical activities in which there is a probability of origin from other activities. The problem was reduced to a classification task. The new method is proposed based on a nested binary classifier. Test experiments were then conducted using several of the most popular machine learning algorithms (linear regression, support vector machine, k-nearest neighbor, decision trees). Each method was separately tested on three datasets varying in characteristics and number of records. We set out to evaluate the effectiveness of the models, basic measures of classifier evaluation, and confusion matrices. The nested binary classifier was compared with deep neural networks. Our research shows that the method of nested binary classifiers can be considered an effective way of recognizing outlier patterns for HAR systems.

EU Enlarged Countries’ Trade With East Asia: Outliers In Export And Import Time Series

From the standpoint of EU enlarged countries, this empirical study investigates the trade relationship with East Asia via an outlier approach in export and import time series. The results show the exports in trial-and-error progress compared to the imports in a developed adjustment. The outlier patterns clearly demonstrate the divergent trade relationship between the sample countries. This study makes a contribution to the outlier approach in the context of international trade. It concludes that the deeper incorporation of EU enlarged countries into East Asia can lead to significant involvement in the global supply chain and highlight the sustainability of economic growth.

Li-S Battery Outlier Detection and Voltage Prediction using Machine Learning

State estimation is essential for enabling battery management systems (BMSs) to monitor, control, and optimize battery performance. The first step toward this is the ability to predict a battery's behavior given its input current and present state. In the early stages of new battery chemistry development, prior to commercialization, lab-fabricated battery cells might be used for characterization and BMS development. Such custom-fabricated batteries are often more prone to anomalies in their cycling behavior, including loss of connectivity and instantaneous internal shorts. The use of battery cycling data containing such anomalies can negatively affect modeling accuracy and system predictability. This paper uses the K-means clustering method to detect outlier patterns in battery cycling, thereby enabling the extraction of sanitized cycling data. A feedforward neural network is then trained to predict battery voltage one step ahead, given the input current and prior voltage history. The paper demonstrates this machine learning approach for cycling data from laboratory-fabricated lithium-sulfur (Li-S) cells. This demonstration highlights both the accuracy of the proposed voltage prediction algorithm and the degree to which the proposed outlier detection algorithm helps improve this accuracy.

Mapping individualised patterns of atrophy in Alzheimer’s disease using neuroanatomical normative models

AbstractBackgroundAlzheimer’s Disease (AD) is highly heterogeneous, with marked individual differences in clinical presentation and aspects of its neurobiology. Neuroanatomical normative modelling is an emerging technique that reveals individual patterns of neuroanatomy by quantifying deviations from normative ranges (Verdi et al., 2021). Using Alzheimer’s Disease Neuroimaging Initiative (ADNI) data, we applied a hierarchical Bayesian regression (HBR) normative model to account for site effects (Kia et al., 2021). We assessed individual patterns of cortical thickness (CT) heterogeneity in AD patients, people with mild cognitive impairment (MCI), and healthy controls.MethodCT across 148 regions of interest (ROIs) was generated using FreeSurfer from 1492 T1‐weighted MRI scans across 63 sites. A reference HBR normative model was trained on a separate healthy dataset of 34,490 to index population variability, predicting CT at each ROI using age and sex. This generated CT z‐scores for each ROI, per participant. Here z‐scores &lt; ‐1.96 were defined as outliers. Outliers were also summed across 148 ROIs to give a total outlier score per participant. The influence of the total outlier score on converting from MCI to AD within 3 years was tested using Cox proportional hazards regression.ResultAD subjects had higher total outlier scores than MCI and control participants (β=10.99,95%CI=[5.55,16.42], p&lt;0.001), with marked differences in temporal regions. Total outlier score predicted memory performance (R2=0.39,p&lt;0.001) and executive function (R2=0.35,p&lt;0.001). Total outlier score was predicted by amyloid‐beta (R2=0.06,p&lt;0.001) and phospho‐tau (R2=0.16,p&lt;0.001). The patterns of neuroanatomical outliers varied markedly between AD patients (Fig.1); the parahippocampal gyrus had the highest rate of AD patients with outliers (47%). Outlier maps of AD patients matched age, sex, cognition and APOE4 genotype, illustrate spatially heterogeneous patterns of outliers (Fig.2). Greater within‐group dissimilarity was seen in AD patients, relative to MCI or control participants (Fig.3). Every 10 points of total outlier score contributed to an 31.4% risk of converting from MCI to AD within 3years (HR=1.028,95%CI=[1.016,1.039],p&lt;0.001) (Fig.4). ConclusionOur novel quantitative estimate of the neuroanatomical heterogeneity of CT suggests the impact of AD on the brain is not consistent between patients. Furthermore, quantify outliers in CT may help predict individuals with MCI at risk of converting to AD.

The heterogeneous amyloid‐positive brain: mapping individualised patterns of atrophy in amyloid‐positive Alzheimer’s disease patients using neuroanatomical normative models

AbstractBackgroundPatterns of atrophy in the brain highly differ between individual Alzheimer’s Disease (AD) patients, however, most clinical research focuses on group‐level differences (Verdi et al., 2021). Here we used a novel technique, neuroanatomical normative modelling, to reveal individual patterns of cortical thickness by quantifying deviations from the normative range. We applied a hierarchical Bayesian regression (HBR) normative model (Kia et al., 2021), to amyloid‐positive AD patients who had clinical amyloid PET imaging at the Imperial Memory Clinic (IMC). Patients had either AD dementia or mild cognitive impairment due to AD. We hypothesised that there would be individual differences in patterns of cortical atrophy in these patients.MethodCortical thickness across 148 regions of interest (ROIs) was generated using FreeSurfer from n=130 (102 AD patients and 28 healthy controls) T1‐weighted MRIs acquired from the IMC. A reference HBR normative model was trained on a separate dataset of n=34,490 healthy individuals to index population variability, which predicted cortical thickness at each ROI using age and sex. This generated cortical thickness z‐scores for each ROI, per patient (z‐score &lt; ‐1.96 = outlier).ResultThe patterns of cortical atrophy outliers were highly varied in amyloid‐positive AD patients. For instance, the largest proportion of outliers in a region was 60% within the superior temporal sulci, if atrophy were homogenous we would expect 100% of outliers to be here (Fig.1). This heterogeneity was also seen when comparing how similar outlier patterns were between patients (Fig.2). We also found that the proportions of outliers differ according to disease severity, e.g. the highest percentage of outliers was 70% within superior temporal sulci within the AD dementia subgroup, and 50% in superior temporal sulci in the mild cognitive impairment due to AD subgroup (Fig.3).ConclusionAmyloid‐positivity results in heterogenous patterns of cortical atrophy. This is more pronounced in AD dementia, though still present in people with mild cognitive impairment due to AD. Neuroanatomical normative maps have the potential to be individualised markers of disease, and with application to longitudinal data could track individual disease progression.

Using machine learning to identify novel hydroclimate states

Anthropogenic climate change is expected to alter drought risk in the future. However, droughts are not uncommon or unprecedented, as documented in tree-ring-based reconstructions of the summer average Palmer drought severity index (PDSI). Using an unsupervised machine-learning method trained on these reconstructions of pre-industrial climate, we identify outliers: years in which the spatial pattern of PDSI is unusual relative to ‘normal' variability. We show that in many regions, outliers are more frequently identified in the twentieth and twenty-first centuries. This trend is more pronounced when the regional drought atlases are combined into a single global dataset. By definition, outlier patterns at the 10% level are expected to occur once per decade, but from 1950 to 2000 more than 6 years per decade are identified as outliers in the global drought atlas (GDA). Extending the GDA through 2020 using an observational dataset suggests that anomalous global drought conditions are present in 80% of years in the twenty-first century. Our results indicate, without recourse to climate models, that the world is more frequently experiencing drought conditions that are highly unusual in the context of past natural climate variability.This article is part of the Royal Society Science+ meeting issue ‘Drought risk in the Anthropocene’.

A procedure for anomaly detection and analysis

Anomaly detection is often used to identify and remove outliers in datasets. However, detecting and analyzing the pattern of outliers can contribute to future business decisions or increase the accuracy of a learning algorithm. Selecting the applicable outlier detection method for a dataset requires human intervention and analysis due to the challenge of choosing an efficient technique suitable for all types of attributes. This work presents a procedure for anomaly detection and analysis. The procedure is feature-wise (i.e., processes each feature independently), uses T different anomaly detection techniques (for T>1), and estimates the best technique using predefined thresholds. It is a generic method that does not depend on the model type and can be applied to supervised and unsupervised learning. In addition, this method does not impute or remove the outliers, as they should be adapted according to the dataset or business requirements. The significant advantage of this method is the ability to use different techniques to detect anomalies since it is applied per feature and not per record, as in traditional anomaly detection methods. Furthermore, the method uses a new measure, Noise Ratio (NR), which describes the level of agreement between our method’s result and traditional anomaly detection techniques. The results showed that all the compared techniques identified non-anomalous features with consistent results between the various algorithms. In the proposed method, NR found up to 20% of the non-anomalous values marked as outliers and improved up to 10% in finding outliers in datasets compared to traditional anomaly detection algorithms.

Study on the Technology Trend Screening Framework Using Unsupervised Learning

Outliers that deviate from a normal distribution are typically removed during the analysis process. However, the patterns of outliers are recognized as important information in the outlier detection method. This study proposes a technology trend screening framework based on a machine learning algorithm using outliers. The proposed method is as follows: first, we split the dataset by time into training and testing sets for training the Doc2Vec model. Next, we pre-process the patent documents using the trained model. The final outlier documents are selected from the preprocessed document data, through voting for the outlier documents extracted using the IQR, the three-sigma rule, and the Isolation Forest algorithm. Finally, the technical topics of the outlier documents extracted through the topic model are identified. This study analyzes the patent data on drones to describe the proposed method. Results show that, despite cumulative research on drone-related hardware and system technology, there is a general lack of research regarding the autonomous flight field.

Detecting Outliers in Data Streams Based on Minimum Rare Pattern Mining and Pattern Matching

Outliers are the major factors to influence the accuracy of data-based processing, thus, they must be discovered from collected datasets to guarantee data security. With the widely use of sensors and other monitoring equipment, data streams are becoming the main form of data. However, the huge scale of data streams results in the number of mined rare patterns very large, which makes it hard to effectively detect outliers through pattern-based outlier detection methods. Since minimal rare patterns (MRPs) can represent rare patterns and the number is much smaller, therefore, the use of MRPs on outlier detection can short the time consumption. Based on this idea, this paper proposes an outlier detection approach based on minimal rare pattern, called ODMRP, which is composed of pattern mining phase and pattern matching phase. Specifically, in the pattern mining phase, an improved minimal rare pattern mining algorithm, namely MRPM, is proposed to mine the MRPs from data streams; It first constructs two matrix structures to store information of transactions and frequent 2-patterns, and then apply “pattern extension” operations to extend frequent 2-patterns to longer patterns, at the same time, rare patterns are removed to prevent them participating into “pattern extension” operation to reduce meaningless time cost; In the pattern matching phase, we use the IM-Sunday algorithm to match the mined MRPs with the patterns stored in outlier pattern library, to find potential outliers. Extensive experimental studies show that the proposed ODMRP method can accurately detect outliers from data streams in less overhead.

Anomaly Detection Based on Convex Analysis: A Survey

As a crucial technique for identifying irregular samples or outlier patterns, anomaly detection has broad applications in many fields. Convex analysis (CA) is one of the fundamental methods used in anomaly detection, which contributes to the robust approximation of algebra and geometry, efficient computation to a unique global solution, and mathematical optimization for modeling. Despite the essential role and evergrowing research in CA-based anomaly detection algorithms, little work has realized a comprehensive survey of it. To fill this gap, we summarize the CA techniques used in anomaly detection and classify them into four categories of density estimation methods, matrix factorization methods, machine learning methods, and the others. The theoretical background, sub-categories of methods, typical applications as well as strengths and limitations for each category are introduced. This paper sheds light on a succinct and structured framework and provides researchers with new insights into both anomaly detection and CA. With the remarkable progress made in the techniques of big data and machine learning, CA-based anomaly detection holds great promise for more expeditious, accurate and intelligent detection capacities.

TG-OUT: temporal outlier patterns detection in Twitter attribute induced graphs

TG-OUT: temporal outlier patterns detection in Twitter attribute induced graphs

Game Outlier Behavior Detection System Based on Dynamic Time Warp Algorithm

This paper proposes a methodology for using multi-modal data in gameplay to detect outlier behavior. The proposed methodology collects, synchronizes, and quantifies time-series data from webcams, mouses, and keyboards. Facial expressions are varied on a one-dimensional pleasure axis, and changes in expression in the mouth and eye areas are detected separately. Furthermore, the keyboard and mouse input frequencies are tracked to determine the interaction intensity of users. Then, we apply a dynamic time warp algorithm to detect outlier behavior. The detected outlier behavior graph patterns were the play patterns that the game designer did not intend or play patterns that differed greatly from those of other users. These outlier patterns can provide game designers with feedback on the actual play experiences of users of the game. Our results can be applied to the game industry as game user experience analysis, enabling a quantitative evaluation of the excitement of a game.

New Robust Part-Based Model with Affine Transformations for Facial Landmark Localization and Detection in Big Data

In this paper, we developed a new robust part-based model for facial landmark localization and detection via affine transformation. In contrast to the existing works, the new algorithm incorporates affine transformations with the robust regression to tackle the potential effects of outliers and heavy sparse noises, occlusions and illuminations. As such, the distorted or misaligned objects can be rectified by affine transformations and the patterns of occlusions and outliers can be explicitly separated from the true underlying objects in big data. Moreover, the search of the optimal parameters and affine transformations is cast as a constrained optimization programming. To mitigate the computations, a new set of equations is derived to update the parameters involved and the affine transformations iteratively in a round-robin manner. Our way to update the parameters compared to the state of the art of the works is relatively better, as we employ a fast alternating direction method for multiplier (ADMM) algorithm that solves the parameters separately. Simulations show that the proposed method outperforms the state-of-the-art works on facial landmark localization and detection on the COFW, HELEN, and LFPW datasets.

Otolaryngologist Characteristics and Outlier Use of Balloon Sinuplasty in the Medicare Population.

Balloon sinuplasty (BSP) is associated with varied practice patterns. This study sought to identify otolaryngologist characteristics associated with BSP utilization. Retrospective analysis of Medicare claims data and the National Physician Compare database. Outlier otolaryngologists were compared to non-outliers. Otolaryngologist characteristics included sex, practice size, geographic setting, years of experience, procedure setting, 10 or fewer endoscopic sinus surgeries per year for 3 or more years, and high number of services per unique Medicare beneficiary. Outlier status was defined as performing an annual total of balloon procedures of 2 standard deviations (SDs) above the mean for all otolaryngologists in the same year. Between January 2012 and December 2017, 1,408 otolaryngologists performed 101,662 endoscopic sinus surgeries and 97,680 BSP procedures. Sixty-six outlier otolaryngologists (4.7%) accounted for 44.3% of all BSP procedures. Outlier status was associated with practice size of 10 or fewer individual providers (OR, 5.15; 95% CI, 2.73-9.74; P < .001), performance of 10 or fewer total endoscopic sinus surgeries per year for 3 or more years (OR, 3.90; 95% CI, 1.59-9.57; P=.003), and high number of overall services per beneficiary (OR 6.70; 95% CI, 1.19-37.84; P=.031). Provider sex, years of experience, and geographic setting were not associated with outlier status. Outlier BSP patterns are associated with a few otolaryngologists who are more likely to be identified in small practices and record low numbers of endoscopic surgeries. Although BSP is an appropriate and effective tool, identification of outlier patterns may help to facilitate peer-to-peer counsel. 3 Laryngoscope, 132:1340-1345, 2022.

Adjustment models for multivariate geodetic time series with vector-autoregressive errors

Abstract In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.