Understanding Least Squares Estimation and Geomatics Data Analysis

Ogundare, John Olusegun

doi:10.1002/9781119501459

Cited by 24 publications

(15 citation statements)

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“…Which is the same metric used to evaluate linear leastsquares models in estimation theory and in linear regression models [47]. From equation (11), a natural method to determine the best estimation of x is to obtain the matrix W Dtrain,λbest , which minimizes the MSE applied to the difference between the true state variables x and the estimated counterparts x:…”

Section: B Least-square Optimization Modelmentioning

confidence: 99%

Design and Implementation of a Machine Learning State Estimation Model for Unobservable Microgrids

et al. 2022

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An observable microgrid may become unobservable when sensors are at fault, sensor data is missing, or data has been tampered by malicious agents. In those cases, state estimation cannot be performed using traditional approaches without pseudo-measurements. To address the lack of observability, this article presents the design and implementation of a novel three-phase state estimation method for unobservable and unbalanced AC microgrids, using machine learning techniques, without pseudo-measurements, and under heteroscedastic (i.e., non-constant variance) noise. The proposed machine learning state estimation (MLSE) makes full use of multiple candidate models trained with a small number of power flow simulations via OpenDSS, through random levels of demand and renewable generation in every simulation, enhanced through a proposed Tikhonov regularization operator. To deal with the heteroscedastic nature of measurements, a recursive average model is proposed to accurately estimate the state variables. Results are obtained using real data from a microgrid located on the main campus of the State University of Campinas (UNICAMP), in Brazil. The method can be easily adapted to microgrids with different configurations, distributed energy resources, and measurements. It is shown that the proposed MLSE outperforms the traditional weighted least square (WLS) state estimator.INDEX TERMS Machine learning, microgrids, Moore-Penrose left pseudoinverse, Tikhonov regularization operator, recursive average model.

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Section: B Least-square Optimization Modelmentioning

confidence: 99%

Design and Implementation of a Machine Learning State Estimation Model for Unobservable Microgrids

et al. 2022

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“…Plus, the precision of the estimated parameter expresses the degree of closeness between the estimated parameter. The precision of adjusted parameters is given usually by the variance or standard deviation [34]. The principle of the LS is the estimation of unknown parameters, given a set of observations, satisfying minimizes the sum of the squares of the residuals [33,34].…”

Section: Least Squares Adjustmentmentioning

confidence: 99%

Uncertainty Quantification of the Traffic Assignment Model

Seger

Kisgyörgy

2020

Period. Polytech. Civil Eng.

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Forecasting of traffic flow in the traffic assignment model suffered to a wide range of uncertainties arising from different sources and exacerbating through sequential-stages of the travel demand model. Uncertainty quantification can provide insights into the level of confidence on the traffic assignment model outputs, and also identify the uncertainties of the input Origin-Destination matrix for enhancing the forecasting robustness of the travel demand model. In this paper, a systematic framework is proposed to quantify the uncertainties that lie in the Origin-Destination input matrix. Hence, this study mainly focuses on predicting the posterior distributions of uncertainty Origin-Destination pairs and correcting the biases of Origin-Destination pairs by using the inverse uncertainty quantification formulated through Least Squares Adjustment method. The posterior distributions are further used in the forward uncertainty quantification to quantify the forecast uncertainty of the traffic flow on a transport network. The results show the effectiveness of implementing the inverse uncertainty quantification framework in the traffic assignment model. And demonstrate the necessity of including uncertainty quantification of the input Origin-Destination matrix in future work of travel demand modelling.

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“…If the traverse is now done with a bearing of a line known, there will be 2 datum defects for lack of fixed or constrained (y, x) coordinates. One of the consequences of datum defects is that they make it impossible to solve least squares adjustment of survey network where coordinates are the unknown parameters [10].…”

Section: Datum Problem Of the Geodetic Networkmentioning

confidence: 99%

Influence of the Datum Definition on the Accuracy of Horizontal Geodetic Control Networks for Engineering Objects

Tuno¹,

Mulahusić²,

Topoljak³

2019

J. Civ. Eng. Constr.

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For the construction of various civil engineering structures, particular care should be taken in the perspective of geodetic control. Therefore, the design and implementation of the geodetic network deserves special attention. This paper is focused on various aspects of datum definitions for tested micro-triangulation network. It was shown that the geometrical distribution of datum points in a minimally constrained solution has a great impact on the accuracy of the geodetic network. Estimates of the accuracies of individual station y-x coordinates, error circles and error ellipses, obtained by free adjustment, where the datum selection was independent of errors in fixed coordinates, revealed much better quality of control points.

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Understanding Least Squares Estimation and Geomatics Data Analysis

Cited by 24 publications

References 0 publications

Design and Implementation of a Machine Learning State Estimation Model for Unobservable Microgrids

Design and Implementation of a Machine Learning State Estimation Model for Unobservable Microgrids

Uncertainty Quantification of the Traffic Assignment Model

Influence of the Datum Definition on the Accuracy of Horizontal Geodetic Control Networks for Engineering Objects

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