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1

Medium- and long-term prediction of polar motion using weighted least squares extrapolation and vector autoregressive modeling

Lei Yu, Zhao Danning, Guo Min

Artificial Satellites : Journal of Planetary Geodesy

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2023

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Vol. 58, No. 2

42--55

EN

This article presents the application of weighted least squares (WLS) extrapolation and vector autoregressive (VAR) modeling in polar motion prediction. A piecewise weighting function is developed for the least squares (LS) adjustment in consideration of the effect of intervals between observation and prediction epochs on WLS extrapolation. Furthermore, the VAR technique is used to simultaneously model and predict the residuals of xp, yp pole coordinates for WLS misfit. The simultaneous predictions of xp, yp pole coordinates are subsequently computed by the combination of WLS extrapolation of harmonic models for the linear trend, Chandler and annual wobbles, and VAR stochastic prediction of the residuals (WLS+VAR). The 365-day-ahead xp, yp predictions are compared with those generated by LS extrapolation+univariate AR prediction and LS extrapolation+VAR modeling. It is shown that the xp, yp predictions based on WLS+VAR taking into consideration both the interval effect and correlation between xp and yp outperform those generated by two others. The accuracies of the xp predictions are 13.97 mas, 18.47 mas, and 20.52 mas, respectively for the 150-, 270-, and 365-day horizon in terms of the mean absolute error statistics, 36%, 24.8%, and 33.5% higher than LS+AR, respectively. For the yp predictions, the 150-, 270-, and 365-day accuracies are 15.41 mas, 21.17 mas, and 21.82 mas respectively, 27.4%, 11.9%, and 21.8% higher than LS+AR respectively. Moreover, the absolute differences of the WLS+VAR predictions and observations are smaller than the differences from LS+VAR and LS+AR, which is practically important to practical and scientific users, although the improvement in accuracies is no more than 10% relative to LS+VAR. The further comparison with the predictions submitted to the 1st Earth Orientation Parameters Prediction Comparison Campaign (1st EOP PCC) shows that while the accuracy of the predictions within 30 days is comparable with that by the most accurate prediction techniques including neural networks and LS+AR participating in the campaign for xp, yp pole coordinates, the accuracy of the predictions up to 365 days into the future are better than accuracies by the other techniques except best LS+AR used in the EOP PCC. It is therefore concluded that the medium- and long-term prediction accuracy of polar motion can be improved by modeling xp, yp pole coordinates together.

2

Improving state estimation in smart distribution grid using synchrophasor technology: a comparison study

Richter M., Komarnicki P., Hauer I.

Archives of Electrical Engineering

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2018

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Vol. 67, nr 3

469-–483

EN

Both the growing number of dispersed generation plants and storage systems and the new roles and functions on the demand side (e.g. demand side management) are making the operation (monitoring and control) of electrical grids more complex, especially in distribution. This paper demonstrates how to integrate phasor measurements so that state estimation in a distribution grid profits optimally from the high accuracy of PMUs. Different measurement configurations consisting of conventional and synchronous mea- surement units, each with different fault tolerances for the quality of the calculated system state achieved, are analyzed and compared. Weighted least squares (WLS) algorithms for conventional, linear and hybrid state estimation provide the mathematical method used in this paper. A case study of an 18-bus test grid with real measured PMU data from a 110 kV distribution grid demonstrates the improving of the system’s state variable’s quality by using synchrophasors. The increased requirements, which are the prerequisite for the use of PMUs in the distribution grid, are identified by extensively analyzing the inaccuracy of measurement and subsequently employed to weight the measured quantities.

3

Particle Filter in State Vector Estimation Problem for Power System

Kozierski P., Lis M., Ziętkiewicz J.

Pomiary Automatyka Robotyka

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2014

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R. 18, nr 1

76--81

EN

Particle Filter is a tool, which has been used more frequently over the years. Calculations with using Particle Filter methods are very versatile (in comparison to the Kalman Filter), which can be used in high complex and nonlinear problems. Example of such a problem is the power system, where Particle Filter is used to state estimation of network parameters based on measurements. Paper presents theoretical basis regarding Particle Filter and power system state estimation. Results of experiment have shown that Particle Filter usually gives better outcome comparing to the Weighted Least Squares method. In extension Multi Probability Density Function Particle Filter is proposed, which improves obtained results so that they are always better than Weighted Least Squares method.

PL

Filtr cząsteczkowy jest narzędziem, które z roku na rok jest coraz chętniej wykorzystywane. Dużą zaletą obliczeń wykorzystujących metody filtru cząsteczkowego jest ich duża uniwersalność - w przeciwieństwie do filtru Kalmana mogą być stosowane nawet w bardzo skomplikowanych i silnie nieliniowych obiektach. Przykładem takiego układu jest sieć elektroenergetyczna, a problem, który został rozwiązany przy wykorzystaniu metody filtru cząsteczkowego to estymacja stanu sieci na podstawie pomiarów. W artykule przedstawiono podstawy teoretyczne dotyczące filtrów cząsteczkowych oraz estymacji stanu w sieci elektroenergetycznej. Przedstawiono także wyniki symulacji porównujących wyniki estymacji wykorzystujących zarówno standardową metodę, jak i metodę filtru cząsteczkowego. W wyniku przeprowadzonego doświadczenia stwierdzono, że zaproponowana metoda estymacji stanu w układzie jest na ogół lepsza od standardowej metody WLS (ważonych najmniejszych kwadratów). W rozszerzeniu zaproponowano filtr cząsteczkowy złożony z kilku funkcji gęstości prawdopodobieństwa, który polepsza estymację wektora stanu. Dzięki zastosowaniu algorytmu otrzymywane wyniki są zawsze lepsze od metody ważonych najmniejszych kwadratów.

4

Normal maximum likelihood, weighted least squares, and ridge regression estimates

Withers C. S., Nadarajah S.

Probability and Mathematical Statistics

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2012

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Vol. 32, Fasc. 1

11--24

EN

There have been many papers published (in almost every statistics related journal) suggesting that normal maximum likelihood is superior or inferior to weighted least squares and other approaches. In this note, we show that the three main estimation methods (normal maximum likelihood, weighted least squares and ridge regression) all have the same asymptotic covariance and that there is no gain in efficiency among them. We also show how the bias of these estimators can be reduced and conduct a simulation study to illustrate the magnitude of bias reduction.

5

Wpływ usytuowania punktów pomiarowych na przebieg prostej

Moszczyński L.

Przegląd Elektrotechniczny

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2011

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R. 87, nr 3

271-273

PL

W obliczeniach liniowej regresji dla danych które nie są homoscedastyczne najdogodniej zastosować metodę regresji ważonej. Celem artykułu jest pokazanie jaki wpływ na najlepiej dopasowaną prostą regresji ważonej miałoby dodanie nowego punktu pomiarowego. Dzięki temu możliwe jest lepsze planowanie eksperymentu.

EN

When we want to calculate a linear regression line for data that is not homoscedastic, the simplest way to do this is to use weighted least squares regression. The aim of this article is to show what influence the addition of a new measurement point has on the course of "best line" in weighted regression. In this way, the experiment can be planned better.