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EN
The paper presents the analysis of the statistical errors of the meteorological parameters predicted by the WRF (Weather Research and Forecasting) model. The model is used for forecasting air pollution in the Silesian Voivodeship with an accuracy of about 70-80%. Thus, the main idea of the research was assessing to what extent the error in the forecast of meteorological parameters affects the error of the air quality forecast, which can be evaluated using the system InfoSMOG – MED for the inhabitants of the Silesian Voivodeship at www.slaskiesmogstop. It was also investigated how the reduction of the mesh size of the forecast of meteorological parameters affects the error of the forecast of these parameters, which was necessary for the next project SMART. The research was carried out for 3 computational domains: Poland, Silesian Voivodeship and Upper Silesia Metropolitan Region, each with a different grid resolution. The predicted temperature and wind speed data were compared with the measured data from the Polish synoptic stations and the stations of the METAR airports meteorological shield located in the respective domains. In addition, the error of the predicted parameters was investigated in the grid where the climatological station is located in the Śląskie Planetarium in Chorzów.
EN
This paper proposes a new approach called the Predictive Kalman Filter (PKF) which predicts and compensates model errors of inertial sensors to improve the accuracy of static alignment without the use of external assistance. The uncertain model error is the main problem in the field as the Micro Electro Mechanical System (MEMS) inertial sensors have bias which change over time, and these errors are not all observable. The proposed filter determines an optimal equivalent model error by minimizing a quadratic penalty function without augmenting the system state space. The optimization procedure enables the filter to decrease both model uncertainty and external disturbances. The paper first presents the complete formulation of the proposed filter. Then, a nonlinear alignment model with a large misalignment angle is considered. Experimental results demonstrate that the new method improves the accuracy and rapidness of the alignment process as the convergence time is reduced from 550 s to 50 s, and the azimuth misalignment angle correctness is decreased from 52′′ ± 47′′ to 4′′ ± 0.02′′.
EN
Asymptotic bias in large quantiles and moments for three parameter estimation methods, including the maximum likelihood method (MLM), moments method (MOM) and linear moments method (LMM), is derived when a probability distribution function (PDF) is falsely assumed. It is illustrated using an alternative set of PDFs consisting of five two-parameter PDFs that are lower-bounded at zero, i.e., Log-Gumbel (LG), Log-logistic (LL), Log-normal (LN), Linear Diffusion (LD) and Gamma (Ga) distribution functions. The stress is put on applicability of LG and LL in the real conditions, where the hypothetical distribution (H) differs from the true one (T). Therefore, the following cases are considered: H=LG; T=LL, LN, LD and Ga, and H=LL, LN, LD and Ga, T=LG. It is shown that for every pair (H; T) and for every method, the relative bias (RB) of moments and quantiles corresponding to the upper tail is an increasing function of the true value of the coefficient of variation (cv), except that RB of moments for MOM is zero. The value of RB is smallest for MOM and the largest for MLM. The bias of LMM occupies an intermediate position. Since MLM used as the approximation method is irreversible, the asymptotic bias of the MLM-estimate of any statistical characteristic is not asymmetric as is for the MOM and LMM. MLM turns out to be the worst method if the assumed LG or LL distribution is not the true one. It produces a huge bias of upper quantiles, which is at least one order higher than that of the other two methods. However, the reverse case, i.e., acceptance of LN, LD or Ga as a hypothetical distribution while LG or LL as the true one, gives the MLM-bias of reasonable magnitude in upper quantiles. Therefore, one should be highly reluctant in choosing the LG and LL in flood frequency analysis, especially if MLM is to be applied.
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