Vehicle parameters have a significant impact on handling, stability, and rollover propensity. This study demonstrates two methods that estimate the inertia values of a ground vehicle in real-time. Through the use of the Generalized Polynomial Chaos (gPC) technique for propagating the uncertainties, the uncertain vehicle model outputs a probability density function for each of the variables. These probability density functions (PDFs) can be used to estimate the values of the parameters through several statistical methods. The method used here is the Maximum A-Posteriori (MAP) estimate. The MAP estimate maximizes the distribution of P(β|z) where β is the vector of the PDFs of the parameters and z is the measurable sensor comparison. An alternative method is the application of an adaptive filtering method. The Kalman Filter is an example of an adaptive filter. This method, when blended with the gPC theory is capable at each time step of updating the PDFs of the parameter distributions. These PDF’s have their median values shifted by the filter to approximate the actual values.
Nutrient pollution such as nitrate (NO3−) can cause water quality degradation in rivers used as a source of drinking water. This situation raises the question of how the nutrients have moved depending on many factors such as land use and anthropogenic sources. Researchers developed several nutrient export coefficient models depending on the aforementioned factors. To this purpose, statistical data including a number of factors such as historical water quality and land use data for the Melen Watershed were used. Nitrate export coefficients are estimates of the total load or mass of nitrate (NO3−) exported from a watershed standardized to unit area and unit time (e.g. kg/km2/day). In this study, nitrate export coefficients for the Melen Watershed were determined using the model that covers the Frequentist and Bayesian approaches. River retention coefficient was determined and introduced into the model as an important variable.
The problem of estimation of the long-term environmental noise hazard indicators and their uncertainty is presented in the present paper. The type A standard uncertainty is defined by the standard deviation of the mean. The rules given in the ISO/IEC Guide 98 are used in the calculations. It is usually determined by means of the classic variance estimators, under the following assumptions: the normality of measurements results, adequate sample size, lack of correlation between elements of the sample and observation equivalence. However, such assumptions in relation to the acoustic measurements are rather questionable. This is the reason why the authors indicated the necessity of implementation of non-classical statistical solutions. An estimation idea of seeking density function of long-term noise indicators distribution by the kernel density estimation, bootstrap method and Bayesian inference have been formulated. These methods do not generate limitations for form and properties of analyzed statistics. The theoretical basis of the proposed methods is presented in this paper as well as an example of calculation process of expected value and variance of long-term noise indicators LDEN and LN. The illustration of indicated solutions and their usefulness analysis were constant due to monitoring results of traffic noise recorded in Cracow, Poland.