Publikationen & Vorträge

Assessing whether datasets follow a normal distribution is essential for valid statistical inference, yet GNSS positioning errors often deviate from Gaussian assumptions under real conditions. Despite the widespread use of normality tests, their performance on GNSS data remains insufficiently characterized, especially under heavy-tailed regimes. This study investigates long-duration GNSS latitude residuals as a one-dimensional case using stationary observations collected over a continuous 48-h period. Normality is evaluated using graphical diagnostics, descriptive statistics, and hypothesis testing, including histograms, box plots, Q–Q plots, skewness, kurtosis, and seven parametric tests. To assess robustness and sensitivity, a Monte Carlo bootstrapping procedure is applied to more than 160,000 latitude samples. For multiple sample sizes and significance levels, 10,000 replicates are used to estimate empirical power and median p-values. The results indicate clear departures from normality, with Shapiro–Wilk and D’Agostino showing the highest sensitivity, particularly for small and moderate samples. GNSS latitude errors are additionally modeled using Student’s t distribution and a Gaussian–Student’s t mixture. These models better represent the empirical distribution, especially in the upper tail, than the Gaussian model. The findings confirm that Gaussian assumptions may underestimate uncertainty in GNSS analysis. They also show that combining normality diagnostics with flexible statistical models improves error characterization under non-Gaussian conditions.

Air-quality measurements performed using unmanned aerial vehicles (UAVs) enable observations that are difficult or impossible to obtain with stationary monitoring systems. Although low-cost CO2 sensors are widely applied in such work, their accuracy is restricted by environmental influences. This study assesses the metrological performance of inexpensive NDIR CO2 sensors using a controlled test chamber. The TESTO probe results show strong temperature sensitivity, with CO2 indications varying by approximately 17 ppm per 1 °C. Measurements at −2.6 °C produced implausibly low concentrations of 275–280 ppm, despite the global baseline being about 430 ppm. Electromagnetic interference and humidity produced negligible effects on the indications. No differences appeared between measurements taken during UAV flight, after landing, or under laboratory conditions. Comparison with the manufacturer-calibrated Figaro CDM7160 sensor revealed a substantial shift in the characteristic at the lowest CO2 concentration level and a marked reduction in sensitivity, which shows that the sensor needs recalibration. The findings confirm that investigated low-cost CO2 sensors provide reasonably accurate absolute measurements only when environmental conditions are correctly compensated. However, their relatively high measurement uncertainty prevents reliable detection of small concentration changes and therefore limits their suitability for precise UAV-based air-quality studies.

Modeling the dynamics of the flow rate system is challenged by the nonlinear behavior and the noisy measurement data. Accurate models require a comprehensive understanding of fluid mechanics, as well as knowledge of all instruments in the measurement chain. This study presents a black-box optimization approach to develop a nominal Fractional-Order (FO) model of a laboratory-scale flow system. The model was constructed by repeatedly solving an optimization problem using preprocessed experimental data and averaging the resulting optimal parameters. The nominal FO model was then validated against unseen, unprocessed measurement data to assess its robustness. The parameter sensitivity of the proposed model was analyzed by introducing +10% and +20% perturbations in each parameter individually. Error analysis evidences that root mean squared, mean absolute, and mean absolute percentage errors with the proposed model have reduced to 9.3%, 5.1%, and 5.3%, respectively, compared to those integer-order models. Furthermore, residual-based distribution analysis confirms the robustness of the approach, with residuals tightly concentrated around the lowest values. Although the FO model incurs a higher computational cost during optimization, it was significantly reduced using an online optimizer. The proposed model demonstrates superior robustness and accuracy, making it a compelling choice for precise modeling.

As part of the project, a system was developed to measure and control the conditions within a terrarium. The system measures air temperature and humidity, as well as soil moisture, and uses this information to control lighting, heating, and misting. Information about the status of the devices can be accessed via a custom-built mobile application (web-based). The application also allows users to set selected parameters, such as lighting periods and temperature. The device is equipped with a microprocessor system based on a Raspberry Pi. The entire system is aesthetically designed. The students equipped the terrarium with decorations, sensors, and actuators, while the electronics were enclosed in a housing produced using 3D printing technology.

As part of the project, a system was developed to maintain optimal moisture levels in two flower pots. Each pot is controlled independently. The input data includes soil moisture and temperature. Depending on the implemented algorithm, the system dispenses water from a reservoir. The entire setup is controlled by a microprocessor-based system built on a Raspberry Pi. The current operating status, temperature, and humidity are displayed on an e-paper display. The whole system is aesthetically designed using 3D printing.

Accurately characterising datasets is crucial for effective statistical modelling, particularly when analysing Global Navigation Satellite System (GNSS) data. While traditional approaches often assume a Gaussian distribution, real-world GNSS datasets frequently exhibit heavy-tailed and skewed properties, prompting the need to explore alternative statistical models. The study examines the suitability of non-Gaussian distributions, specifically the Laplace, skew-normal, skew-t, and generalised hyperbolic (GH) distributions, for modelling GNSS data obtained from a stationary receiver. Using empirical GNSS datasets, we estimate parameters within confidence intervals (CIs) through weighted maximum likelihood estimation (WMLE). Model performance is assessed using log-likelihood analysis, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and root mean squared error (RMSE). Our comparative analysis shows that heavy-tailed and skewed distributions, particularly those offering greater flexibility in capturing extreme deviations, consistently outperform the conventional normal distribution. Among the non-Gaussian models considered, the GH distribution provides the best overall performance. These results emphasise the importance of selecting appropriate statistical models to improve uncertainty quantification in GNSS-based measurements.

Regulated flow systems exhibit a variable dynamic behavior when subjected to distinct inputs. The significant non-linear behavior of the system at low inputs and the difference in the output pattern for the increase and decrease in flow pose challenges in modeling. One way is to identify separate sets of parameters for each input-output data set and develop distinct models. However, this approach is computationally expensive when designing a single controller covering the whole input range. To overcome the said limitation, we used a Principal Component Analysis (PCA) based estimation technique. The developed Linear Parameter Varying (LPV) dynamic model describes real measurement values of a laboratory flow system. The data treatment consists of (1) an automated input-output data acquisition, (2) 3rd-order model estimation from measured data, (3) the reduction of the dynamic parameters using PCA, and (4) the development of a reduced LPV model for the entire input range. The LPV model presents its output response comparable to the experimentally taken flow rates. The proposed modeling technique can help design a single controller sufficient to achieve the desired output applicable in the whole measuring range. The effectiveness of our approach suggests its use for synthesizing an LPV controller for flow systems.

Accurate positioning obtained from the Global Navigation Satellite System (GNSS) is crucial for many applications; however, environmental and instrumental factors, such as satellite geometry, signal multipath, and atmospheric delays, often degrade its accuracy. Traditional uncertainty quantification and filtering methods, such as the Kalman Filter (KF), assume that the measurement noise follows a Gaussian distribution. In practice, real-world GNSS data often violate this assumption, showing skewness, heavy tails, and outliers that distort the estimates and reduce the accuracy. This study systematically evaluates the impact of non-Gaussian noise on GNSS positioning accuracy and introduces a unified framework that integrates robust statistical methods and nonlinear filtering. Specifically, we compared the performance of the KF, Median Absolute Deviation (MAD), and Particle Filter (PF) on stationary GNSS data. The evaluation used comprehensive accuracy and uncertainty diagnostics, including the root mean square error (RMSE), probable circular error (CEP), estimated position error at 95% (R95), covariance analysis, and nonparametric bootstrapping. The results demonstrate that Gaussian-based models fail under heavy-tailed noise, whereas MAD and PF achieve superior reliability by suppressing outlier influence and capturing complex error distributions. The proposed framework advances GNSS uncertainty quantification by bridging robust statistics and nonlinear filtering. It offers a statistically sound and practical approach for real-world environments in which non-Gaussian noise is prevalent.

In statistical analysis, evaluating the normality of large datasets is crucial for validating parametric tests, particularly in areas such as Global Navigation Satellite System (GNSS) measurements, where data often exhibit non-normal characteristics resulting from their variability and errors. This research aims to transform the measured GNSS data and to assess the effectiveness of transformation methods in achieving normality. Techniques like logarithmic, quantile and rank-based Inverse Normal Transformation (INT) were evaluated using visual methods (histograms, Q-Q plots), descriptive statistics (skewness, kurtosis) and statistical tests, including Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Lilliefors (LF), D’Agostino K-squared (DA), Shapiro-Wilk (SW), Jarque-Bera (JB), Cramérvon Mises (CM), and Pearson Chi-square (Chi2) tests. The sensitivity of these tests to deviations from normality was assessed through the Receiver Operating Characteristic (ROC) analysis and the Area Under the Curve (AUC) values at a significance level of 0.1, using Monte Carlo (MC) simulations across the varying sample sizes. The results showed that untransformed latitude data consistently failed normality tests, while transformed data displayed normal characteristics. The rank-based INT showed superior effectiveness, influenced by the original distribution and characteristics of the dataset. The findings underscore the importance of tailored transformations in large-scale data applications, enhancing the accuracy and applicability of parametric statistical methods in geospatial and other industrial domains.

The availability of two additional tunable parameters compared with Proportional Integral Derivative (PID) controllers makes it possible to incorporate fractional-order (FO) integral/derivative actions. The selection of the optimization algorithm and objective function is important for tuning the fractional-order PID controller. This paper presents the formulation of the FOPID controller design as an optimization problem and its solution using four built-in algorithms in MATLAB. Each algorithm solves the optimization by minimizing two cost functions resulting eight sets of controller parameters. To overcome the sensitivity of algorithms to the initial and boundary values of the parameters, we considered nine different initial and boundary conditions. The proposed method considers the minimum of the optimal values obtained in each case. This provides globally-optimal FOPID controllers. To validate its efficiency, the proposed method uses a Twin Rotor Aerodynamic System (TRAS) as an example. Comparison with a nonlinear approach shows that the proposed approach ensures tracking with minimal and smooth control efforts.

Particulate matter (PM) suspended in the air significantly impacts human health. Those of anthropogenic origin are particularly hazardous. Poland is one of the countries where the air quality during the heating season is the worst in Europe. Air quality in small towns and villages far from state monitoring stations is often much worse than in larger cities where they are located. Their residents inhale the air containing smoke produced mainly by coal-fired stoves. In the frame of this project, an air quality monitoring network was built. It comprises low-cost PMS7003 PM sensors and ESP8266 microcontrollers with integrated Wi-Fi communication modules. This article presents research results on the influence of the PM sensor location on their indications. It has been shown that the indications from sensors several dozen meters away from each other can differ by up to tenfold, depending on weather conditions and the source of smoke. Therefore, measurements performed by a network of sensors, even of worse quality, are much more representative than those conducted in one spot. The results also indicated the method of detecting a sudden increase in air pollutants. In the case of smokiness, the difference between the mean and median indications of the PM sensor increases even up to 400 µg/m3 over a 5 min time window. Information from this comparison suggests a sudden deterioration in air quality and can allow for quick intervention to protect people’s health. This method can be used in protection systems where fast detection of anomalies is necessary.