Methods and Algorithms for Correcting Kinematic Equations in the Problem of Determining the Orientation of an Object

Algorithms of a strapdown inertial orientation system with an inertial measurement module consisting of a three-component gyroscope, accelerometer, and magnetometer are considered. The aim of the work is to improve the algorithms for processing sensor information to ensure the asymptotic stability of the system, tuning for the Schuler period and the low-pass filter with a given bandwidth. The kinematic Poisson equations with positional and integral-positional correction based on the information of accelerometers and magnetometers are considered. The stability and frequency characteristics of the system in relation to the sensor output signals are analyzed. It is shown that the positional correction in each channel does not allow you to adjust the system for the Schuler period. The integral-positional correction allows this adjustment, but in relation to the gyroscope signals, the system is a bandpass filter and does not suppress noise in the bandwidth. The advantages of using positional correction with cross-links in the sense of tuning the frequency characteristics of the system to the Sharper frequency and the third-order low-pass filter are shown. The analysis of the influence of angular velocities confirmed the asymptotic stability of the system with their changes in a given range. The results of mathematical modeling confirmed the compensation of errors in the initial orientation system display, the reduction of noise power in the estimates of the orientation angles in relation to the noise in the sensor signals, and the ability to configure the system for the Schuler period.

Synthetic rainfall for Germany based on simulations from two stochastic models

<p>For planning of urban drainage systems using hydrological models, long, continuous precipi-tation series with high temporal resolution are needed. Since observed time series are often too short or not available everywhere, the use of synthetic precipitation is a common alternative.</p><p>This contribution discusses the results of a research project, providing 5-minutes continuous stochastic point rainfall data for entire Germany for urban hydrological applications. Two different stochastic rainfall models are employed: a parametric stochastic model based on Alternating-Renewal processes and a non-parametric approach based on Resampling. Using rainfall observations from about 800 stations in Germany, the parameters of the models are regionalized. Rainfall and discharge characteristics are utilised for the evaluation of the model performance using a subset of 45 stations.</p><p>The results show, that stochastic rainfall from either of the models is better suited for urban hydrologic design, compared to the common practice scenario, where data from the nearest precipitation station is used. Notably, it could be shown that a mixture of generated rainfall from both models leads to a compensation of errors and further improves results, contrasted with using only data from one single model.</p>