## 2 Power Spectral Density of Selected Disturbances
The amplitude of the oscillations increased slightly with the temperature increment. After reaching a constant temperature, the mean signal value stabilized and approached zero. These phenomena can also be observed in the PSD charts in Figure 8. The gyroscope drift due to temperature change is approximated by a line with a slope of \(-\)2 dB in the frequency range 0.001-0.09 Hz (Figure 8, upper subplot). For a stabilized operating temperature of the sensor, this drift is in fact very difficult to determine via the power spectral density plot. However, in the high-frequency range, the phenomenon of increasing noise is observed, which is the result of the influence of higher temperature on the electrical and mechanical vibrations in MEMS systems [(43; 44)]. This change is clearly observed for the tested gyroscopes in Figure 8 for the frequency range of 300-500 Hz. The noise level increases, but in practice, due to the programmable low-pass filter built into the system, it does not affect the quality of the measurements. Figure 5: Representation of the one-sided PSD for a hypothetical accelerometer, based on [(23)]. Figure 6: Plots of angular velocity \(p\), linear acceleration \(a_{z}\), and gyroscope temperature values during static recording of data from the IMU. In the tested system, the cut-off frequency was set to the maximum value, which is 256 Hz. Figure 9 shows the collective PSD characteristics for the gyroscopes installed in the pitch and yaw channel, obtained on the basis of data recorded during the same experiment. These relationships are consistent with the results obtained for the angular velocity of the roll. Figure 8: One-sided PSD for \(10^{6}\) samples of roll rate (PCIM-01 IMU) after device start (**top**) and with stabilized sensor temperature (**bottom**). Noise coefficients (sequence 1/2): K = 0.00125, B = 0.003, N = 0.0035/K = 0.00085, B = 0.002, N = 0.0035. Figure 7: PRP-W2 flight data recorder and PCIM-01 IMU [42] (**left**) installed on board an I-31T airplane (**right**). Figures 10 and 11 show the one-sided PSD determined for the set of accelerometers of the IMU system, which is one of the measurement modules of the PRP-W2 recording system. The measurement data for accelerometers and gyroscopes are from the same measurement session (Figures 6-11). In the case of PSD plots obtained for accelerometers, similarly to gyroscopes, the phenomenon of temperature drift in the frequency range from \(10^{-3}\) to \(10^{-1}\) Hz can be observed (Figure 10). Nevertheless, the influence of the increased operating temperature of the system on the noise level in the highest frequency range has a completely different character. According to the information in the literature [45], an increase in the temperature of the sensor shifts the resonance frequency of the electromechanical vibrations of the MEMS accelerometer towards lower frequencies. However, this fact can hardly be interpreted unambiguously on the basis of the analysis of the PSD diagram obtained (Figures 10 and 11). As in the case of the tested gyroscopes, the level of noise in this range has no practical importance. In the analyzed accelerometer system, the low-pass filter cut-off frequency was set to a maximum value of 260 Hz. The range of the analysis and noise comparison of individual gyroscopes and accelerometers was limited to two intervals. The first interval was when the sensors were warming up, and the second was when sensors reached a constant operating temperature (time intervals are marked in Figure 6). The values of the determined noise coefficients are presented in Tables 1 and 2 and compared with the results obtained with the Allan variance method. \begin{table}