###### Abstract
Compressor blades can oscillate with a frequency of several thousand hertz [11]. In the case of piston engines, vibrations with frequencies reaching hundreds of hertz should be expected [12]. The aircraft oscillation frequency, characteristic of short-period motion, is counted in single hertz for small sport aircraft [13] and in tenths of hertz for large structures [13; 14]. The period of oscillation in phugoid motion reaches even hundreds of seconds [14]. The same applies to the amplitudes of the co-occurring phenomena, which, depending on the class of the phenomenon and the phase of flight, may be close to measurement noise, and in another extreme case--reach beyond the operating range of the measuring equipment, even leading to its destruction. For a proper choice of measurement system elements, it is necessary to take into consideration several aspects, such as, for instance, environmental conditions or measurement system properties. First, it is necessary to analyze the properties of the measured signals (typical frequencies appearing in the system, as well as signal bands). With the knowledge of signal properties, sensors can be selected. The properties of the sensors are of great significance. They also determine the behavior of calculated signals. Very important data registered on board aircraft are attitude angles. They are calculated from angular rates and corrected by accelerations. As mentioned, the properties of attitude angles depend on angular rate and acceleration sensor properties, as well as the data estimation algorithm. When analyzing the applicability of sensors, the nominal operating range of the system (measurement range), acceptable environmental conditions, and errors occurring in static and dynamic conditions are usually taken into account. Measurement frequency is determined by the purpose of measurements and data collection, as well as the task and kind of aircraft. Usually, for control, it is necessary to measure accelerations and angular rates with frequencies from 10 Hz up to 400 Hz. For other purposes, the desired frequencies are much higher. For sensor selection, it is vital to verify MEMS stochastic properties. The properties of sensors strongly influence the calculated attitude. Figure 1 shows a general scheme of the attitude and heading reference system (AHRS). Figure 1: AHRS scheme. \(P\), \(Q\), \(R\)—measured angular rates; \(a_{x}\), \(a_{y}\), \(a_{z}\)—measured acceleration; \(H_{x}\), \(H_{y}\), \(H_{z}\)—magnetic field strength vector components. The AHRS system provides attitude angles and headings. Angular rate sensors measure angular rates \(P\), \(Q\), and \(R\), in the body frame. To calculate attitude and heading, angular rates are transformed from the body frame to the earth frame. Next, angular rates \(\dot{\Phi}\), \(\dot{\Theta}\), and \(\ddot{\Psi}\) in the earth frame are integrated and corrected. For correction, two algorithms are usually used. The first one is the Kalman filter [15], and the second one is the complementary filter [16], also used in several other solutions [15; 17; 18; 19; 20]. The Kalman filter minimizes the estimated value variance error, which makes it highly popular. However, its disadvantage is its computational complexity, which increases computational costs [21]. For this reason, it is the complementary filter that is applied in some solutions for the calculation of attitude and heading angles. From the angular rate, an angle can be easily calculated:  
\[\varphi_{G}=\int as_{g}dt \tag{1}\]  
where  
\(as_{g}\)--angular speed from gyroscopes;  
\(\varphi_{G}\)--angle calculated from gyroscopes. Another way to estimate the angle is by calculating it from accelerometer data, e.g.,:  
\[\varphi_{acc}=\tan^{-1}\frac{a_{y}}{a_{z}} \tag{2}\]  
where  
\(a_{y},a_{z}\)--horizontal and vertical acceleration from accelerometers. Angles calculated from gyroscope data are burdened with low-frequency errors (drift). Angles calculated from accelerometers are burdened with noises, which are high-frequency errors.