## 3 Allan's Method of Variance
The noise coefficient of the gyroscope \(K\) could not be identified with the AV method in the case of the gyroscope measuring the angular velocity \(P\), while when it comes to the angular velocity \(R\), an approximate value was obtained due to the characteristic slope of less than 0.5 dB/dec in the analyzed range. Similar tests were also carried out for the triaxial accelerometer, and the AV results obtained are presented in the graph in \[\sigma(\tau)^{2}=\frac{1}{2}\langle{(\overline{y}_{i+1}-\overline{y}_{i})}^{2}\rangle \tag{11}\]9 The values of the determined noise coefficients are presented in \[\sigma(\tau)^{2}\cong\frac{1}{2(N-1)}\sum_{i=1}^{N-1}{(\overline{y}_{i+1}- \overline{y}_{i})}^{2} \tag{12}\]0  
According to the gyroscope manufacturer's data, the ARW value (white noise coefficient N) determined at a signal sampling frequency of 10 Hz is 0.005 deg/\(\sqrt{\mathrm{s}}\). In the experiment, the signal was sampled with a frequency of 1000 Hz, obtaining ARW values in the range of 0.00305-0.004 deg/\(\sqrt{\mathrm{s}}\) (Table 1). The root mean square (RMS) noise value read from the catalog data for the tested gyroscope set is 0.06 deg/s for a signal with a bandwidth limited by a digital low-pass filter to 92 Hz. The experimentally determined RMS values for gyroscopes with a stabilized operating temperature, at a sampling frequency of 1000 Hz and a bandwidth limited to 256 Hz, were:  
* \(\mathrm{RMS_{p}}=0.077\) deg/s;
* \(\mathrm{RMS_{q}}=0.079\) deg/s;
* \(\mathrm{RMS_{r}}=0.084\) deg/s. \[\sigma(\tau)^{2}\cong\frac{1}{2(N-1)}\sum_{i=1}^{N-1}{(\overline{y}_{i+1}- \overline{y}_{i})}^{2} \tag{12}\]1 The Allan variance for a hypothetical gyroscope, based on [23]. \[\sigma(\tau)^{2}\cong\frac{1}{2(N-1)}\sum_{i=1}^{N-1}{(\overline{y}_{i+1}- \overline{y}_{i})}^{2} \tag{12}\]2 Allan variance of the tested gyroscopes for (\(p\), \(q\), \(r\) angular rate) measurements at a fixed temperature of the PCIM-01 IMU (PRP-W2 recording system); AV = \(\sigma(\tau)\). The RMS noise value read from the catalog data for the tested set of accelerometers in the measurement range \(\pm 2\) g is 0.039 m/s\({}^{2}\) and concerns a signal with a frequency of 100 Hz. The experimentally determined RMS values for gyroscopes with a stabilized operating temperature, at a sampling frequency of 1000 Hz (bandwidth limited to 256 Hz by a digital filter at the output of the MEMS system), and the measurement range set to \(\pm 4\) g, were:  
* \(\mathrm{RMS_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{  \mathrm{  }}}}}}}}}}}}}\) = 0.027 m/s\({}^{2}\);
* \(\mathrm{RMS_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{  }}}}}}}}}}}}}}}\) = 0.028 m/s\({}^{2}\);
* \(\mathrm{RMS_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{  }}}}}}}}}}}}}}}}}\) = 0.040 m/s\({}^{2}\). \[\sigma(\tau)^{2}\cong\frac{1}{2(N-1)}\sum_{i=1}^{N-1}{(\overline{y}_{i+1}- \overline{y}_{i})}^{2} \tag{12}\]3 Allan variance of the tested accelerometers measured at a fixed temperature of the PCIM-01 IMU; \(\mathrm{AV}=\sigma(\tau)\). The power spectral density value determined by the manufacturer of the three-axis accelerometer is 0.0039 \(\rm(m/s^{2})/Hz^{-0.5}\) for a signal with a frequency of 10 Hz. According to Equation (26), the \(RMS\) noise value for this signal is 0.0194 \(\rm m/s^{2}\):  
\[\sigma(\tau)^{2}\cong\frac{1}{2(N-1)}\sum_{i=1}^{N-1}{(\overline{y}_{i+1}- \overline{y}_{i})}^{2} \tag{12}\]4  
The \(RMS\) values obtained experimentally are comparable to the manufacturer's data. However, it should be noted that the sampling frequency of the tested system was 1 kHz, while the catalog data refers only to sampling rates of 10 and 100 Hz.