# Analysis of Satellite Compass Error's Spectrum
## 2 Materials and Methods
### Conducted Experiments
#### 2.3.1 Twenty-Four-Hour Stationary Measurement Experiment  
The stationary experiment results displayed the typical characteristics of this type of test. It was performed from 27 April 1300 UTC to 28 April 1200 UTC, 2020 in the suburban area of Gdynia, Poland, in the vicinity of a wall of a one-story building, partially obscuring the sky from the north side. The compasses' antennas were placed 4 m above the ground (Figure 5(b)). Data were recorded using the NMEA 0183 protocol through the RS-232 and RS-422 serial ports. The satellite constellation was assessed before data registration and the cut off angle of 20 degrees was applied. GPS satellite elevation during the test is presented in Figure 7 and their visibility is presented in Figure 8. The Advanced Navigation compass was set to the stationary variant of measurements. The following settings were applied for Furuno SC50: sampling frequency, 1 Hz; position smooth, 5 s; (SOG) speed over ground smooth, 5 s. A sampling frequency of 1 Hz was set for the Novatel compass.  
It must be emphasized that the heading determination needs signals from at least five satellites, in contrast to the position determination, which requires four. Only four satellites have been available twice during the data registration (this occurred at about 0300 UTC and 0600 UTC on 28 April). The largest distortions between real time and average heading value in this test were observed for the FURUNO SC50 compass (Figure 9b). The maximum heading distortion for this compass is 2.8 degrees. The offset values fluctuated between \(-\)2.0 and \(+\)2.8 degrees. Similar results were observed for the Advanced Navigation compass with heading distortion values in the range of \(-\)2.2 to \(+\)2.7 degrees (Figure 9a). The lowest values of the exchange rate distortion registered for the NOVATEL PWRPAK 7D-E1 compass, however, during the tests, its antennas were 1.2 m apart, which is twice the distance of the other two cases. The heading distortion in this case varied from \(-\)0.7 to \(+\)0.8 degrees (Figure 9c).  
The root mean square of the heading distortion for the Furuno compass is 0.6 degrees, for Advance Navigation is 0.4 degrees and for Nov  
Figure 8: Visibility of satellites (**a**) and dilution of precision coefficients (**b**) in the measurement area on 27–28 April 2020. Notes: Visibility (**a**): red—4 satellites, brown—5 satellites, yellow—6 satellites, dark green—7 satellites, light green—8 satellites, blue—9 satellites. DOP (Dilution of Precision (**b**): red—geometrical DOP, green—position DOP, blue—vertical DOP, brown—horizontal DOP, magenta—time DOP. (Source: Trimble Planning 2.9, 2010).  
Figure 9: The example subsets of stationary heading registrations by the Advanced Navigation compass (**a**), the Furuno compass (**b**) and the Novatel compass (**c**) (27, 28 April 2020).  
In order to perform the spectrum analysis of the signal in the frequency domain, the presentation of the frequency band in the range above f = 0.1 Hz was abandoned due to the negligible variability of the signal amplitude--heading distortion, which is typical for stationary measurements. Stationary registration results are very similar for all three compasses, characterized by a very low frequency of heading changes, falling in the band lower than 0.02 Hz. However, the amplitudes of these changes vary. The maximum value for the Furuno compass was 0.21 degrees, for Advanced Navigation 0.19 degrees, and for the Novatel product, it was only 0.08 degrees. Undoubtedly, this is due to the length of the base line between antennas, but it can be assumed that this is also the result of the different method of filtration or azimuth calculation. Heading registration spectrum for the three compasses are shown in the Figure 10.