# Analysis of Satellite Compass Error's Spectrum
## 2 Materials and Methods
### Conducted Experiments
#### 2.3.2 Automotive Experiments  
The analysis of heading oscillations in compass indications in stationary conditions were performed based on calculating distortions from the average value. In this case, the direction of the compass does not matter. In dynamic conditions, the reference direction is needed. Therefore, the tests were conducted in such conditions that the direction of movement of the object was known and determined by natural conditions, i.e., on a straight sections of road or tram track. Knowing the heading of the vehicle during movement, the distortions of individual readings and the oscillations were calculated, treated as corrected measurements, and analyzed using a Fourier analysis. Matlab scripts were written to perform the analysis.  
Automotive experiments, with the antennas mounted on the roof of the car, were carried out on a straight section of a rural road with a length of 1550 m and a direction of 342/162 degrees. There are single tall trees in the central part of the test section, along the road, and from the east side, which can occasionally cause interference. This is visible in the Figure 11 in the form of a break in position data registration due to incidental obstruction of the satellite signal. Such a gap is a result of a specific configuration of the satellites during this test. During other tests, similar gaps occurred in other places. Unfortunately, it was not possible to guarantee a repetitive configuration of the satellites, however, these records can be treated as examples of how important and diverse the impact of obstructions on the work of such compasses can be. The devices have options to adjust to the vehicle movement, that is, the Novatel compass has \"sampling frequency: 1 Hz\" and Furuno has \"position smooth, 1 s; SOG smooth, 1 s; sampling frequency, 1 Hz\". In addition, it is worth noting that the compasses have advanced inertial systems for the stabilization of readings, but this did not ensure the complete elimination of rapid changes at the time of appearance of another configuration of the satellites received by the device due to the appearance of obstructions.  
Figure 10: Heading registration spectrum for the three compasses: (**a**) Advanced Navigation, (**b**) Furuno, (**c**) Novatel. Stationary experiment, 27, 28 April 2020.  
Measurements were carried out at speeds of 10, 20 and 30 km/h. Raw heading records for the compasses used in this part of the experiment are presented in Figure 12 for the Furuno compass and Figure 13 for the Novatel compass.  
Figure 11: Positions recorded during the road test with the gap in data registration visible on the map view.  
Figure 12: Raw heading records for the Furuno compass for the speeds of 10 km/h (**a**), 20 km/h (**b**) and 30 km/h (**c**).  
Figure 13: Raw heading records for the Novatel compass for the speeds of 10 km/h (**a**), 20 km/h (**b**) and 30 km/h (**c**).  
The frequency spectrum of the signals presented above are plotted in Figures 14 and 15.  
In the context of a reaction to rapid changes in the satellite constellation, there is also a question regarding the impact on the stability of compass indications based on inertial sensors that are able to support the work of the radio (satellite) segment [23]. An example of the behavior of the Advanced Navigation compass in the case of complete obscuring of satellite signals (667 s after the start of registration) is shown in Figure 16. A clear drift of values is observed, which was similar in other tests, although the directions of the drift were different. After approximately 100 s, no information about the heading was reported by the device.