# Analysis of Satellite Compass Error's Spectrum
## 2 Materials and Methods
### Conducted Experiments
#### 2.3.3 Tests on Tram Rails  
The tram experiment was performed on 28 November 2018 along the route indicated in Figure 17 with the use FURUNO SC50 only. The experiment was conducted in Gdansk on a several-kilometer tram rail with variable sky visibility conditions, with the aim of assessing the performance (accuracy) of the satellite compass operation in non-standard terrain conditions. The measuring instrument used in the experiment was placed on a trolley of the DWF 300 series tram and pulled behind a tram [22] above the tram rails axis. The task of this measurements was more complex, and we now use only a small part of this registration made on the rail part, characterized by a constant direction (Figure 17). Figure 14: Frequency spectrum for the Furuno compass raw heading records in Figure 12 for the speeds of 10 km/h (**a**), 20 km/h (**b**) and 30 km/h (**c**). Figure 15: Frequency spectrum for the Novatel compass raw heading records in Figure 12 for the speeds of 10 km/h (**a**), 20 km/h (**b**) and 30 km/h (**c**). For this analysis, it is important that the tram route ran through an urbanized area and some sky obstructions were observed during the registration. The GPS satellite elevations are presented in Figure 18.  
Figure 16: Raw heading value results during the stationary test with the Advance Navigation compass used as an example. The orange line denotes the satellite signals in the moment of being completely obscured. Figure 17: Position registration of the tram from 23:06:25 (UTC) - Universal Time Coordinated to 23:07:25 UTC. The satellite compass requires a signal from at least five satellites for each antenna to determine vehicle heading. Based on Figure 19, it can be seen that a condition of a visibility of at least five satellites to quantify the heading of the vehicle with the arbitrarily assumption of the elevation cut-off at 20 degrees has been met during the experiment. The presented test was started at 2200 UTC with the visibility of six GPS satellites (Figure 19). The problem occurred when the number of visible satellites was reduced to four (from 0230 UTC to 0300 UTC on 29 November 2018). Based on the data registered from 22:59:27 UTC on 28 November 2018 to 03:26:41 UTC on 29 November 2018, the parts of the straight tram rail section have been chosen. Data have been recorded from the 419 th second to 479 th second of the run, which is from 23:06:25 to 23:07:25, from the position (LAT) Latitude: 54.386780\({}^{\circ}\) N, (LON) Longitude: 018.591723\({}^{\circ}\) E to the position LAT: 54.383415\({}^{\circ}\) N, LON: 18.5968183\({}^{\circ}\) E. Heading oscillations for a vehicle on tram rails were observed in the range of \(-\)0.8. to + 0.5 degrees. The values of the heading distortions and the frequency spectrum of the heading record changes are presented in Figure 20.  
Figure 18: GPS satellite elevations on 28, 29 November 2018. (Source: Trimble Planning 2.9, 2010). Figure 20: (**a**) Heading distortions. (**b**) Frequency spectrum of the heading records. Heading distortions and the frequency spectrum of the heading records from 23:06:25 to 23:07:25, from the position LAT: 54.386780\({}^{\circ}\) N, LON: 018.591723\({}^{\circ}\) E to the position LAT: 54.383415\({}^{\circ}\) N, LON: 18.5968183\({}^{\circ}\) E. (Source: [PERSON]). The heading distortion analysis in the time domain in Figure 20 confirms the declared accuracy of the device indications in accordance with the technical specification of the device, which is 0.51 degrees (RMS)--Root Mean Square error. The spectrum analysis of the signal in the frequency domain in Figure 20 differs from that recorded during the stationary tests because oscillations appear at frequencies higher than 0.02 Hz. The maximum amplitude is slightly higher than that during the stationary record.