2.3. Conducted Experiments

In this paper, two kinds of experiments are reported: stationary and dynamic. During the stationary part of experiments, all the antennas were situated on a building roof or bench in a suburban area. The second part of tests was conducted using an automotive vehicle driven directly out of the urban area; however, the horizon was partially by trees. In addition, we used the part of our previous experiments conducted in Gdańsk on tramway routes and published in [22] when the surprisingly low accuracy of the Furuno compass was observed. We intended to verify how significant the influence of the surroundings was on the observed errors in that investigation.

The stationary experiment results displayed the typical characteristics of this type of test. It was performed from April 27 1300 UTC to April 28 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 6b). 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 1Hz was set for the Novatel compass.

Experimental setup: (a) on a car roof for the automotive tests; (b) on a house roof for the stationary sets. Photo: K. Zwolak.

GPS satellite elevations during the experiment on 27–28 April 2020. (Source: Trimble Planning 2.9, 2010).

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).

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 April 28). 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 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).

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 Novatel is 0.2 degrees.

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.

Heading registration spectrum for the three compasses: (a) Advanced Navigation, (b) Furuno, (c) Novatel. Stationary experiment, 27,28 April 2020.

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.

Positions recorded during the road test with the gap in data registration visible on the map view.

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.

Raw heading records for the Furuno compass for the speeds of 10 km/h (a), 20 km/h (b) and 30 km/h (c).

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 Figure 14 and Figure 15.

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).

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).

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.

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.

The tram experiment was performed on November 28, 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).

Position registration of the tram from 23:06:25 (UTC) - Universal Time Coordinated to 23:07:25 UTC.

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.

GPS satellite elevations on 28,29 November 2018. (Source: Trimble Planning 2.9, 2010).

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.

GPS satellite visibility on 28,29 November 2018. (Source: Trimble Planning 2.9, 2010).

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 November 29, 2018). Based on the data registered from 22:59:27 UTC on 28.11.2018 to 03:26:41 UTC on 29.11.2018, the parts of the straight tram rail section have been chosen. Data have been recorded from the 419th second to 479th second of the run, which is from 23:06:25 to 23:07:25, from the position (LAT) Latitude: 54.386780° N, (LON) Longitude: 018.591723° E to the position LAT: 54.383415° N, LON: 18.5968183° 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.

(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° N, LON: 018.591723° E to the position LAT: 54.383415° N, LON: 18.5968183° E. (Source: K. Jaskólski).

The heading distortion analysis in the time domain in Figure 20a 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 20b 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.

Another example of a registration on tram rails is shown in Figure 21 and research scores with a few course deviations are shown in Figure 22. In the heading record, there are four observed significant distortions from the track direction, which result from sky obstructions caused by high buildings in the vicinity of rails. The spectrum of this record differs significantly from others, which is undoubtedly caused by these four clearly distorted parts.

Position registration of the tram from 00:25:17 UTC to 00:30:37 UTC.

Heading distortions from 00:25:17 UTC to 00:30:37 UTC (a) and a frequency spectrum of heading changes (b).