# Analysis of Satellite Compass Error's Spectrum
## 4 Discussion  
The motivation to conduct the research was the authors' experience, published in [18], and especially the results described in the paper [22], in which the results of Furuno compass errors turned out to be surprisingly high. In this paper, the authors were interested in a solution that would be potentially useful on a small floating object used for hydrographic measurements. The issue of the accuracy of the position determined by such a device was purposely not analyzed here, because today it seems to be a trivial issue and comes down to the choice of support service (augmentation) of the GNSS system. This text focuses on the issue of accuracy of the heading, based on the knowledge that the accuracy of the heading measured with each type of compass has different dynamic characteristics. An assessment of a measurement of heading uncertainty on a moving object requires taking into account changes in object orientation angles, because the readings will include both this information and the inaccuracy of the compass or any other gauges. For this reason, three different compasses were tested during static and dynamic experiments. Dynamic experiments, with heading reference data included, were carried out at different speeds on straight sections of tram rails and on straight sections of a roads. The results of stationary experiments confirm the clear relationship between the antenna base line length (distance between antennas) and heading accuracy. Analyzing the compass documentation, this relationship can be presented in a form of a curve, presented in Figure 23. The curve presented here is obtained by interpolating the sparse data regarding the Novatel compass with the quadratic function. The red square represents the manufacturer's information regarding the Furuno compass, which is consistent with data on Novatel. However, Advance Navigation data deviate from this relationship. The results of stationary tests confirm the declarations of the Novatel and Furuno compass manufacturers, although the Advance Navigation compass tests showed an error of twice the value--0.4 degrees. Figure 23: Theoretical relationship between the heading accuracy and the base line length between antennas, based on the Novatel data published in the device documentation (**black curve**). Declared accuracy of the Furuno compass as a function of baseline (**red square**) and of the Advanced Navigation compass (**green triangle**). For dynamic applications, knowledge of the error spectrum is extremely important. This spectrum is characterized by the dominance of very low frequencies, which is understandable with the use of filtration and inertial sensor support. One can clearly indicate the 0.02 Hz value as the upper limit of these oscillations for all tested compasses. However, in dynamic conditions, higher frequencies appear, which result from slight changes in the orientation of the object during movement. In addition, there are also harmonics, which are in fact the results of rapid deviations of results from previous values. The reason is that despite the solutions using inertial sensors and filtration, these compasses are still sensitive to changes in the temporary constellation of satellites used for calculations. Even during the stationary tests, one can easily identify the relationship between changes in indicated heading values and changes in the satellite constellation. This statement is confirmed by the analysis of the devices' behavior at the time of signal obstructions. It is always associated with a sharp change in the value at the compass output, although the natural change in the set of satellites seems to have less effect on the results than the short-term screening of one or two satellites, which disappear after a few seconds. The suppositions that appeared in relation to the results presented in [22], that the accuracy of the entire population of the recorded results do not reflect the whole truth regarding the compass, were also confirmed.