# Analysis of Satellite Compass Error's Spectrum
## 2 Materials and Methods  
### Background  
Despite many tests confirming the usefulness of multi-antenna GNSS receivers for measurements related to spatial orientation, devices that met the criteria specified in international conventions have been developed no earlier than in 2005. Large errors appeared periodically in all the previous constructions, which were related to the changing satellite constellation parameters. An example of such measurements, taken in 2004 with the Crescent compass installed on the roof of the building is shown in Figure 2.  
The MX 575 compass, which as the first receiver of a certificate allowing it to be used as a heading transmitting devices, was introduced in 2005. It could be used as a backup source of heading information in IMO-compliant (International Maritime Organisation) vessels. One of the important solutions was the use of the MEMS-type (Microelectronic Mechanised System) gyroscope, which stabilizes the indications when \"raw\" measurements in the radio domain turn out to be temporarily inaccurate. Modern constructions often have a triad of gyroscopes and accelerometers. They are integrated systems, able to continue working for several minutes even in the event of satellite signals disappearance. The dynamic properties of such devices largely depend on the details of an algorithm used for the calculation and filtering of signals. The traditional gyro-compass has an electromechanical sensor, whose center of gravity is shifted relative to the geometric center, and thus behaves like a pendulum oscillating with a period of about 84 min (Schuler period, Schuler tuning). [PERSON] made a proposal in 1923 that gyro compasses lend themselves to particularly successful tuning when the curvature of the Earth is taken into consideration. In this way, the instruments can be made insensitive  
Figure 2: Heading measured with a satellite compass during stationary measurements [2]. to the disturbances that are caused by the result of the accelerations of the carriers along the surface of the Earth. According to this requirement, the instruments have to be tuned to an oscillation period of 84.3 min. Thus, the classical gyrocompass has its own fluctuation with a long period. There are no kinematic problems in satellite compasses, however, the results depend on changes in the satellite constellation and the properties of the measurement-processing algorithm. This is an issue addressed by the authors of this article. Manufacturers commonly describe the quality of such devices by declaring their accuracy based on an average square error or using similar methods. The assumption of white noise may not be true. Dynamic errors are caused by dynamic factors affecting the system, such as vibrations, roll, pitch or linear acceleration. According to [3] 'this error may have an amplitude and frequency related to the environmental influences and the parameters of the system itself'. However, for implementation in more complex measuring systems, when the fundamental issue is the selection of devices with different error characteristics, the question regarding the error frequency spectrum is important. The basic principle of integrating devices that perform similar functions is to vary the output error rate. There are two main types of satellite compasses available on the market now: dual-antennas and tri-antennas. The most popular are dual-antenna constructions, which give the opportunity to measure two angles in transverse directions to the base between two antennas (pitch or roll in addition to heading). Designs with three antennas give the opportunity to measure all three angles of orientation of the carrier. Besides the number of antennas, there are devices with a constant distribution of antennas and movable antennas, so the distance between them can be changed by the owner or by the fitter. Additional sensors, commonly made in MEMS technology, are used to stabilize angular measurements. In addition to gyroscopes, these devices are often equipped with accelerometers.