# Hyperbolic Asynchronous Method of a Radio Navigation Technique
## 4 Theoretical Investigations
### Analysis of Theoretical Investigation Results  
Due to the planned comparative analyses, the scenarios of the planned computational tests have been adjusted to the possible measurement tests in practice. For organizational reasons it was assumed that the measurement tests would take place in the open water of the Gulf of Gdarsk. Therefore, the scenarios for computational research were based on this basis, assuming the use of three or four reference stations for cost reasons. Bearing in mind what has been written above, the calculation of the effect of the frequency bandwidth of the asynchronous locating system and the position of the localized terminal (UT) on the efficiency of determining the position of that terminal was performed. The plan of these studies included:  
Figure 9: Algorithm of the simulator operation—UT position calculation. * in the preset mode, the absolute error \(\delta_{d}[m]\) distribution for different bandwidths of the B[MHz] system was investigated, which allowed for the assessment of the operational capabilities of this system,
* in the set route mode, the distribution of absolute error was examined, also for different bandwidths of the system, which in turn allowed for the assessment of its performance for specific trajectories,
* development of histograms of the absolute error of the tests was performed, and
* development of a stabularized comparison of the efficiency of the examined system was performed. The simulation and measuring test area with the location of three reference stations is shown in Figure 10.  
The results of absolute error \(\delta_{d}[m]\). distribution tests carried out in the area mode for the location of reference stations shown in Figure 10 and for different B-bandwidths of the system are shown in Figures 11-15. Analyzing the results presented in Figure 16, it can be concluded that the system provides access to a location service throughout the entire internal area covered by reference station locations, but with different accuracy depending on the location of the localized terminal. The absolute efficiency of the system, determined by error, is better the more central to the reference stations the location of the localized terminal is. This corresponds to the performance characteristics of synchronous navigation systems. However, an important conclusion that should be taken into account in further research is that an important factor affecting the accuracy of terminal localization (UT) in a system with a spread spectrum is the bandwidth of that system--the greater the bandwidth, the better the localization efficiency. Figure 10: Illustration of a simulation and measuring test ground with marked locations of the three reference stations. Figure 11: The absolute error \(\delta_{d}[m]\) area distribution for 3 reference stations and for \(B=1\) MHz. Figure 12: The absolute error \(\delta_{d}[m]\) area distribution for 3 reference stations and for \(B=2\) MHz. Figure 14: The absolute error \(\delta_{d}[m]\) area distribution for 3 reference stations and for \(B=8\) MHz. Figure 13: The absolute error area \(\delta_{d}[m]\) distribution for 3 reference stations and for \(B=4\) MHz. In turn, the results of absolute error distribution tests carried out in the mode on a given route for three reference stations are shown in Figure 16 for different bandwidths of the system. Figure 16: CDF (Cumulative Distribution Function) related to absolute error \(\delta_{d}[m]\) for three reference stations and for different B-band widths. Figure 15: The absolute error \(\delta_{d}[m]\) area distribution for 3 reference stations and for \(B=10\) MHz. Analyzing the results of CDF (Cumulative Distribution Function) related to the absolute error distributions shown in Figure 16, it can be concluded that the accuracy of the performance of an asynchronous locating system working with the spread spectrum is better the larger its operating band. This corresponds to the previous conclusion. In the next step, absolute error histograms of the performed tests were developed.