Comparison of Two Methods of Signal Smoothing in the Development of Navigation Systems

The development of navigation systems and solving problems related to this process sometimes requires consideration of methods of smoothing signals used in these systems. In particular, the importance of this issue is observed in the case when navigation is technically implemented using digital signal processing methods. The comparison of a saturation classes of an Abel-Poisson summing method and a Gauss-Weierstrass summing method as signal smoothing methods has been carried out in this paper. Their saturation orders have been established and the difference between signals classes to which these methods are applicable has been demonstrated. We have also established that despite the same order of saturation, in the problems of smoothing signals, the Gauss-Weierstrass summing method is applicable to smoother signals than an Abel-Poisson summing method, which is demonstrated graphically. In the course of the research, we have confirmed experimentally the theoretical calculations. We have established how much higher the degree of smoothness of a signal smoothed using the Gauss-Weierstrass method can be compared to signals that can be smoothed using the Abel-Poisson method.