Applying nonparametric estimation of the regression function to increase the accuracy of navigation problem solution

The article deals with the task of missing data recovery when solving a navigation problem using satellite navigation systems. The study revealed a correlation relationship between the changes in pseudo-distance (the distance from the object to the navigation satellite calculated taking into account the error of the consumer's time scale). In other words, the change in the distance between the receiver and one satellite is correlated with the change in the distance between the receiver and another satellite. On the basis of the discovered dependence was formed the hypothesis that the increment of pseudo-distance relative to the previous moment of time on a short time interval changes linearly. To confirm this hypothesis, a graph was constructed, which confirmed it. A nonparametric algorithm for recovering missing data based on this hypothesis was proposed. As part of the study, random omissions were introduced into the pseudodistance measurements. The purpose of the skips was to simulate conditions in which a navigation receiver loses signal from some navigation satellites (e.g., due to high building density). After the skip insertion, the developed algorithm was applied to recover the missed values. The results showed that the difference between the real and reconstructed pseudo-distance values did not exceed one percent. This allows us to confirm the effectiveness of the developed algorithm in solving the navigation problem for conditions of signal loss from satellites.