Estimating the Orbital Parameters of a Nanosatellite When Measuring the Total Electron Content in the Ionosphere Based on the Retransmission of GPS Navigation Signals

A method for estimating the orbital parameters of a nanosatellite-relay, implemented by measuring the total electron content in the ionosphere based on relaying GPS navigation signals at frequencies of 150/400 MHz, is substantiated. The method involves estimating the Cartesian coordinates of the nanosatellite-relay based on the results of measurements of the total ranges “navigation satellite – nanosatellite relay – ground receiving point”, obtaining estimates of the orbital plane inclination angle and the longitude of the ascending node using the least squares method, and estimating the remaining orbital parameters using the maximum likelihood method. Simulation results and accuracy characteristics of the proposed method are presented. It is shown that for a typical signal-to-noise ratio in the equipment of the receiving point and an observation time of the nanosatellite-relay of 600–800 s, the mean square errors in estimating the orbital parameters of the nanosatellite-relay are: for angular quantities – fractions of arc seconds, the semi-major axis of the ellipse – 4–5 m, eccentricity – 2–3 ppm.