Determination of the Orbit of an Unknown Ultra-Small Spacecraft Based on the Circular Perturbed Motion Model and Measurements of the Doppler Frequency Shift

Abstract

In this work, the determination of the orbit of an unknown ultra-small spacecraft based on Doppler measurements of the telemetry signal frequency is studied. The reception and processing of telemetry radio signals was carried out by the ground station of the Belarusian State University. In the model of perturbed circular motion, the radio signals of a small satellite were processed and the parameters of its orbit were determined. Based on a probabilistic estimate of the elevation angle and Doppler frequency shift of an ultra-small spacecraft from 10–20 measurements, a set of orbital parameters is determined for the estimated time of receiving telemetry signals. For antenna systems, the dynamics of changes in the elevation angle, azimuth, and Doppler frequency shift of telemetry radio signals for the next flights of an unknown ultra-small spacecraft was predicted. The calculated absolute errors in predicting the elevation angle, azimuth, and Doppler frequency shift did not exceed $$3^{\circ}$$ , $$3^{\circ}$$ and 250 Hz, respectively, which is sufficient for successful telemetry reception and decoding. Using the NORAD database of orbital parameters, the Chinese nanosatellite LUOJIA-1 01 of the Cubesat (6U) format (number 43485 in the NORAD system) was identified.