Doppler Effect Estimation and Compensation for Satellite Systems in Geolocation Problems

The framework of the article is a theoretical investigation of the Doppler effect on electromagnetic signals. The target application is relevant to satellite missions with resource-constrained systems based on low-cost hardware platforms and the innovation of the paper is on the error compensation strategy and on the proposal of an approximate polynomial model. In particular, the scenario of interest considers a non-cooperative emitter of electromagnetic waves on the surface of the Earth and a receiver able to perform Angle of Arrival measurements embarked on a satellite in Low Earth Orbit. Assuming the problem of geolocation is solved, and starting from the kinematics of the satellite and its relative motion with respect to the emitter, the correction on the frequency is derived with respect to the orbital parameters, which is a common representation of data for satellite systems. The purpose of the paper is not only to provide a reference model to predict the necessary correction on the frequency of the signal due to the Doppler effect, but also to present a real-time strategy for compensation in the pipeline of signal processing after its geolocation. The main goal of the paper is to give real-time estimation and compensation strategy for the Doppler factor considering only the current instantaneous kinematic information, without the information on the history of the signal over time. Furthermore, data fitted from simulations show that a first degree polynomial model has a maximum error prediction on the order of less than 0.01 percent around Nadir pointing and can be appealing for fast computation of this correction with low-cost hardware based on Field Programmable Gate Array.