Study and performance analysis of positioning algorithms based on Doppler measurements

In recent years, the use of Doppler shift measurement for the determination of a user's position, velocity and time is becoming of great interest for the new LEO and MEO constellations as an evolution of the trilateration techniques used in global navigation satellite systems. The concept of using Doppler measurements is not new: it was the basis of the first navigation system, Transit, which operated from 1964 to 1969 before being succeeded by the GPS system. Given the technological evolution and new scenarios embedding large number of LEO satellites an interest in revisiting the Doppler ranging and position concept using modern processing solution has arisen. Recent research on Doppler shift in GNSS has focused mainly on the following applications: accurate determination of user velocity, autonomous positioning using Doppler measurements, and enhancement of the classical GNSS system. In this thesis we have conducted an analysis of positioning performance based on both Doppler and pseudorange measurements in different scenarios. Initially, we extended the traditional resolution algorithm based on the LS estimator to Doppler measurements, enabling us to develop an algorithm capable of estimating 3D position, velocity, and receiver clock drift. Subsequently, in the first part of the simulations, we focused on evaluating the performance with both a static receiver and a dynamic receiver with satellites from the GPS constellation. Our findings indicate that for medium-orbit satellites, traditional positioning outperforms Doppler-based positioning. In the second part of the thesis, we set up a theoretical framework in which we investigated how the orbital altitude, and consequently the speed of the satellites, impact positioning. The analysis revealed that, as the orbital radius decreases, Doppler positioning performance progressively improves compared to the previous simulation. However, it also highlighted a problem already known from the literature i.e., convergence is not always guaranteed under cold start conditions of the algorithm. Consequently, we employed simulations to estimate the convergence radius for initializing the positioning algorithm.