High-performance velocity, frequency and time estimation using GNSS

GNSS (Global Navigation Satellite System) receivers provide PVT solution, where PVT stands for Position, Velocity and Time. In general, the main interest of the common GNSS user is on the position solution and as a consequence the main focus of the research is the improvement of the position solution accuracy. However, many applications exist in which the measurement of both velocity and/or time is crucial and this is the reason why the focus of this thesis is on the Velocity and Time solution. The PVT solution is computed through trilateration techniques, based on a TOA (Time Of Arrival) ranging technique, therefore the PVT solution is correlated to the measurement of time. In particular, the position solution is related to a time measurement while the velocity solution is correlated to a frequency measurement. Different factors that affect the velocity estimate on one side and the time estimate on the other side are taken into account in this thesis, that in classic PVT solution are usually neglected. In the velocity/frequency estimate, the significant measurement is the change in the user-satellite distance, i.e. a relative measurement, thus the measurements errors that remain constant during the time interval over which the velocity is estimated cancel out. Carrier-phase difference solution enables velocity accuracy in the order of 1 mm/s, a high-level accuracy which is crucial for many applications, including Inertial Measurement Unit (IMU) calibration, motion compensation for Synthetic Aperture Radar (SAR) and flight reference systems. Thanks to the cancellation of the common errors, that in the position solution represents the very larger error sources, in the velocity solution other minor effects become the limiting error sources. The first goal investigated in this thesis is to look for the accuracy limit that can be achieved in the velocity/frequency solution. The second objective is to investigate the problem of high- accuracy time solution. As well as the position, the time is an absolute measurement, affected by large error sources. Furthermore, the clock error is in common to all the satellite measurements, and due to this, the common errors among the satellites are not told apart and are in general attributed to the clock measurement. As a result, lots of error sources that are not involved in the position solution become dominant in the time solution. A main limiting factor in the timing accuracy is represented by the errors in ionospheric delay estimate, where many error sources are involved, in particular the unknown bias due to the receiver hardware. After a part to introduce GNSS and its basic principles, with the focus on the aspects that are more relevant for the dissertation and that allow one to outline the motivations of the work, the thesis is divided in three main parts, two regarding in particular the velocity/frequency solution and the last one focused on the high-accuracy time solution. The first step to improve the velocity solution was to notice how the performance is much worse on the vertical solution than on the horizontal and how highly correlated the vertical solution is to the local frequency estimate. This is due to the geometry of GNSS, that implies that users on the Earth or close to the Earth (as aircrafts) can see satellites all around them on the horizontal direction, but they cannot see satellites under them, which is rejected in a poorer geometry on the vertical direction. Due to this characteristic, an error on the pseudorange, as the clock error is, reflects on the vertical solution more heavily than on the other dimensions. As a result, the vertical solution can be about three times worse than the horizontal and from the covariance matrix of the solution it can be seen how the correlation is high in particular between the vertical and the clock solution. This fact is true both for the position and for the velocity solution, which means that the vertical velocity accuracy is highly correlated to the local oscillator frequency. As a result, a way to improve the vertical velocity accuracy is to obtain a better estimate of the local frequency. In this thesis, models for the local oscillators and ways to integrate the frequency estimate in the GNSS solution are investigated. Another important aspect to improve the performance of the velocity measurement is to improve the accuracy of the GNSS measurement. Since the measurement used to obtain precise velocity is the carrier phase, which enables accuracy in the order of 1 mm/s, the goal to improve the accuracy on the carrier-phase measurement is crucial. With this objective, novel Digital Phase Lock Loops (DPLLs) has been designed, both of second and third order, with an adaptive bandwidth algorithm. The objective was to tune the loop bandwidth according to the input signal dynamics and noise, and use a bandwidth small enough to reduce the noise effects as much as possible, but wide enough to properly track the input dynamics. Since the PLL is designed for precise velocity measurement, the performance in terms of dynamics tracking ability is crucial. The last part of the analysis concerns the time solution. In most of cases in GNSS, high importance is given to the position accuracy, while the residual common biases are included in the receiver clock error. This approach makes the time solution not very accurate. Since the main bias which affects the time solution is the ionosphere delay, in this thesis the accuracy of the Total Electron Content (TEC) estimate is investigated, with the focus on the measurement bias. All the measurements which this thesis refers to are made using GPS (Global Positioning System) only, nevertheless sometimes in the thesis it is talked about GNSS in general. This is because the approaches considered in this thesis are tested here using GPS, but they can be applied to all the GNSSs.