A Statistical Theory for GNSS Signal Acquisition

Acquisition is the first stage of a Global Navigation Satellite System (GNSS) receiver and has the goal to determine which signals are in view and provide rough estimates of the signal parameters. The main objective of the thesis was to provide a complete and cohesive analysis of the acquisition process clarifying different aspects often neglected in the literature. The thesis provides the statistical tools required for the characterization of the acquisition process. In particular, the signal presence is determined by searching several candidates for the signal code delay and Doppler frequency which define a cell of the acquisition search space. Thus, the acquisition process is characterized by the strategy adopted for searching for the signal parameters and the way a decision metric is compute for each cell of the search space. Given this observation, the thesis introduces the concepts of cell and decision probabilities. Closed-form expressions are derived for three different acquisition strategies and the relationships between cell and decision probabilities are provided. Front-end filtering and quantization are also considered and their impact on the acquisition process is analysed. The methodology developed is applied to the acquisition of new composite GNSS signals which are made of a data and pilot channels. Algorithms for combining data and pilot channels are introduced and characterized from a statistical point of view. In particular, expressions for the detection and false alarm probabilities are derived for different combining strategies. The second part of the thesis deals with the problem of acquiring GNSS signals in the presence of interference. Different interference source and several mitigation techniques are considered and characterized from a statistical point of view. Theoretical results have been verified by Monte Carlo simulations and, where possible, by means of real data. In particular the NordNav R30 front-end has been used for collecting real GPS signals that have been used for testing the different algorithms considered in the thesis.