Comprehensive Analysis of Acquisition Time for a Multi-Constellation and Multi-Frequency GNSS Receiver at GEO Altitude

<h3>Abstract</h3> The utilization of global navigation satellite systems (GNSSs) in the space service volume, such as the geostationary Earth orbit (GEO) altitude, has recently attracted significant interest owing to their potential advantages in performance and cost. Because the acquisition of the satellite signal represents a fundamental function of a GNSS receiver, the expected amount of time for successful acquisition, or mean acquisition time (MAT), as well as the acquisition performance itself, must be analyzed. Owing to the limited number of satellites and poor geometry at the GEO altitude, GNSS receivers often utilize signals originating from the sidelobes of the transmitting antenna pattern, which results in a weak signal power and a high Doppler shift. This paper presents a research methodology for a comprehensive analysis of acquisition time, with a particular focus on operations at the GEO altitude, considering the utilization of sidelobe signals. A generalized mathematical and probabilistic model is provided for the acquisition performance and MAT analysis of multi-constellation and multi-frequency signals. In particular, a realistic MAT model is proposed, based on a detailed computational performance analysis of the acquisition algorithm applied to an actual spaceborne receiver. A geometric simulation was conducted using the publicly available antenna patterns of the Global Positioning System (GPS), Galileo, and Quasi-Zenith Satellite System to incorporate orbital and signal characteristics into the determination of the search space. A method is proposed to modify the antenna patterns for other systems whose patterns are not publicly available, while preserving the sidelobe characteristics. Based on realistic scenarios and receiver parameters, acquisition-related analysis results for cold and warm starts, including the search space, dwell time, and MAT for GEO altitude receivers, are provided. The methods and results were verified through a Monte Carlo simulation configured via a software simulator and receiver pair.