Precision Limits of Low-Energy GNSS Receivers

Limitations on position-time precision are analyzed in energy-constrained GNSS receivers. The goal of this work is to determine the combination of sampling rate, number of quantization bits, number of satellites tracked, and coherent integration time that maximizes the position-time precision under a fixed low-energy constraint. In this paper, only the measurement errors due to spectrally flat Gaussian thermal noise are considered. Analytical expressions relating the foregoing parameters to precision and energy consumption are developed. Based on these expressions, a constrained optimization problem is formulated. Optimal solutions indicate that under a tight energy constraint energy should be allocated toward increasing the sampling rate at the expense of the other parameters. Moreover, the quantization resolution should be set above 1-bit only under an energy surplus. Interestingly, optimum settings under tight energy constraints approximately match those chosen by the designers of energyefficient commercial GNSS receivers.