In this paper, we derive the Cramér-Rao bounds (CRBs) on the positioning errors for narrow-band low earth orbit positioning, navigation, and timing (LEO-PNT) systems. Fisher information analysis is performed to characterize the CRBs for errors in Doppler and carrier phase measurements. In addition, we analyze the effect of the carrier phase and Doppler on the CRB for positioning. Numerical simulations were conducted in different settings. To show the relevance of CRB, we compare our results to the maximum likelihood (ML) estimator. Our findings show that using the carrier phase significantly improves the positioning in LEO-PNT systems.
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Kang et al. (2024) studied this question.
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