Estimation Bounds of Beat Signal in the R-Mode Localization System

The R-Mode system is a terrestrial navigation currently under development, which exploits existing means of medium frequency radio transmission. positioning and timing performance depends on the estimation signals' phase offset, from ranging information derived. For an analogous problem such as single-tone estimation, Cramér-Rao bound (CRB) describes minimal achievable in mean squared error sense. R-Mode, involves offset for beat signal, can be described difference two aiding carriers next to signal. This estimates are not statistically independent finite observation, we show this paper. effect becomes stronger short observation times, important near real time application. In contribution, interested signal models relevant R-Mode: combined with MSK A closed-form lower CRB proposed aforementioned well generalization phase-difference estimation. Based derivation, optimized bit sequences shown improve estimates. validity proposal verified based simulation setup. Measurements acquired during measurement campaign serve further justify usefulness bound. Some possible applications coverage prediction associated estimators' performance.