R‐Mode is a terrestrial navigation system under development for the maritime domain that provides backup in case of a GNSS outage. This paper describes the first test results for real‐time positioning on board a ship using medium frequency R‐Mode signals. The estimation and positioning algorithms used are described in detail and it is shown how they are integrated into the R‐Mode receiver developed by the German Aerospace Center. Moreover, during two daytime experiments with lower and higher dynamic movements of a ship in the Baltic Sea, we were able to achieve a 95% horizontal positioning accuracy of better then 12 m in the center of three R‐Mode transmitters. This demonstrates the first time that the medium frequency R‐Mode has provided positioning at sea.

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

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