Navigation by Moon Doppler Effect

摘要

As a back-up navigation method for Polaris submarines, the feasibility of moon doppler navigation on abistatic basis is investigated. The problem is that of finding the latitude and longitude of a vessel by measuring doppler shift and time rate of change of doppler shift in radio waves transmitted from a fixed site and reflected from the moon. For a prescribed navigation accuracy, one must determine the necessary precision in measuring doppler frequency and time rate of change of doppler frequency. A sample calculation is made for a location on the western edge of the Norwegian Sea, and it is found that if the probable error in latitude is specified to be 0.8 naut mi and the probable error in longitude to be 1.3 naut mi, the probable error which can be allowed in doppler shift is 0.796 cps and the permissible probable error in time rate of change of doppler shift is 9.511 x 10' cpsps, with a transmitted frequency of 2200 Mc. The calculated value for doppler frequency was 2459 cps, and that for doppler rate was 0.1381 cpsps. This means that doppler frequency must be measured to an accuracy of 0.0324 percent and doppler rate to an accuracy of 0.0689 percent, for this particular example. The measurement of doppler frequency seems within the realm of technical capability in the near future. The accuracy of the measurement of doppler rate is still in question. However, it appears that the rate can be computed within the required accuracy by fitting an approximate analytical expression to the set of points representing the measured doppler shift and differentiating the expression, or by using finite difference methods with the observed data to get the time derivative. Propagation effects due to variation of index of refraction in the atmosphere have not been taken into account. These effects may be important, and should probably be the subject of investigation in the near future.