The intersection of a Loxodrome with a great circle

The intersections of a loxodrome (rhumb line) and a great circle are of interest for some navigational problems, but a closed-form solution cannot be formulated. An algorithm is given for computing approximations to any desired degree of accuracy using Newton's method. By using the equatorial angle φ as an independent variable all solutions can be found rapidly using the modest computational capabilities of a personal computer     

Polarization Mismatch Errors in Radio Phase Interferometers

An analysis is presented which deals with the effects of polarization mismatch errors on the accuracy of a phase interferometer used for position location of unknown emitters relative to known calibration emitters. Closed-form expressions for the induced phase difference between interferometer antennas are derived for several combinations of receiving and transmitting antenna polarizations. Errors contributed by mechanical misalignment between antennas, as well as effects of power loss attributable to polarization mismatch, are also considered. The analysis leads to the conclusion that circularly polarized interferometer and transmitter antennas are best suited for the position location application, if it is assumed that polarization tracking of the interferometer antennas is not available. It is shown that a reasonable amount of ellipticity can be tolerated before the phase error becomes significant.     

The Effect of Multipath Reflections on Spaceborne Interferometer Accuracy

This paper presents a discussion of multipath disturbance of a satellite interferometer. A mathematical expression is developed, in which an upper bound of the error of the measured angle difference and position locations owing to multipath is expressed in terms of geometrical system parameters and the amplitude and phase of the multipath signal. Because diffuse reflection from a rough surface is predominant, the spectrum of multipath reflections is calculated. Multipath rejection by filtering is discussed, and curves for the position errors are presented.