Airborne Direction Finding---The Theory of Navigation Errors

The situation where n stationary, accurately located, direction-finding stations fix the position of an unknown emitter by intersecting angular bearings has been previously investigated by Stansfield for the case where the angular bearings have small, normally distributed errors. The most probable location of the emitter and the surrounding confidence regions were determined. Stansfield's solution is here extended to include the case of airborne direction finding, which introduces uncertainties in the locations of the direction-finding stations. These uncertainties arise from navigation errors and increase the uncertainty of the fix, which is reflected in an increase in the variance of the solution. The increase in uncertainty is derived for celestial, dead reckoning, and direction-finding (Loran, Shoran, etc.) navigational procedures. Small, normally distributed navigation errors are assumed. In addition, a model in which celestial position fixes are taken between direction-finding cuts is investigated. The various procedures are compared.