Propagation-of-Error Equations for Airborne Doppler Navigation

The general equations for the propagation of error with distance traveled for the case of fix-corrected Doppler navigation along a path which consists of one or more rhumb-line legs are derived and shown to consist of a combination of six types of error variances. The specific expressions when the position-finding system used for fix correction is either a rho-theta (i.e., VORTAC) or a hyperbolic (i.e., Loran) type are given. The expressions for the resulting error spreads in terms of RMS or arbitrary x and y coponents are shown to be straightforward and easy to apply in most cases. The exact expressions for the size and spatial orientation of the elliptical equiprobability error contours are shown to be more complex and more difficult to apply practically. However, it is pointed out that the RMS error specification method is easily applicable in all of the practical cases considered. The use of the RMS error circle approximation is always safe although in some cases it may lead to ¿overdesign.¿