Probable Accuracy in Acquisition Aids for an Orbiting Vehicle

Efficient operation of a tracking system requires that certain acquisition aids be available to each station prior to vehicle approach. One method of deriving such aids is based on extrapolation of vehicle position from a set of orbital parameters. Since in general, extrapolation errors tend to increase with time, orbital parameters must be updated periodically to provide for automatic acquisition. A statistical analysis is presented for assessing extrapolation errors in vehicle position. Starting with a set of orbital elements and a prescribed distribution of errors in the latter, an upper bound is obtained for a statistical parameter associated with the magnitude of the vehicle position error vector. This upper bound is time-dependent and is applied to estimate the related errors in acquisition aids. Thus, all estimates depend upon the time lapse which has expired since the orbital parameters were updated. The method of analysis is general and may be applied to a wide class of tracking systems. An example is included to indicate the magnitude of errors for a particular hypothetical vehicle.