Some probabilistic properties of the line-of-sight angle error to a remote object (Corresp.)

Closed-form expressions are derived for the distribution and the expectation of the error of the line-of-sight angle to a remote object when the rectangular position coordinates are independent identically distributed normal variates. Generalized results also are provided both for the cumulative distribution function for a hyperspace of
N
dimensions and for a spherically symmetric probability density function in three-dimensional space.