Geometric dilution of precision for bearing-only passive location in three-dimensional space

Geometric dilution of precision (GDOP) is a measurement of localisation accuracy in bearing-only passive location. However, the current GDOP expression is available only for two dimensions; while GDOP is widely adopted in spatial application, consequently, the explicit GDOP expression in three-dimensional (3D) space using the Cauchy-Binet formula is derived. The derived GDOP expression is used in two examples, which shows that the localisation accuracy is affected by both the number of sensors and the observation geometry.