Optimality Analysis of Sensor-Target Geometries for Bearing-Only Passive Localization in Three Dimensional Space

Optimality analysis of sensor to target observation geometry for bearing-only passive localization is of practical significance in engineering and military applications and this paper generalized predecessors' researches in two-dimensions into three dimensional space. Based on the principles of Cramer-Rao lower bound (CRLB), Fisher information matrix (FIM) and the determinant of FIM derived by Cauchy-Binet formula, this paper configured the optimal observation geometry resulted from maximizing the determinant of FIM. Optimal observation geometry theorems and corresponding propositions were proved for N≥2 sensors in three dimensions. One conjecture was proposed, i.e., when each range of N(N≥4) sensors to the single target is identical, configuring the optimal geometry is equivalent to distributing N points uniformly on a unit sphere, which is one of the worldwide difficult problem. Studies in this paper can provide helpful reference for passive sensor deployment, route planning of detection platform and so on.