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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.
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 of geometry theorems and corresponding propositions were proved for N ≥ 2 sensors in three dimensions. One conjecture was proposed, ie, 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 Studies in this paper can provide helpful reference for passive sensor deployment, route planning of detection platform and so on.