Statistical Efficiency of Composite Position Measurements from Passive Sensors

Combining line-of-sight (LOS) measurements from passive sensors (e.g., satellite-based IR, ground-based cameras, etc.), assumed to be synchronized, into a single composite Cartesian measurement (full position in 3D) via maximum likelihood (ML) estimation, can circumvent the need for nonlinear filtering-which involves, by necessity, approximations. This ML estimate is shown to be statistically efficient, even for small sample sizes (as few as two LOS measurements), and as such, the covariance matrix obtainable from the Cramer-Rao lower bound (CRLB) provides the correct measurement noise covariance matrix for use in a target tracking filter.