Optimal TOA-Sensor Placement for Two Target Localization Simultaneously Using Shared Sensors

This letter analyses the optimal placement of sensors for the simultaneous localization of two targets on the 2-dimensional (2-D) plane. Multiple sensors measure circular time-of-arrival (TOA) signals with a high signal to noise ratio (SNR). The case considered is where there are $n$ shared sensors measuring both targets and $m$ sensors for each individual target, giving a total of $n+2m$ sensors. In this case, the minimum trace of the inverse Fisher information matrix (FIM), i.e., Cramer-Rao lower bound (CRLB), is $2\sigma ^{2}/(n+m)$ . A placement scheme for the sensors is presented which achieves the tr(CRLB) of the optimal sensor-target geometry. This confirms the intuitive result that optimal sensor placement can occur when shared sensors are on the middle line between the two targets. Simulation examples demonstrate the effectiveness of the placement scheme with different geometries.