Optimization of multistatic passive radar geometry based on CRLB with uncertain observations

In the present paper, we derive the Cramer-Rao Lower Bound (CRLB) with uncertain observations, namely for P_d<;1, for the 2D position measurements of a multistatic passive radar, to optimize the geometry of the system. This is an extension of the enumeration method CRLB to the multisensor case, where it is considered that the multiple receivers could detect or miss the target independently of one another. This version of the CRLB with uncertain observations is the correct measure for the realistic performance assessment of a passive radar, since typically passive radars show low values of P_d and neglecting the target miss probability, in the standard evaluation of the CRLB, provides unreliable performance assessments. The obtained CRLB is then used inside the multistatic passive radar optimization scheme derived by the authors in, to select the broadcast transmitters and the receiver locations providing the highest accuracy. The proposed approach is illustrated by means of a case study: a multistatic passive radar based on two transmitters of opportunity and a single receiver. For this case, we analyse how the Signal to Noise Ratio and the detection probability affect the measurement accuracy and the estimation accuracy and, finally, we use the theoretical CRLB to select the two transmitters among the available ones and choose the receiver location, for a target flying a specific trajectory.