CRLB with Pd<1 fused tracks

This paper presents mathematical procedures to calculate the Cramer-Rao lower bound (CRLB) for a target track obtained by fusing two tracks given by two interactive multiple model (IMM) trackers filtering the plots received by two radars. The target under tracking is a ballistic target (BT) in reentry phase and it is assumed that the two sensors could have a detection probabilities Pd less than 1. Accurate BT tracking is required for: (i) impact point prediction, (ii) support to the kill assessment, and (iii) threat classification. Note that, to improve the performance, the method can be extended to the fusion of more than two sensor tracks. The paper is organized as follows: the problem is introduced in section 1; section 2 briefly recalls the models of BT dynamic and of the radar measures. Section 3 presents the tracking algorithm based on the IMM approach; section 4 contains the description of the CRLB evaluation problem and section 5 the results achieved in comparing the fusion of two BT tracks (each track is obtained from the IMM algorithm described in section 4) with the CRLB; Monte Carlo simulations is also used to quantify the fused track accuracies. Section 6 is pertinent to conclusions and follows on of the activity while references are reported in section 7.