**5. False Estimation Scenarios in MDSC**

The MDSC scheme has a deficiency of correctly estimating the locations when the distance between two targets is smaller than the LFM range offset difference of two moving targets, as shown in Figure 15. In this case, the grouping results are never able to generate the correction pairing information.

**Figure 15.** Two moving target MDSC of Figure 7 Case 3. The signal is traced by minus two fd\_offset Hz DSC (blue-dotted line) and minus one fd\_offset Hz DSC (red line). Since the target 1 pair is always enclosed by target 2 in such scenarios, the grouping rule always pairs the target 2 left detection with target 1 right detection at each DSC.

The ambiguous estimation scenarios of MDSC are grandly evaluated in Figure 16 with the targets velocity sweep from zero up to Mach 15 and distance is between zero and 80 km for a comprehensive analysis of unambiguous range estimation and possible false scenarios. The MDSC demonstrates a robust and accurate range estimation with zero root-mean-square error (RMSE) in unambiguous scenarios in Figures 5 and 6. These two cases have a grand-coverage of most of the two-moving-target scenarios in terms of relative distances and velocities variation. However, the ambiguous Case 3 scenario in Figure 7 introduces the high RMSE in the range estimation due to the constantly miss-matching pairing results of two targets in MDSC, which is shown in the left of Figure 16. The Case 3 scenario indicates that the space between targets is insufficient to prevent one target detection pair to enclosure the other target detection pair, such as the distance (x label) < 22.74 km and the velocity difference = Mach 14.06 (y label) or distance = 14.2 km and the velocity difference > Mach 0.93. The higher the velocity difference, the longer the distance required to avoid these misleading scenarios [14].

These misleading results are introduced by the false pairing outcomes in MDSC processes in the Figure 7 Case 3 condition. These ambiguous conditions can be classified as two real-life scenarios:


**Figure 16.** The range estimation error chart. Applying multi-Doppler-shift-compensation (MDSC) scheme estimates two non-stationary targets. The target distance is swept from 0 to 80 km while the velocity difference is swept from 0 to 15 Mach.
