*2.3. Toy Model Implementation*

A toy version of the scheduling problem with three targets and two radars is shown in Figure 3. Given knowledge about each target's trajectory and a set of radars, time windows for each target–radar pair can be calculated to ensure the maximum radar coverage. The time windows can be calculated simply by checking whether a target is inside the coverage of the radar or not; the coverage and assignments of each radar are colored differently depending on the radar. Suppose that each radar can track only a single target at a given time (*ncapa* = 1), and the quality of measurement from a single radar is sufficiently high that simultaneous tracking by multiple radars is not needed in the given instance. The assignment results for the situation in Figure 3a are obtained as in Figure 3b. For Target *t*1, since Time Window *TW*1,2 includes Time Window *TW*1,1, only Radar *r*<sup>2</sup> tracks the target. For Target *t*2, *r*<sup>2</sup> tracks it because the time window exists only for *r*1. For *t*3, *r*<sup>1</sup> tracks *t*<sup>3</sup> first because Time Window *TW*3,1 starts before Time Window *TW*3,2, and then *r*<sup>1</sup> hands over the target to *r*<sup>2</sup> at Interval 7. For stable tracking, both radars *r*<sup>1</sup> and *r*<sup>2</sup> simultaneously measure the target during the handover period in Interval 7. The planning horizon is divided into intervals of equal length for

checking tracking status. Let us look at the results for Intervals 5 and 6 in Figure 3b. Because, from the assumption of the problem, each radar can track only a single target, the assignment in Time Window *TW*3,1 starts from the release time of Interval 6, *γInt* <sup>6</sup> , rather than the release time of *TW*3,1, *<sup>γ</sup>TW* 3,1 , and the time interval corresponding to Interval 5 of Time Window *TW*3,1 is excluded. The assignment to Time Window *TW*3,1 continues until *δTW* 3,1 . After the handover from *r*<sup>1</sup> to *r*2, *r*<sup>2</sup> tracks *t*<sup>3</sup> until Time Window *TW*3,2 is finished.

**Figure 3.** Conceptual diagram for sensor assignment considering target handover (refer to Table 1 for definitions of the symbols). (**a**) Physical circumstance description. (**b**) Description of time windows and handover procedure for seamless tracking.
