**3. Results**

The MINS system was tested using measurement data from the WATSAR radar system [37]. Before starting the navigation calculations, it was necessary to determine the value of ||Δ**r***ntr*||. If the value is too high, it leads to a shift between two image parts generated using INS data from the successive instances. The threshold value should also not be too low, as it would result in a short duration of INS instances, potentially shorter than the duration of the synthetic aperture, which in the WATSAR system was about 0.606 s. Taking into account the class of IMU used in the WASTAR system, the threshold was experimentally established and equaled 0.25 m.

After the threshold is exceeded, the errors of the *INSi*−<sup>1</sup> instance still increase, but the time duration of this instance is limited to the time of the overlap. In a test flight (named here flight no 1), six INS instance switches were performed. Table 1 summarizes the duration of individual instances and the final values of position errors in relation to the INS/GPS trajectory.


**Table 1.** MINS results for flight no 1.

The time duration of instances is varied and ranges from 2.053 to 6.966 s. The reasons for this variation are initialization errors of INS instances and INS/GPS errors—GPS errors cause small step changes in Δ**r***<sup>n</sup> b*,*INS*,*INS*/*GPS*. Figure 4 shows the position error of the first instance of flight no 1.

**Figure 4.** INS instance (no 1) position error in flight no 1.

A visualization of the UAV flight trajectory determined by the MINS system for flight no 1 is shown in Figure 5. The white markers indicate locations where the instances were initialized.

**Figure 5.** MINS trajectories for flight no 1.

A visual comparison of the position errors of the classic INS and the proposed MINS, determined with respect to the INS/GPS data, is shown in Figure 6, while Figures 7 and 8 show analogous results for the velocity and the velocity errors.

**Figure 6.** INS (blue) and MINS (black) position error with respect to the INS/GPS trajectory, North axis.

**Figure 8.** INS (blue) and MINS (black) velocity error with respect to the INS/GPS trajectory, North axis.

Thanks to the INS instance switching mechanism, the error in determining the navigation elements is kept at a low level, similar to the INS/GPS system, and the value of maximum error is related to the adopted threshold, which triggers a new instance. In the MINS system, the INS instances are initialized using INS/GPS data, thus the MINS trajectories originate on the INS/GPS trajectory. A random character of data presented in Figure 8 is caused by the error calculation mechanism, where from "smooth" INS data the "noisy" INS/GPS results were subtracted.

The MINS results are used by the NCA [36]. According to the procedure shown in Figure 2, INS overlaps lead to the navigation corrections overlap, which is presented in Figure 9.

**Figure 9.** Navigation corrections data overlap.
