**4. Discussion**

MINS-based MOCO results were compared with those obtained using other MOCO methods: INS [16] and INS/GPS [34]. Based on the corrections, the radar terrain images of the region presented in Figure 10 were calculated. The radar terrain image obtained without MOCO correction, for flight no 1, is shown in Figure 11. Figure 12 presents an image obtained using INS-based MOCO, Figure 13 shows an image calculated using INS/GPS-based MOCO, whereas Figure 14 shows an image obtained using the proposed MINS system.

**Figure 10.** Aerial photography of the imaged area.

**Figure 11.** Radar terrain image obtained without navigation correction.

**Figure 12.** Radar terrain image obtained with the use of INS data; yellow line—the north edge of the taxiway determined using an INS-based image.

**Figure 13.** Radar terrain image obtained with the use of INS/GPS data; yellow line—the north edge of the taxiway determined using INS-based image, red line—the north edge of the taxiway determined using an INS/GPS-based image.

**Figure 14.** Radar terrain image obtained with the use of MINS data.

The total flight duration along the scanned area was approximately 29 s and was limited by the Visual Line of Sight (VLOS) UAV rules. Along the azimuth direction, the scanned swath had a length of 680 m. During imaging, the UAV moved along a semilinear trajectory. Its rectilinear shape was imposed by the radar aperture synthesis algorithm implemented in our system and described in [38]. In general, the applied SAR procedure allows for a nonrectilinear UAV motion as its displacements from an assumed linear trajectory are compensated using navigation corrections and the MOCO procedure. However, during large maneuvers (e.g., rapid turns) the spatial resolution of the image can be degraded. Therefore, our system is typically used for SAR imaging during flights along almost rectilinear trajectories. In order to present data representative for a normal operational use of the system, only straight flight trajectories were considered.

The geometric distortions of images were determined by measuring the angle between northern edges of the taxiway, whose true value is 159◦. In Figure 12 (INS-based MOCO), the edge is marked in yellow, and the measured angle is 157◦. The two-degree discrepancy is related to the slowly growing INS positioning errors with a final value of 11.7 m. In the case of INS/GPS-based MOCO, the taxiway edge is marked in red (Figure 13), while the measured angle is concise with the true one. In this image, the geometric distortions are reduced thanks to the INS error correction with the GPS receiver and the Kalman filter. In addition, in the case of the proposed MINS system, the taxiway angle has a proper value. In this system, the positioning error is kept low by the instance switching mechanism.

Vertical white lines, presented in Figure 15, mark the ranges of radar measurements with INS overlaps. As can be seen, these overlaps do not deteriorate the image quality or geometric conciseness of the image.

**Figure 15.** Radar terrain image obtained using MINS-based MOCO. Overlap bounds are marked white, whereas the red line is an image line chosen to determine SR, PSLR, and ISLR.

Radar terrain images obtained using the three considered MOCO methods (INS, INS/GPS, and MINS) were also compared using quality indicators such as image contrast (IC), entropy (E), spatial resolution (SR), PSLR, and ISLR [25,29,39–41]. The results are presented in Table 2.


**Table 2.** Parameters of the quality of the selected synthetic aperture radar (SAR) image.

The image obtained using MINS-based MOCO has a better (higher) contrast than the image calculated without the navigation correction (IC increases from 4.06 to 8.01). This result is also better than the contrast of the INS/GPS-based image (IC = 7.56) and comparable to the contrast of the INS-based image (IC = 8.32). The improvement is also visible in the image entropy. Due to the usage of MINS-based MOCO, a reduction (improvement) of entropy was achieved in relation to the image without MOCO (E decreases from 14.43 to 13.84). The obtained result is also better than the entropy of the INS/GPS-based image (E = 13.94) and similar to the result obtained with a traditional INS (E = 13.83). The SR, PSRL, and ISLR parameters are determined based on point-like objects in the images. For this purpose, during preparations to the experiment a set of corner reflectors was placed in the central part of the imaged area and arranged in the shape of an arrow. In Figures 15 and 16, the horizontal red line marks the image line running through a corner reflector located in the lower arm of the arrow, for which SR, PSLR, and ISLR were calculated. The normalized amplitude of image pixels measured along this line is presented in Figure 17.

**Figure 16.** Image of the arrow made of corner reflectors: (**a**) with the INS/GPS-based MOCO, (**b**) with the MINS-based MOCO; red line—an analyzed row.

**Figure 17.** Normalized amplitude of the selected corner reflector image: (**a**) with the INS/GPS-based MOCO, (**b**) with the MINS-based MOCO.

Compared to the image obtained using the INS/GPS system, in the case of the MINS-based image the amplitude of sidelobes is lower (which is an advantage), while the main lobe is apparently wider. As a result, the SR of the MINS-based image (SR = 0.278 m) is slightly better than in the INS-based image (SR = 0.304) and theoretically worse than the result obtained with INS/GPS-based MOCO (SR = 0.119). In the case of the INS/GPS method, however, it should be noted that high-level sidelobes deteriorate the practical resolution, which can be seen in Figure 16. Visualization of the normalized amplitude in 2D is shown in Figures 18 and 19.

MINS-based MOCO allowed the best (lowest) values of PSLR and ISLR to be obtained among three analyzed navigation systems (PSLR = −8.57 dB, ISLR = −10.68 dB). The improvement with respect to the INS/GPS-based image (PSLR = 2.99 dB, ISLR = −1.52 dB) results from the smoothness of the navigation data calculated by the MINS system. The improvement with respect to the INS-based image (PSLR = −8.45 dB, ISLR = −10.50 dB) results from lower navigation errors, which led to a better fitting of the assumed reference function in the azimuth compression of the SAR algorithm. It should be noted that after evaluation of MOCO efficiency, the speckle noise of the SAR image can be reduced using techniques presented in [42,43].

**Figure 18.** Normalized amplitude of corner reflector with INS/GPS-based MOCO.

**Figure 19.** Normalized amplitude of corner reflector with MINS-based MOCO.

Similar tests were carried out for other UAV flights. Figure 20 shows the trajectory obtained using the MINS system for another analyzed flight (called here flight no 2). The time duration of this trajectory was approximately 24 s. Table 3 contains the values of quality indicators calculated for images obtained during this flight and using three MOCO methods.

The results show that among all three verified MOCO methods, the worst values of the considered quality indicators were obtained using the INS/GPS method. Better results are ensured using the INS-based MOCO, however, it should be noted that this image has geometric distortions. The best results were obtained using the MINS system. The corresponding image has the lowest values of SR, PSLR, and ISLR. The proposed method also allowed the best contrast and entropy to be obtained. The results obtained for two different flights led to the same conclusions. The comparison of the image

of the arrow and corresponding signal amplitudes obtained for the classic INS and for the proposed MINS system are presented in Figures 21 and 22.

**Figure 20.** MINS trajectories for flight no 2 (multicolor r line) and INS trajectory (blue line).


**Table 3.** Parameters of the quality of the selected SAR image.

**Figure 21.** Image of the arrow made of corner reflectors for flight no 2: (**a**) with the INS-based MOCO, (**b**) with the MINS-based MOCO; red line—an analyzed row.

**Figure 22.** Normalized amplitude of the selected corner reflector image: (**a**) with the INS-based MOCO, (**b**) with the MINS-based MOCO.
