**5. Conclusions**

The article discusses a method of calculating UAV navigation elements (position, velocity, and attitude) using the proposed multi-instance INS (MINS). The motivation for its development was the analysis of the pros and cons of the INS- and INS/GPS-based MOCO methods used in SAR algorithms and the search for a new method which profits from the advantages of existing MOCO procedures but avoids their drawbacks.

The results obtained from the proposed MINS system are smooth, similar to the classical INS output. Moreover, thanks to the initialization of new INS instances, errors in MINS are kept at a low level, similar to the INS/GPS systems.

The presented MINS system was tested using real measurement navigation and radar data. Based on the obtained results, it can be concluded that the radar images calculated using MINS data combine the positive features of INS- and INS/GPS-based images. Thanks to the MINS error control, a significant reduction of geometric distortions was obtained, analogous to the results achieved with the use of the INS/GPS system. On the other hand, thanks to the INS instance switching procedure, it is possible to avoid abrupt changes of the position and velocity data, which is a drawback of the INS/GPS system. Moreover, the proposed mechanism allows for high contrast and entropy to be maintained and for the improvement of the PSRL and ISLR in relation to the INS-based images.

The proposed MINS system is based on chosen ideas presented in [15,19,21]. The authors added an INS instance switching algorithm that uses overlaps. Thanks to this procedure, each synthetic aperture uses corrections based on only one INS instance; therefore, there are no abrupt changes in the navigation elements which are characteristic of the INS/GPS integrated navigation system. As a result, the duration of the measurement session is not limited (contrary to the system presented in [21]) and, at the same time, the errors of measured flight trajectory are periodically corrected.

Further works related to the MINS algorithm are possible, and they should concern the use of a more complex filter than presented in [34]. By enriching the dynamics model with additional state variables, such as accelerometer and gyroscope biases and scale factor errors, as well as changing the structure of the loosely integrated INS/GPS system into a tightly integrated one, where GPS satellite pseudoranges and range rates are used instead of the position and velocity, it would be possible to improve the accuracy of the INS/GPS system. This would also positively influence the accuracy of the MINS system and consequently the quality of the radar terrain images.

The MINS-based MOCO can be an alternative to autofocus methods, especially in real-time systems, which aim to quickly obtain high-quality images. The advantage of the proposed method is the fact that the image synthesis is performed without iterations, and navigation corrections are calculated in a parallelly-working subsystem, independently of the SAR system calculations.

**Author Contributions:** Conceptualization, M.L., P.K.; methodology, M.L., P.K.; software and validation, M.L., P.K.; investigation, M.L., P.K.; writing-original draft preparation, M.L.; writing-review and editing, P.K. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This project was supported by the National Centre for Research and Development, Poland, in the frame of the Applied Research Program under Research Project PBS/B3/15/2012.

**Acknowledgments:** We would like to thank our colleagues from MUT and WB Electronics S.A. who participated in data collection.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
