# Non-ideal Motion Error Analysis in GMTIm

**Abstract **This chapter mainly discusses the non-ideal motion error compensation issue in GMTIm with real SAR data. Pointing at the problem that existing GMTIm algorithms have poor performances in the real SAR data processing, the impact of Doppler centroid is analyzed. The signal model of a moving target with non-ideal motion error is established, and the platform velocity error and cross-track velocity error of the moving target are analyzed. Moreover, an error estimation and compensation algorithm is presented, and a whole practical SAR data processing scheme with the algorithms in the frontal chapters is proposed. Finally, simulations and real data are utilized to prove the effectiveness of these algorithms.

## Introduction

The GMTI and GMTIm algorithms in several main working modes are discussed in the frontal chapters. Compared with GMTI, the GMTIm has a higher requirement to the signal processing. GMTIm uses the out-comings of GMTI, and is the foundation of the target recognition.

In traditional GMTIm algorithms, it is assumed that the moving target will be perfected focused with the precise estimations of the motion parameters. In simulations, this assumption is valid. However, in real data processing, we find that this assumption is valid only when the data has a steady echo character and the target has a simple motion. That is, the moving target cannot be perfectly focused in the existence of non-ideal phase errors even though the GMTIm algorithm is performed. Therefore, non-ideal motion error corrections must be added in the GMTIm algorithm.

This chapter mainly focuses on the non-ideal motion error compensation in GMTIm. The WAS mode has a short synthetic aperture time, thus the motion error is negligible. The geometry of FMCW SAR is the same as pulse SAR, so the stripmap SAR is used in this chapter to analyze the non-ideal motion errors. The motion errors are firstly analyzed, and then PGA algorithm is introduced.

© Springer Nature Singapore Pte Ltd. 2017

J. Yang, *Study on Ground Moving Target Indication and Imaging Technique of Airborne SAR,* Springer Theses, DOI 10.1007/978-981-10-3075-8_6

After PGA algorithm, the higher order phase errors are assumed to be compensated. However, the moving targets are still unfocused in most real data processing occasions. The impact of the non-ideal motion errors on the Doppler centroid is analyzed in this chapter. The signal model of a moving target with non-ideal motion errors is established, and two sorts of motion errors, i.e., platform velocity error and cross-track velocity error, are the causes of the Doppler centroid smear. A practical GMTIm algorithm is proposed to estimate and compensate these errors, and simulations and real data are used to validate the effectiveness of the algorithm.

This chapter is organized as follows. The motion error and PGA algorithm are introduced in Sect. 6.2. The signal model with non-ideal motion errors is established in Sect. 6.3. Section 6.4 analyzes two sorts of motion errors, and a practical GMTIm algorithm is proposed and testified in Sect. 6.5. In Sect. 6.6, we draw the conclusions.