# Non-ideal Motion Error Estimation and Correction Algorithm

## Algorithm. Principle

To achieve an acceptable imaging quality in real application, the motion error must be estimated and compensated. Two sorts of motion errors can be compensated separately according to the processing steps as follows.

The INS data can be utilized for the platform velocity error compensation. In modern airborne SAR systems, the platform velocity history is recorded by the INS system. With the actual platform velocity V_{a}(t_{a}), the actual PRF history *PRF(t _{a}) *can be calculated according to Eq. 6.4.1.

As to the single moving target imaging, the compensation of the platform velocity error can be considered as a scaling transformation problem. The aim of the correction is to adjust the PRF in each azimuth sample to the same scale. The correction filter in 2-D time domain can be expressed as

where *PRF _{ave}* represents the average PRF, and

*f*is the average Doppler centroid of the moving target that estimated by Hough transform.

_{dc}After the platform velocity error compensation, the platform velocity and the PRF of the system are considered constant, and the residual Doppler centroid error is regarded as the result of the cross-track velocity error.

Since the motion of the moving target is not recorded by the system, the actual motion of the moving target should be estimated from the echo. After the RCM correction, the energy of the moving target is concentrated into a single range cell. By using the FrFT, the azimuth time-frequency distribution of the moving target can be obtained, and the Doppler centroid error caused by the cross-track velocity error can be estimated from it. The principle of our cross-track velocity error estimation algorithm is shown in Fig. 6.9.

A reference moving target without motion errors can be simulated, and the time-frequency distribution of the ideal moving target can be used to extract the information of the cross-track velocity error. The Doppler centroid error A*f _{dc}* can be extracted from the time-frequency distribution of the moving target, and the cross-track velocity error can be obtained as

The correction filter of the cross-track velocity error can be expressed as

**Fig. 6.9 ****The principle of the motion error estimation algorithm**

After the motion error compensation, the imaging resolution of the moving target can be significantly improved. Using the CLEAN technique [11], the flowchart of our whole moving target processing strategy can be illustrated as shown in Fig. 6.10.