## 4 Measurement Accuracy Analysis  
According to Equation (8), the antenna beam azimuth pointing measurement error includes the measurement error \(\Delta t_{A}\) at the satellite's ceiling time, the measurement error \(\Delta t_{B}\) at the beam alignment time, satellite velocity error \(\Delta V_{S}\), and space-to-earth range error \(\Delta R_{0}\). The satellite speed measurement error is within 1m/s, the precision track data can reach 0.1 m/s [18; 19; 20]; after the slant range calibration, the accuracy of the slant range can reach 1 m [21; 22]. Since the orbital altitude of LEO SAR satellites is generally in the range of 500 km to 800 km [23], and the speed is approximately 7500 m/s [24], the ratio of satellite speed measurement error and the ratio of slant range measurement error is very small, and the resulting error can be ignored.  
For the SAR transmit antenna pattern, the main lobe is relatively wide, and it is difficult to accurately determine the peak position. The energy center of the beam main lobe can be determined by the algorithm in Section 3, when the received data is complete and the value of N is large, and the measurement error theoretically does not exceed 1 PRT. However, due to the receiver's measurement error, improper recording start time, or insufficient data recording time, the data processing cannot achieve the desired effect, which causes the measured pulse position \(t_{B}^{\prime}\) to be inconsistent with the theoretical position \(t_{B}\), and introduces measurement error. This measurement error is equal to the difference between the extreme position of the measured data and the extreme position of the theoretical data. Since the theoretical data is not available, we use the fitting data \(P_{f}(t)\) instead of the theoretical data to obtain an estimate of the difference between the two. To synthesize the error of two parts, the error of measuring the beam center position is:  
\[\delta t_{B}=\big{|}t_{B}^{\prime}-t_{B}\big{|}+1 \tag{10}\]  
Range migration is also a very slow process. For low-resolution spaceborne SAR, only one or two range gates may be used in the synthetic aperture time, through the method of Section 3, the range pulse compression data is interpolated (generally 32 multiples are enough), and the range migration gate's amount can be enlarged to interpolation multiples, and achieve accurate positioning, and the measurement error theoretically does not exceed 1 PRT. However, due to various reasons, the measured data is not ideal, which causes the measured pulse position \(t_{A}^{\prime}\) to be inconsistent with the theoretical position \(t_{A}\) and introduces measurement error. Similarly, this measurement error is equal to the difference between the actual measurement data extreme position and the theoretical data extreme value position. Since the theoretical data is not available, here we use the fitting data \(R_{f}(t,\tau)\) instead of the theoretical data to obtain an estimate of the difference between the two. To synthesize the error of two parts, the error \(\delta t_{A}\) of measuring the center position of the range migration curve is:  
\[\delta t_{A}=\big{|}t_{A}^{\prime}-t_{A}\big{|}+1 \tag{11}\]  
Based on the above analysis, the antenna beam azimuth pointing measurement error is:  
\[\delta\alpha=\sqrt{\left(\delta t_{A}\right)^{2}+\left(\delta t_{B}\right)^{2 }}\cdot V_{S}/R_{0} \tag{12}\]  
where \(\delta\alpha\) is the squint angle measurement error of the antenna beam, the unit is radians.