## 4 Results and Application  
### Validation of Coherent Integration Time Optimization Model  
The proposed model precision results are compared with the experimental results to verify the effectiveness of the coherent integration time optimization model in this section. The measured precision is calculated as described in Section 2. With the power waveform processing time \(T_{\text{I}}=1\) s unchanged, the precision variation \(\sigma_{\text{h}}^{\text{obs}}(T_{\text{c}})\) with coherent integration time can be determined by varying the value of \(T_{\text{c}}\). To avoid the error interference caused by aircraft turning, two straight flight trajectories are selected for precision calculations. Figure 4B illustrates the inverted SSH sequence when \(T_{\text{c}}\) is 10 ms during the experiment. The corresponding SSH residual sequence is shown in Figure 4C. The coherent integration time optimization model has been acquired in the following steps as described in Section 3. Obtain auxiliary data during the experiment, including the position and velocity information of the receiver after dual-frequency orbit determination, the GPS satellite position and velocity using the IGS precision ephemeris interpolation method, wind speed (-7 m/s) and payload parameters. These simulation parameters are listed in Table 1. The elevation angle is computed with the bistatic geometry. The computation of the variations in the effective incoherent average number and altimeric sensitivity with coherent integration time can be obtained by applying Equations (17)-(19). Figure 4: Experimental area and IF data processing results. (**A**) The specular points tracks of the raw IF data. (**B**) Measured SSH relative to the WGS84 reference ellipsoid. (**C**) SSH residual after subtracting the fitted value. By substituting the intermediate results into Equation (7), the coherent integration time optimization model can be calculated. A comparison between the variance of the model and the measured result is shown in Figure 5. To evaluate the effectiveness of the model, the mean deviation of precision \(\left\langle\left|\sigma_{h}^{m}(T_{c})-\sigma_{h}^{\text{obs}}(T_{c})\right| \right\rangle\right\rangle\) is used. \(\sigma_{h}^{m}(T_{c})\) is the precision calculated by the model, whereas \(\sigma_{h}^{\text{obs}}(T_{c})\) is the measured precision. The results show that the average deviation between the red and blue curves is 0.85 m, and the average deviation between the red and black curves is 0.16 m. Therefore, the proposed model considering the correlation of the waveforms is in good agreement with the measured result. The model curve and the measured curve differ by a certain amount. On the one hand, the measured precision result is generally worse than that of the model, with an average of 0.16 m. This may be due to the lack of beamforming in the signal processing, which causes the SNR to decrease. On the other hand, the trend of the measured curve fluctuates. As opposed to the simulated results, the actual measurement results may contain other stochastic factors such as aircraft mechanical vibrations, attitude changes, \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Parameter** & **Value** \\ \hline Receiver height & \(\sim\)3000 m \\ Transmitter altitude & 20,200 km \\ Receiver velocity & 50 m/s \\ Antenna temperature & 200 K \\ Antenna gain & 15 dBi \\ Elevation angle & 70\({}^{\circ}\) \\ Processing interval & 39,102–40,721 \\ Power waveform processing time & 1 s \\ Wind speed & 7 m/s \\ Process method & iGNSS-R \\ Sampling frequency & 80 MHz \\ Carrier frequency & 1575.42 MHz (GPS L1) \\ Receiver bandwidth & 35 MHz \\ Waveform retracking method & DER \\ Filter bandwidth & 12 MHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Air-based simulation parameters that are consistent with those for the experiment described in Section 2. Figure 5: The variation of the precision with coherent integration time under different conditions. Red indicates the measured result.