## 6 Results and Discussion  
As the IFR tracking approach has a lower tracking threshold SNR for aerobraking flight, we first compare the carrier estimation performance for the two approaches. When the CNR is set to 22.6 dBHz, the Doppler and Doppler rate estimation results with an IFR estimation approach for aerobraking flight are shown in Figure 24, and the estimation errors are shown in Figure 25.  
Figure 23: Simulation results of an IFR tracking approach for parachute deployment at CNR = 26 dB-Hz: (**a**) Doppler rate; (**b**) Doppler frequency. Figure 24: Estimation result of an IFR tracking approach for one aerobraking flight trial at CNR = 22.6 dB-Hz: (**a**) Doppler rate; (**b**) Doppler frequency. Figure 25: Estimation errors of an IFR tracking approach for one aerobraking flight trial at CNR = 22.6 dB-Hz: (**a**) Doppler rate errors; (**b**) Doppler frequency errors. With a CNR of 23 dBHz, the Doppler and Doppler rate estimation results with a 2D search approach for the whole EDL flight are shown in Figure 26, and the estimation errors are shown in Figure 27.  
The root mean square of the Doppler frequency and Doppler rate for the two approaches are summarized in Table 3. With the help of direct instantaneous frequency rate estimation and the extending of the coherent integration time as long as possible, the r.m.s. for both Doppler frequency and Doppler rate have been largely reduced. While the performance of IFR tracking approach is excellent, it does not work well for parachute deployment until the CNR goes above the tracking threshold, which is 29 dB/Hz with 0.1 s of coherent integration time. The RMS of Doppler frequency for an IFR tracking approach is 0.57 Hz, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Estimation Approach** & **IFR Tracking (22.6 dB-Hz)** & **2D Search (23 dB-Hz)** \\ \hline Doppler rate & 1.97 Hz/s & 82.7 Hz/s \\ Doppler frequency & 0.45 Hz & 26.6 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Root mean square (RMS) of estimation results. Figure 27: Estimation errors of a 2D search approach for one EDL flight trial at CNR = 23 dB-Hz: (a) Doppler rate errors; (b) Doppler frequency errors. Figure 26: Estimation result of a 2D search approach for one entry, descent, and landing (EDL) flight trial at CNR = 23 dB-Hz: (a) Doppler rate; (b) Doppler frequency. with an outlier only occurring at the time instant of parachute deployment, as shown in Figure 21b. Another simulation shows that with the same CNR (29 dB/Hz), the RMS of Doppler frequency by a 2D search approach using the same value of processing parameters is 17.9 Hz, which indicates that the IFR tracking approach still has a better estimation performance. On the other hand, the IFR tracking approach relies heavily on the a priori Doppler phase to engage the direct estimation of instantaneous frequency rate without squaring loss, and facilitate the extending of the coherent integration time, while the 2D search approach does not need any a priori information to estimate the signal parameters, and makes a decision on the detection of the signal presence. Thus, the 2D search approach, which is a standard open loop batch processing manner, has a better robust estimation performance. The threshold SNR is around 22.5 dB/Hz for the whole EDL flight, including the critical parachute deployment mission phase, while the IFR tracking approach could achieve a much more accurate estimation. In the practical approach, these two approaches could be combined to enhance the carrier tracking performance while still preserving an excellent performance of carrier detection when the signal is lost due to the brownout and blackout encountered in the Mars atmosphere EDL flight [25]. The performance of both approaches could be improved by the reduction of parameter search space.