Direct Instantaneous Frequency Rate Estimation to Improve the Carrier Estimation Performance in Mars Entry, Descent, and Landing Flight  
[PERSON]  
1 Department of Electronic Engineering, Tsinghua University, Beijing 100084, China; [EMAIL_ADDRESS] (W.H. ); [EMAIL_ADDRESS] (J.F.) 1  
[PERSON]  
1 Department of Electronic Engineering, Tsinghua University, Beijing 100084, China; [EMAIL_ADDRESS] (W.H. ); [EMAIL_ADDRESS] (J.F.) 1  
[PERSON]  
1 Department of Electronic Engineering, Tsinghua University, Beijing 100084, China; [EMAIL_ADDRESS] (W.H. ); [EMAIL_ADDRESS] (J.F.) 1  
[PERSON]  
2 Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China;[EMAIL_ADDRESS] (G.D.); [EMAIL_ADDRESS] (Z.Z.) 2  
[PERSON]  
2 Correspondence: [EMAIL_ADDRESS]; Tel. : +86-136-1125-5659222  
does not rely on the landing status of the probe (meaning that the measurements for scientific study could still be acquired even if the probe fails in the EDL flight, e.g., Beagle 2, Mars Polar Lander, and Schiaparelli) and could work in real time. Meanwhile, as the EDL flight is the most critical and challenging flight phase in a Mars robotic soft landing exploration, monitoring the onboard executions results, including the aerobraking maneuver, parachute deployment, heat shield ejection, and final landing, are key information for subsequent mission flight operations. As practiced in NASA's Mars robotic explorations, carrier detection and reconstruction could also play a critical role in the direct determination of the spacecraft flight dynamics, as well as the synchronization and demodulation of the downlink information [7; 8]. Besides, reconstructed carriers are also used to derive the planetary wind models as realized in VEGA (Venera and Gallei), Galileo, and Huygens [9; 10; 11]. Among all of the above scenarios, the carrier frequency accuracy is the critical concern. In this paper, we focus on the carrier estimation performance in Mars entry, descent, and landing flight phases. In deep space telecommunications, the downlink carrier is usually a sinusoidal signal and could be modeled as a polynomial phase signal (PPS) at high flight dynamic scenarios. A lot of the literatures have been focused on the parameter estimation performance of the carrier, in which the frequency maximum likelihood estimator (MLE) is the most famous one, as it has the asymptotic properties, but a multidimensional search process is required. Numerous instantaneous frequency estimators have also been developed, such as the phase locked loop, extended Kalman filter, and cross-product automatic frequency control loop, as well as the LMS (least mean square), RLS (recursive least square), spectrogram peak, and peak of WVD (Wigner-Ville distribution) [12; 13]. [PERSON] showed that the frequency maximum likelihood estimator has the lowest threshold signal to noise ratio (SNR) and outperforms the other estimators [13]; thus, it fits the need of carrier estimation in Mars EDL, and frequency MLE is also the typical carrier reconstruction algorithm for Mars EDL flight in NASA's Mars missions [8; 14]. In the frequency MLE approach, which is a two-dimensional maximum energy search algorithm, one of the key processing parameters is the coherent integration time, which heavily influences the estimation performance of the carrier. However, due to the existence of the large frequency rate, the frequency resolution in the fast Fourier transform (FFT) computation has to be large enough to accommodate the unknown signal dynamics; thus, the coherent integration time is quite limited, which degrades the estimation performance of the carrier frequency. The accurate flight dynamic model based on the knowledge of the Martian atmosphere and gravity field [15] helps to compensate for the Doppler frequency rate, which facilitates the extension of the coherent integration in the FFT computation [8], yet the Martian atmosphere model is not easy to be acquired.