Incoherent averaging of Fourier transforms helps to reduce the noise fluctuation [16], while the processing gain is still moderate. Besides, as all of the cell combinations of possible frequency and frequency rate have to be tested in the 2D search space, the chance that the energy of a noise-only frequency cell exceeds the energy of a signal plus noise frequency cell seems to be large, which is not beneficial for frequency estimation. Recently, a cubic phase function (CPF) has been proposed to directly estimate the instantaneous frequency rate of the PPS [17; 18]. With the introduction of direct frequency rate estimation, the coherent time could be extended, and the parameter search space could be reduced, which are both beneficial for performance improvement. Due to the cross-product operation inherent in the computation of the CPF statistics, the squaring loss issue at low SNR conditions has to be overcome, which leads to the development of the integrated CPF (ICPF) [19] and coherently integrated (CICPF) [20] estimators. The incoherent integration is used in ICPF, which still limits its capability to suppress the noise effect. Meanwhile, the phase has to be aligned for different frequency rate cells in the coherent integration of CICPF, which still seems to be complexed. If another CPF statistic could be developed that works well at low SNR conditions, the carrier estimation performance may be improved for Mars EDL flight. In this paper, we propose an instantaneous frequency rate (IFR) tracking approach to improve the carrier estimation performance. A priori Doppler phase model derived from previous estimations is used to generate the proposed sequential CPF statistics, which proves to have good performance for IFR estimation at low SNR. Estimation performances have been evaluated and compared between the 2D maximum energy search algorithm and the proposed IFR tracking approach for the Mars EDL flight, and the results show that the IFR tracking approach could estimate the carrier frequency more precisely for the aerobraking flight phase. The root mean square (RMS) of frequency estimation error is around 0.45 Hz, with 0.25 s coherent integration when carrier power to noise power density ratio is 22.6 dB/Hz. For the parachute deployment flight phase, the 2D maximum energy search approach has a lower estimation threshold SNR, while the estimation accuracy of the IFR tracking approach still outperforms the 2D search approach when the carrier-to-noise density ratio (CNR) is set to the threshold of IFR tracking approach for parachute deployment phase. The paper is organized as follows. Section 2 lays out the basic signal model and looks back to the basic thought of the frequency maximum likelihood estimation model. Section 3 makes an analysis of the signal dynamics based on the released trajectory of the Mars Science Laboratory EDL flight. Section 4 reviews the basic theoretical formulas for 2D maximum energy search, analyzes the effects of processing parameters, and reevaluates the estimation performance without the Martian atmosphere model by simulation on the released trajectory. Section 5 gives a comprehensive study of the prosed IFR tracking approach. Section 6 compares the estimation accuracy and makes a discussion. Section 7 summarizes the basic conclusion for the whole paper.