This paper focuses on the carrier estimation performance improvement in Mars item, descent, and landing (EDL) flights. Carrier reconstruction could be used for trajectory derivation and Martian atmosphere profile inversion, and is the critical information for mission operations, as it helps determine the flight status of the spacecraft, demodulate the downlink information. The current approach is maximum likelihood estimation based on a two-dimensional (2D) maximum energy search algorithm, which computes the grid energy over all the combinations of frequency cells and frequency rate cells among the search space. Although it has good performance on robust estimation, the frequency estimation accuracy is limited due to the short coherent integration. An instantaneous frequency rate tracking approach based on the cubic phase function (CPF) is proposed that directly estimates the instantaneous frequency rate over the frequency rate cells, followed by the frequency estimation among the frequency cells. A sequential estimation method is introduced to propose the sequential CPF statistics, which uses the a priori Doppler phase information to suppress the noise squaring loss inherent in the standard CPF statistics. Simulations have been made on the released Mars Science Laboratory EDL trajectory for the two approaches, which show that considerable estimation improvement has been achieved for aerobraking flight by the new algorithm.