The precision dynamic measurement of absolute gravity based on the cold atom interferometer can provide a new method for marine gravimetry, so that it has attracted more attention. Based on the homemade shipborne cold atom interferometric absolute gravity measurement system, we carry out a series of measurement experiments in a certain area of the South China Sea. Under dynamic conditions, the suppression of measurement noise is essential for the improvement of the measurement performance. According to the physical model of the measurement system, in this paper a data processing method is proposed based on the extended Kalman filter algorithm for the absolute gravity dynamic measurement. The observed atomic interference fringe data are filtered in the time domain to estimate the absolute gravity value. Based on this processing method, the sensitivity of absolute gravity measurement under the condition of ship speed less than 2.1 km/h is improved from 300.2 mGal/Hz^1/2 to 136.8 mGal/Hz^1/2 (T = 4 ms). Comparing the processed data with the data calculated from the earth gravity model (XGM2019), it is found that both of the data are in good agreement. These results confirm the effectiveness of the data processing method proposed in this paper, and provide a new processing method of suppressing the measurement noise of shipborne cold atom interferometric absolute gravity measurement system.