Measuring the blood pressure as accurately as possible can save a lot of human lives. Hence, it is very important to find an optimal method to determine the systolic and diastolic pressures out of the measured oscillometric blood pressure waveform (OBPW). Recently, studies have shown that by working in the frequency domain, outperforming results could be obtained for the separation of breathing from cardiac activity. In this paper, we present a new implementation of the Kalman filtering algorithm to estimate the envelope of the cardiac activity. Even though the alternating Kalman filter algorithm has subharmonic infiltrations, it offers an envelope that, when applied together with the Windkessel model for calibration, substantially reduces the error of the calibrated systolic and diastolic pressures. This important result validates the non-linear model for the OBPW, as well as the Windkessel model for calibration.