Elevated umbilical artery pulsatility is a widely used biomarker for placental pathology leading to intra-uterine growth restriction and, in severe cases, still-birth. It has been hypothesized that placental pathology modifies umbilical artery pulsatility by altering the degree to which the pulse pressure wave, which originates from the fetal heart, is reflected from the placental vasculature to interfere with the incident wave. Here we present a method for estimating the reflected pulse wave in the umbilical artery of human fetuses using asynchronously acquired Doppler ultrasound measurements from the two ends of the umbilical cord. This approach assumes non-dispersive and loss-less propagation of the waves along the artery and models the reflection process as a linear system with a parameterized impulse response. Model parameters are determined from the measured Doppler waveforms by constrained optimization. Velocity waveforms were obtained from 142 pregnant volunteers where 123 met data quality criteria in at least one umbilical artery. The reflection model was consistent with the measured waveforms in 183 of 212 arteries that were analyzed. The analysis method was validated by applying it to simulated datasets and comparing solutions to ground-truth. With measurement noise levels typical of clinical ultrasound, parameters describing the reflected wave were accurately determined.