Transabdominal Fetal Pulse Oximetry (TFO) faces several challenges, including the acquisition of noisy Photoplethysmogram (PPG) signals that contain a mixture of maternal and weak fetal information and scarcity of the data points on which an estimation model can be calibrated. This paper presents a novel algorithm that addresses these problems and contributes to the estimation of fetal blood oxygen saturation from PPG signals sensed through the maternal abdomen in a non-invasive manner. Our approach is composed of two critical steps. First, we develop methods to approximate the contribution of pulsating and non-pulsating fetal tissue from the sensed mixed signal. Furthermore, we leverage prior information about the system under observation, such as the physiological plausibility of fetal SpO2 estimates, to mitigate measurement noise and infer additional data samples, enabling improvements in the inferred SpO2 estimation model. We have validated our approach in-vivo, using a pregnant sheep model with a hypoxic fetal lamb. Compared with gold standard SaO2 obtained from blood gas analysis, our fetal SpO2 estimation algorithm yields the cross-validation mean absolute error (MAE) of 6.29% and correlation factor of r=0.82.