Autonomous fetal ultrasonography with a robotic ultrasound (US) can potentially solve the issue of the shortage of ob-gyn physicians in prenatal care. In fetal cardiac diagnosis, acoustic shading derived from the fetal skeleton makes the scanning procedure using a robotic US cumbersome. We hypothesize that fetal bone distribution can be used for determining the fetal position and for subsequently estimating the heart position. This paper serves a method for estimating fetal heart position for autonomous cardiac diagnosis. Our proposed system is comprised of following three processes. First, the fetal bone distribution is generated by following steps: detect shadow areas derived from fetal bones; calculate the three-dimensional (3D) position of the bones; and identify bone types (skull, spine, and others) based on its shadow features. Next, the fetal head position and body axis are estimated based on the generated 3D bone distribution. Finally, the fetal chest position and thoracic sagittal axis of the fetus are estimated based on anatomical structures, and the position of the heart is determined. We validated the proposed method by evaluating the accuracies of bone detection and heart position estimation with three pregnant volunteers. The false positive rate of bone detection is less than 10%, which is sufficient for the proposed method; further, the estimation error for the heart position was within an acceptable error of 15 mm. These results demonstrate the sufficient accuracy of the proposed estimation method and suggest the potential of autonomous fetal cardiac diagnosis using robotic US scanning.