This paper deals with a complex problem in scientific sensing and imaging. To overcome some inherent problems in the conventional ECG (Electrocardiogram), we investigate in depth an ‘unassisted’ approach which enables ECG measurement without the placement of sensing leads on the body. Specifically, it uses a bathtub at home with tap water in it and passive sensing leads placed on its inner surface – while the subject lies in it. In this investigation we use a widely accepted assumption that the electrical activity of the heart may be, largely, represented by a 3-D time-varying Current Dipole (3D-CD). To determine the sensing matrix responsible for transforming the 3D-CD into the potential distribution on the bathtub’s internal surface, the 3D-CD signals are applied to a bathtub-containing-ellipsoid model in COMSOL tool. The sensing matrix thereby estimated is then utilized to back reconstruct the 3D-CD signals from the bathtub leads signals. NRMSEs (Normalized Root-Mean-Squared Errors) on the order of 0.02 to 0.05 are observed. The approach is also successfully extended to the case of two ellipsoids, one inside the other, representing a pregnant female subject. Critically important from a practical standpoint, the paper examines sensitivity with respect to the locations of the two 3D-CDs in the bathtub, and reports the encouraging results. Images of the potential distribution in the composite volume in the bathtub are presented as well.