A system, comprising: one or more pairs of body-surface electrodes, which are configured to be attached to a body of a patient and to transmit electrical signals into the body; a shaft; a basket catheter coupled to the distal end of the shaft and comprising a plurality of expandable spines, each expandable spine having a plurality of outer-facing electrodes and a plurality of inner-facing electrodes, each of the plurality of inner-facing electrodes disposed directly opposite a respective one of the outer-facing electrodes, the inner-facing electrodes facing an internal volume of the basket catheter defined by a surface of revolution about the shaft defined by the expandable spines; and a processor, which is configured to: receive signals indicative of electrical potentials that are acquired by an outer-facing electrode of the outer-facing electrodes and an inner-facing electrode of the inner-facing electrodes of the basket catheter inserted in a heart cavity of the patient, resulting from the transmitted electrical signals, wherein the outer-facing electrode and the inner-facing electrode are disposed directly opposite each other; and at the same time: based on the signals indicative of the electrical potentials acquired by the outer-facing electrode, estimate a proximity of the basket catheter to surface tissue of the heart cavity; and based on the signals indicative of the electrical potentials acquired by the inner-facing electrode, estimate a position of the basket catheter within the heart cavity. one or more pairs of body-surface electrodes, which are configured to be attached to a body of a patient and to transmit electrical signals into the body; a shaft; a basket catheter coupled to the distal end of the shaft and comprising a plurality of expandable spines, each expandable spine having a plurality of outer-facing electrodes and a plurality of inner-facing electrodes, each of the plurality of inner-facing electrodes disposed directly opposite a respective one of the outer-facing electrodes, the inner-facing electrodes facing an internal volume of the basket catheter defined by a surface of revolution about the shaft defined by the expandable spines; and a processor, which is configured to: receive signals indicative of electrical potentials that are acquired by an outer-facing electrode of the outer-facing electrodes and an inner-facing electrode of the inner-facing electrodes of the basket catheter inserted in a heart cavity of the patient, resulting from the transmitted electrical signals, wherein the outer-facing electrode and the inner-facing electrode are disposed directly opposite each other; and at the same time: based on the signals indicative of the electrical potentials acquired by the outer-facing electrode, estimate a proximity of the basket catheter to surface tissue of the heart cavity; and based on the signals indicative of the electrical potentials acquired by the inner-facing electrode, estimate a position of the basket catheter within the heart cavity. receive signals indicative of electrical potentials that are acquired by an outer-facing electrode of the outer-facing electrodes and an inner-facing electrode of the inner-facing electrodes of the basket catheter inserted in a heart cavity of the patient, resulting from the transmitted electrical signals, wherein the outer-facing electrode and the inner-facing electrode are disposed directly opposite each other; and at the same time: based on the signals indicative of the electrical potentials acquired by the outer-facing electrode, estimate a proximity of the basket catheter to surface tissue of the heart cavity; and based on the signals indicative of the electrical potentials acquired by the inner-facing electrode, estimate a position of the basket catheter within the heart cavity. based on the signals indicative of the electrical potentials acquired by the outer-facing electrode, estimate a proximity of the basket catheter to surface tissue of the heart cavity; and based on the signals indicative of the electrical potentials acquired by the inner-facing electrode, estimate a position of the basket catheter within the heart cavity.