A battery state-of-health monitoring and prognosis method includes training off-line parity-relation parameters between extracted battery voltage and current signals during off-line battery discharge events using at least one good off-line battery. Portions of terminal voltage and current signals of an on-board battery corresponding to an on-board engine cranking process are extracted, and battery voltage of the on-board battery are estimated based on the parity-relation parameters and the extracted portions of the on-board battery current signals. A diagnostic residual defining a deviation between the battery voltage estimation of the on-board battery and extracted portions of the on-board battery terminal voltage signals is generated. A measure of battery state-of-health based on the diagnostic residual is then provided.