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With hybrid and electric vehicle developments, battery-monitoring systems have to meet the new requirements of the automobile industry. This paper deals with one of them, the battery's ability to start a vehicle, also called battery crankability, through battery-resistance estimation. A fractional-order model obtained by system identification is used to estimate the internal resistance of lead-acid batteries. Fractional-order modeling permits an accurate simulation of the battery electrical behavior with a low number of parameters. Moreover, the high-frequency gain of the fractional model is directly linked to the battery resistance. A resistance-estimation method based on a frequency-invalidation method is, thus, proposed. It is demonstrated that the battery's available power that defines battery crankability is correlated to the battery resistance. Thus, a battery-crankability estimator using the battery resistance is suggested. Validation tests are carried out with various batteries. This estimator cannot be embedded in a microcontroller due to the linear-matrix-inequality-based optimization algorithm in the invalidation-model method used. A simplified algorithm is finally proposed, and its efficiency is proved.