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This brief addresses two estimation problems relevant to traction control for motorcycles: longitudinal vehicle velocity estimation and wheelie (i.e., front wheel lifting off the ground during acceleration) detection. Two methods to estimate the vehicle body velocity are discussed and compared: a complementary filter and a Kalman filter. The Kalman filter reduces the noise affecting the estimate of the longitudinal vehicle velocity by an order of magnitude without introducing any phase lag. Furthermore, a wheelie detection algorithm is developed. The approach is based on the fault detection paradigm and detects wheelies in 70 ms. Both methods are computationally efficient and industrially viable. Track tests on an instrumented sport motorcycle are employed to illustrate and validate the methods.