A sensor fusion method for state estimation of a flexible industrial robot is developed to enhance the performance. By measuring the acceleration at the end-effector, the accuracy of the arm angular position, velocity, and acceleration estimates are improved. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; one using the extended Kalman filter (EKF) and one using the particle filter (PF). In a simulation study on a realistic flexible industrial robot, the position performance is shown to be close to the fundamental Cramer-Rao lower bound (CRLB), outperforming the previous non-accelerometer method. The technique is also verified in experiments on the ABB IRB4600 robot, where the dynamic performance for the accelerometer method is significantly better, even when model errors are present.