This work presents an intention decoding algorithm that can be used to control a 4 degrees-of-freedom shoulder-elbow exoskeleton in reaching tasks. The algorithm was designed to assist the movement of users with upper-limb impairments who can initiate the movement by themselves. It relies on the observation of the initial part of the user's movement through joint angle measures and aims to estimate in real-time the phase of the movement and predict the goal position of the hand in the reaching task. The algorithm is based on adaptive Dynamic Movement Primitives and Gaussian Mixture Models. The performance of the algorithm was verified in robot-assisted planar reaching movements performed by one healthy subject wearing the exoskeleton. Tests included movements of different amplitudes and orientations. Results showed that the algorithm could predict the hand's final position with an error lower than 5 cm after 0.25 s from the movement onset, and that the final position reached during the tests was on average less than 4 cm far from the target position. Finally, the effects of the assistance were observed in a reduction of the activation of the Biceps Brachii and of the time to execute the reaching tasks.