Abstract: A method and system to decode neural activity in the motor cortex to infer at least the position and velocity of a subject's hand from neural spiking activity of some number of nerve cells. In one embodiment the method includes simultaneously recording electrical activity of the nerve cells in the primary motor cortex to obtain neural data; and modeling the encoding and decoding of the neural data using a Kalman filter, where a measurement model assumes a cell firing rate to be a stochastic linear function of at least the position and velocity of the hand, and where the measurement model is learned from training data in conjunction with a system model that encodes a manner in which the hand moves.