It is often advantageous for ground vehicles to operate at or near their performance limits, with respect to vehicle traction. Real-world performance requirements result in maximization of the vector sum of accelerations to account for both longitudinal and lateral motion. At the core of this work is a traction control algorithm that operates on the same correlated input signals that a human expert driver would in order to maximize traction. An adaptive gradient ascent algorithm is proposed as a solution to vehicle traction control, and a real-time implementation is described using linear operator techniques, even though the tire-ground interface is highly non-linear. Two variations of the algorithm are presented, and both use a dynamic filter to estimate the gradient of the dynamic system with respect to the input. The first method uses measurements of the longitudinal and lateral accelerations of the vehicle, while the second method uses measurements of the traction forces directly. Performance of the proposed adaptive traction control algorithm is demonstrated using a series of driving maneuvers in which the longitudinal and lateral accelerations are maximized simultaneously or selectively. The simulations demonstrate the ability of the first algorithm to simultaneously maximize longitudinal and lateral acceleration, while the second algorithm demonstrates the ability to more selectively maximize individual traction forces. The algorithms developed in this work are well suited for efficient real-time control in ground vehicles in a variety of applications in which it is necessary to maximize both