A global navigation satellite sensor system (GNSS) and gyroscope control system for vehicle steering control comprising a GNSS receiver and antennas at a fixed spacing to determine a vehicle position, velocity and at least one of a heading angle, a pitch angle and a roll angle based on carrier phase position differences. The roll angle facilitates correction of the lateral motion induced position errors resultant from motion of the antennae as the vehicle moves based on an offset to ground and the roll angle. The system also includes a control system configured to receive the vehicle position, heading, and at least one of roll and pitch, and configured to generate a steering command to a vehicle steering system. The system includes gyroscopes for determining system attitude change with respect to multiple axes for integrating with GNSS-derived positioning information to determine vehicle position, velocity, rate-of-turn, attitude and other operating characteristics. A vehicle control method includes the steps of computing a position and a heading for the vehicle using GNSS positioning and a rate gyro for determining vehicle attitude, which is used for generating a steering command. Alternative aspects include multiple-antenna GNSS guidance methods for high-dynamic roll compensation, real-time kinematic (RTK) using single-frequency (L1) receivers, fixed and moving baselines between antennas, multi-position GNSS tail guidance (“breadcrumb following”) for crosstrack error correction, guiding multiple vehicles and pieces of equipment relative to each other and earth-moving equipment and method applications.