Methods and apparatus for: (a) the correction of one or more elements determined from a first set of continuous gyro and accelerometer measurements comprising using a second set of discontinuously measured higher accuracy accelerometer measurements doubly integrated in an inertial coordinate system, (b) determining relative movement of a vehicle using a first set of acceleration measurements that do not include components of acceleration caused by the Earth's gravitational field, and a second set of acceleration measurements that do include components of acceleration caused by the Earth's gravitational field; and (c) correcting errors in an inertial navigation system positioned in a vehicle comprising using independently measured changes in position of the vehicle relative to an inertial coordinate frame.