An inertial navigation system employs geophysical (earth's magnetic and gravity) field sensors to measure body rotations of an aircraft or other vehicle. In effect, these replace expensive laser ring gyros used in conventional inertial navigation systems. The vector components of the geomagnetic field may be incorporated directly into the state vector describing the vehicle's attitude, acceleration, velocity, and position. A predictive filter (e.g. Kalman) operates on measured and predicted geophysical field components and on-board accelerometers. Predicted geophysical field components are obtained from maps and/or models of the earth's magnetic and gravity fields.