Vehicle position estimation system

A method for estimating a position of a vehicle, the vehicle including a gradiometer, the method comprising:

• calculating, by a processor, a gravity vector using a gravity spatial derivative generated by the gradiometer and a plurality of body velocities generated by a body velocity source;
• calculating, by the processor, a gravity potential based on the gravity vector;
• estimating, by the processor, an inertial measurement unit (IMU)-based position of the vehicle using the gravity vector, a body acceleration, and a body attitude, the body acceleration and the body attitude being of the vehicle and being generated by an IMU;
• estimating, by the processor, a gravity vector-based position of the vehicle using the gravity vector;
• estimating, by the processor, a gravity map-based position of the vehicle using the gravity potential and one or more gravitational maps;
• estimating, by the processor, the position of the vehicle based on the IMU-based position, the gravity vector-based position, and the gravity map-based position;
• and
• controlling at least one of the vehicle and a second vehicle based on the position of the vehicle.

A non-transitory computer-readable medium for estimating a position of a vehicle, the vehicle including a gradiometer, the non-transitory computer-readable medium including instructions that when executed by a processor cause the processor to:

• calculate a gravity vector using a gravity spatial derivative generated by the gradiometer and a plurality of body velocities generated by a body velocity source;
• calculate a gravity potential based on the gravity vector;
• estimate an inertial measurement unit (IMU)-based position of the vehicle using the gravity vector, a body acceleration, and a body attitude, the body acceleration and the body attitude being of the vehicle and being generated by an IMU;
• estimate a gravity vector-based position of the vehicle using the gravity vector;
• estimate a gravity map-based position of the vehicle using the gravity potential and one or more gravitational maps;
• estimate the position of the vehicle based on the IMU-based position, the gravity vector-based position, and the gravity map-based position;
• and
• control at least one of the vehicle and a second vehicle based on the position of the vehicle.