Inertial Navigation Systems calculate position by measuring acceleration. But they are unable to measure gravitational acceleration since gravity always acts equally on the test mass and the instrument platform.
Inertial Navigation Systems use Inertial Measurement Units (IMUs) to sense acceleration. Essential components of IMUs include triads of
• Accelerometers to measure linear acceleration
• Gyroscopes to measure angular acceleration
An IMU consists of two triads: 3 accelerometers and 3 gyroscopes. This provides 6-axis measurements of linear and angular acceleration, from which the state vector can be calculated by a Computational Unit (CU).
The combination of IMU and CU is used to determine the attitude, position, and velocity of the system based on the raw measurements from the IMU and a known initial starting position.
Apollo Inertial Measurement Unit
The accelerometers measure the combined linear acceleration plus the pseudo-acceleration caused by gravity. To obtain the system's linear acceleration due to motion, the gravitational pseudo-acceleration must be subtracted from the accelerometer measurement using assumptions of the local gravitational acceleration.
For instance, if the system was sitting on the kitchen table, the vertical axis accelerometer would report a 1g vertical acceleration despite the fact it is stationary, while if it were in free-fall it would report zero acceleration despite the fact it is accelerating.
The CU could easily compensate for gravity if the system were in a known uniform gravitational field. But spacecraft operate in variable gravitational fields. Think of a satellite in Low Lunar Orbit or NRHO
An IMU in free-fall will always "think" it is travelling in a straight line at a constant velocity despite the fact it is travelling in a curved path.
How do Inertial navigation Systems compensate for their inability to measure gravitational acceleration? Do they carry a “Gravitational Ephemeris”?