# How can aircraft determine true north for inertial navigation systems?

Aircraft use GPS and inertial navigation systems in combination. Sometimes INS needs alignment (i.e. to be told where it is AND what orientation it has). How can an aircraft be be aligned to true north for proper INS alignment? Are markings at the parking location good enough?

An inertial system is referenced to the north on the ground, by sensing Earth's rotation.

The pilot will just provide the current latitude to allow this process to work accurately. Some platforms can also be fully realigned in flight ("alignment in motion") using the GPS, but the accuracy is currently not as good as for a static alignment.

How inertial works

Regardless of the underlying exact technology (mechanical gyroscope, laser, MEMS, ...) and the name (INS, IRS, ...), an inertial system contains:

• 3 gyroscope units to sense rotation movements
• 3 accelerometer units to sense gravity and other linear accelerations

The 3 pairs (a gyroscope and an accelerometer) are disposed along 3 orthogonal axis.

Boeing 737 NG IRS (source)

An inertial system must be aligned before use.

• Alignment on the horizontal plane (roll and pitch angles)
• Orientation on true north (parallel to the Earth rotation axis)

Alignment

The alignment process is quite slow because it's iterative and stops when the values obtained have converged enough. This convergence is quicker at the equator. Twenty minutes is not unusual at 45° latitude.

Local vertical

The vertical at the location can be determined from the acceleration of the gravity (sensed by the 3 accelerometers when the system is not horizontal). Knowing the vertical, the horizontal plane is normal to this vector and the attitude of the aircraft can be determined.

True north

Earth rotation is sensed by the 3 gyroscopes, and the result allows to determine the north pole-south pole axis. However north pole direction cannot be known without knowing local latitude, and vice-versa.

The practical way to proceed is:

• Set an initial value for latitude (it can be assumed).
• From approximate latitude, determine north direction approximately.

then:

• From approximate north, refine latitude.
• From refined latitude, refine north direction.
• etc.

The more iterations the more accurate north direction. However the north direction has not to be so accurate for navigation (a CDI is also an approximate instrument).

When the north direction has been determined the alignment is complete. Note that this process requires the aircraft to be motionless, which prevents it to be executed in flight.

The inertial will use north direction to provide aircraft heading, not to compute aircraft actual position.

Latitude/longitude (initial location)

Aircraft position is determined in flight based on a known initial position and double integration of aircraft acceleration sensed by the 3 accelerometers.

The initial position is provided, usually by the crew.

On the Boeing 737, the FMS Control Display Unit is used to select the current position from different sources (last position, airport reference point, gate coordinates (source)

Alignment in-flight

Older inertial systems can be partially realigned in flight if the reference is lost (the position is lost). But the north direction and the current position will be lost. The system will still be able to provide aircraft attitude.

The two IRS switches in the normal (navigation) position. The ATT position would be used after a realignment in flight, only the attitude would then be available. The ALIGN position is used the start the alignment process (source)

Other inertial systems can reacquire the position from the GPS and determine again the bearing of the north.

• The acceleration due to Earth rotation can't be told apart from that due to gravity. However, the rotation itself can, since the gyroscopes will maintain fixed plane of rotation relative to universe. – Jan Hudec Feb 28 '16 at 14:10
• @JanHudec: I simplified my post and included your feedback. Thanks. – mins Feb 28 '16 at 17:41
• Firstly GPS gives position but NOT orientation, hence not true north or any other orientation information. I have since read confirming my understanding that a LINS on the ground by detecting gravity and earth rotation can determine latitude and true north by itself, (Though not longitude.) To speed up alignment it is best to park a/c at a known position at aerodrome with known orientation marked with parking position and north. How does person who paints on the parking position coordinates AND direction to north. Does he/she use the stars? – Cahal Cormican Feb 29 '16 at 20:04
• @CahalCormican: GPS doesn't provide north indication, it's calculated by inertial: right. North is entered based on ramp markings: wrong, it's not necessary. Ramp coordinates are determined using differential GPS surveying and then loaded into the FMS database by database updates each 28 days. The precision of the D-GPS is about 10 cm, but can be improved further with longer integration time, when required. There is not survey based on stars, it is not precise enough, it can used by spacecraft remote from the GPS constellation. – mins Feb 29 '16 at 22:19
• This all sounded true and informative until this statement "The inertial system can determine the latitude by sensing local acceleration, but not the longitude. Longitude is provided, usually by the pilot. Latitude is provided as well at the same time." which is contradictory to what you wrote in the beginning "The pilot will just provide the current latitude to allow this process to work accurately". – Craig K Mar 1 '16 at 2:11