# How does IRS estimate the alignment time?

In modern airliners, e.g. A320, once the IRS is starting the alignment process, there is an ECAM message that indicates the alignment time, e.g. IRS IN ALIGN <7 MIN.

How can the IRS estimate the alignment time? From what I understand, the alignment is usually performed using a Kalman filter, which drives the state of the system to a convergence. Is there something in the algorithm that produces convergence time?

The time remaining is predetermined – a pre-set time function that is carried out. You can actually keep aligning for longer (more on that later), but as far as the required accuracy is concerned, you'd be wasting time unless the plane is at a high latitude.

[The ALIGN] mode requires 10 seconds of initialization during which the initial BITE is completed and ten minutes of alignment characterized by a Kalman filter. The filter gains are predetermined functions of align time developed for an optimum final alignment error that considers the sensor noise characteristics and the aircraft disturbances that may occur during alignment, such as wind gusts, refueling and passenger-loading. [...]

The fine alignment: implementation uses a seven-state Kalman filter with a pre-set gain schedule to perform the alignment function.

— DTIC ADA143244: Advances in Strapdown Inertial Systems. Lecture Series Held in Athens, Greece on 14-15 May 1984, in Rome, Italy on 17-18 May 1984 and in Copenhagen, Denmark on 21-22 May 1984 https://apps.dtic.mil/sti/citations/ADA143244

### Boeing example

Before the 777 and 787, the INS mode selections were OFF, ALIGN, NAV, and ATT.

• Going from OFF to ALIGN (momentarily) then NAV is the ~7-minute alignment
• Going from NAV to ALIGN (and reentering present position) then back to NAV is a fast alignment (~30 seconds) between flights
• Going from OFF to ALIGN (and staying there) is used at high latitudes (for the Boeing 747-400 that's between 70°12.0' and 78°15.0'), and takes a minimum of 17 minutes (after which NAV is selected).

### Now, where did this 17 come from?

That last bullet point is where it gets more interesting, and then more clear by going back in time:

Since by the 747-400's time the technology was well-known and not new anymore, the flight manuals started to skip what exactly happens in the alignment process, unlike the Carousel IV's manual – the first INS to be installed as default equipment.

The Carousel IV's manual explains the INS alignment sub-modes 8 to 0, which were counted down—with that in mind, see this excerpt:

As you can see, the C-IV can be left to go through another five (5) predetermined steps of 3.4 minutes each (3.4 times 5 is 17) to further improve the alignment; this more clearly shows how alignment is based on time-based steps.

In the newer 777 and 787 with only OFF and ON selections, the unit decides for itself if it's high latitude or not, and based on that it will show the predetermined time remaining.

• Do you know the function to determine the alignment time? IIRC it is a function of latitude, resulting in shorter alignment times the closer you are to the equator. Commented Nov 30, 2021 at 17:28
• @Bianfable: I found more details on the time-steps and high-latitude alignment, see update :)
– user14897
Commented Dec 16, 2021 at 18:21

Alignment of an IRS is done by mathematical ‘levelling’ of the accelerometers and gyrocompassing to determine true north. As this is a purely mathematical process it’s simple enough to predict how close to a solution you are…..a bit like installing software on your PC where it gives you a progress countdown.

• Installing a software is writing a pre-determined amount of data to a disk. So if you know the speed at which you write the data, you know how long it will take. For IRS alignment, you do not know the end state, so you could not know how long it will take to reach the end state Commented Nov 30, 2021 at 13:45
• Gyrocompassing measures topple so given that the RLGs will be sensing the magnitude, which dictates the alignment time, I’m sure that it’s not too difficult to work out how long it will take to finish gyrocompassing and therefore alignment.
– Nic
Commented Nov 30, 2021 at 15:56
• "Installing software on your PC". You obviously don't use Windows and its notoriously sketchy estimates of time remaining... Commented Dec 16, 2021 at 18:52