According to the paper, one nautical mile per day was state of the art in 2006. They are shooting for one mile/month now

https://link.springer.com/article/10.1134/S207510871401009X

Thanks I'm interested to take a look in detail.

From the abstract

> In 2006, we presented at DGON symposium in Stuttgart [2] the design and navigation results of MARINS, the first FOG-based navigation system within the class of 1 nautical mile per day. This navigation system in now in production...

> have we reached the limits of the technology or can we still improve the performance of our sensors?

> Of course, the present FOG design is not good enough for the required performance, even in a strictly controlled environment.

This is a discussion of how it could be improved not what is available in production and certainly not close to being available within a phone - which was the original point.

Fibre optic gyros can be miniturized to millimeter dimension, if it wasn't for ITAR.

High end civilian IMU's typically use mechanical gyros which have been obsolete for decades. Also, a phone isn't typically moving constantly like the oceans so error rates would be lower.

This is drift for a "static" million dollar marine grade (i.e. highest grade we currently have) INS not in the ocean or moving. Drift is measured in non-moving conditions. These are the fiber optic and laser sytems you are referring to.

Even if we could make that cheap and small enough it would still need regular corrections far more frequently than a week to be as good as a GPS is now.

You could use some smart heuristics to make corrections without a gps lock, like resetting the location to "home" if it is near enough and sits motionless over night, or making an adjustment whenever the location drifts too far from the known locations of currently connected cell towers.

You won't get close to GPS accuracy with these. The uncertainty from cell tower triangulation is huge (relatively). But yes, some kind of beacon that works like GPS on a local scale or detection of known mapped landmarks could be used for corrections but there are issues with these too. These could assist GPS location rather than replace it entirely.

> These could assist GPS location rather than replace it entirely.

Of course, that was the proposal. There's more datapoints if you're willing to get creative, wifi networks (already used for this), cooperative comparison with other mobile devices in a local meshnet, acoustic cues from the environment, machine analysis of captured images, etc. Obviously dead reckoning without gps is going to require a multi-pronged approach.

> cooperative comparison with other mobile devices in a local meshnet

Please explain how this will work?

I could imagine a secure location service that allows your phone to compare its current expected position with other nearby phones' expectations of their positions. If it's over bluetooth or wifi, the positions should be within meters of each other. This could provide an input to a kalmann filter type position estimator to help reduce drift as you (for example) walk down the street.

This doesn't make a lot of sense tbh.

What do you mean?

You don't think such a system is practical, or you don't think such a system is technologically feasible?

Or you just don't understand the system I'm describing?

I think there are both feasibility and practicality issues with the cooperative estimation scheme you are describing. Without already knowing where the phones are very accuratly there will be a lot of noise. Would need a lot more detail to really understand what you intend but first reaction is that it'd be very difficult to do well.

If you really care you could sketch out what exactly it is and how it'd work for yourself for a couple of devices (or more) and see what issues you uncover.

You might be right but I have doubts. Most weapons are INS guided despite the long fly times of cruise missiles etc. ITAR has a massive chilling effect on development, I wouldn't be surprised if we had error rates of less than a meter a day in mobiles if development wasn't severely curtailed

This works the other way - you get to prove your assertion that inertial navigation could work with cheap miniaturized sensors. Anyone can cast a doubt without proof.

If your acceleration sensor is off by 1 part per million, 9.8 m/s^2 (i.e. gravity) will turn into a positioning error of ~73km in one day.

Cruise missiles combine (using Tomahawk as an example) GPS, visual terrain-matching, radar terrain-matching, and INS. Because they know INS needs those constant corrections.

> Most weapons are INS guided despite the long fly times of cruise missiles etc.

And because of a long fly time or imprecise initial reference point (a submarine is floating) some do corrections. One of the coolest one for ICBMs is to use celestial navigation to correct errors. They'd have a window with a camera and would "look" for a few stars.

Drift is over a given time, not distance. Missiles generally have an very short fly time, even if they're going really far.

Cruise missiles are very different from (quasi-)ballistic or anti-aircraft missiles - they fly at subsonic speeds at low altitudes (usually using a turbojet) to avoid interception. For example, the classic Tomahawk flies at ~900km/h, with the long-range variants having a range of 2500km, giving a maximum flight time on the order of hours, and so a pure INS drift on the order of low hundreds of meters.

sensor fusion combines multiple sensors with different characteristics such as:

- GPS; widespread, low accuracy

- INS; always available, high short-term accuracy, terrible long-term accuracy

- terrain-matching: large-scale corrections.

The different characteristics allow one sensor to correct another to a degree to produce an overall stable position.

Not sure what IMUs you're using, but we've been using civilian MEMS and FOG IMUs for years now. You still can't make anything purely inertial good enough to keep position accurately enough to be a GPS replacement for more than a few hours.

Plus the gyros would have to be powered at all times -- that's not gonna work on mobiles.

So this is why my smartwatch can tell me my speed before it has a GPS lock, including indoors? Very cool! But of course, as you say, the reports of my absolute position are very inaccurate.

Velocity can come from dopplar shift of the GPS carrier frequencies. This is very accurate. An IMU can be used for walking speed estimation but it won't be as accurate using a human gait model or direct integration.

No, any position-solution produced before a GPS lock will be due to the approximation produced by either using the last-known position or the cell-tower triangulation. That information is also used as a seed for the GPS lock to speed up the time-to-fix.