Which we have, not only is there a coarse scale global magnetic field model (two versions, in fact) there are detailed high resolution maps for large areas of the world (eg: all of Mali, all of Australia, most of Canada, much of the central 'stans) where mineral exploration has taken place.

The positioning is complicated by the drift over time (there's a "new" global model every five years and for specific times & locations interpolation is performed) and fluctuates daily (as the Earth turns there's a diurnal pulsing in the induced magnetic field).

This is where "a bit of signal processing" comes into play.

The good news is the maths, the field testing, and the application of it is all a good 50 years old.

Typical exploration mapping company:

http://mcpharinternational.com/services/mining-exploration/a...

High resolution gridded geophysics for the Northern Territory, magnetics, gravity, radiometrics, etc:

http://www.nt.gov.au/d/Minerals_Energy/Geoscience/index.cfm?...

Thanks! Very interesting.

There are solutions that do not need any pre-established magnetic field maps, because they simply derive velocity from local magnetic field disturbances and use magnometer measurements as an additional input for odometry calculations, using data fusion algorithms (e.g Kalman filtering). This allows to basically eliminate the drift induced by two successive integrations with low-cost IMUs.

And with enough sensors (4 magnetometers) you can reconstruct 3D trajectory.

The following thesis is fascinating and very instructive: http://pastel.archives-ouvertes.fr/docs/00/50/10/05/PDF/pdfV...

Chapter 5 is very instructive, in particular the section Measuring magnetic fields gradients to derive velocity.

Excerpts: If the body moves, then the sensed magnetic field must change according to Maxwell’s equations. If the magnetic measurements do not change significantly, then the solid body is not moving. This permits us to rule out velocity drifts in our estimation. Ultimately, this improves the position information obtained by integrating the velocity estimate.

Note that they don't use the raw magnetic field, but its gradients, i.e a physical quantity that is intrinsequely local. Filtering out the earth's magnetic fields becomes quite easy (I suppose..) since these gradients are fast-varying quantities in comparison. Kind of like when you use an accelerometer: gravity is low-frequency, motions are high-frequency.

Very interesting link... From 5.4.3, it actually looks like their magnetic positioning system works better in an indoor environment with lots of magnetic perturbations.

I would not have expected that result, but thinking about it more it does make sense. They are estimating "where have I moved" using the local magnetic field, which is very different than how GPS works "where am I in relation to a fixed constellation".