AUTONOMOUS UNDERWATER VEHICLES
Chris: My graduate research focused on using a fleet of small autonomous underwater vehicles (AUVs / robot subs) to measure the magnetic signature of naval surface vessels (aka ships). Thanks to everyone at the University of Idaho on the project and our sponsors at the Office of Naval Research!
WHY
Some mines still depend on magnetism. Some military vessels have loops of copper wire used to cancel the magnetism of the vessel's steel hull, but we need a pretty good map of the original magnetic signature to do that.
The Navy already has facilities for doing this in port, but vessels pick up a new magnetic signature when they travel around the world (this is why ships would zig-zag while traversing the ocean in WWII). So it would be nice to have a way to measure the magnetic signature while they're out in the ocean.
KALMAN FILTERING
To make this magnetic map of a ship's hull, the AUVs need to know where they are relative to the ship. This would be trivial if GPS worked underwater, but ... it doesn't. So they need a more advanced technique. A Kalman filter lets us combine a variety of complex and imperfect measurements (depth sensors, sonar pings from buoys, compass) with a model of how a submarine moves in order to accurately estimate its current state (heading, velocity, and position). Kalman filters are also used for cruise missiles or the space shuttle.
The figure below shows an AUV navigating from left to right using a Kalman filter: the black "+" marks are ground truth, actual position based on a Navy sonar tracking position, the blue dots are the AUV's best guess using a Kalman filter at where is while navigating, while the red line is made by an acausal Rauch-Tung-Striebel filter that smooths out the Kalman filter's guess after the run is complete (hindsight is 20/20 principle at work). Together, they produce some pretty accurate navigation.
MAGNETOMETER CALIBRATION
Once we've located the ship and the subs, we can measure the magnetic signature.
But this measurement is corrupted by flaws in the magnetometer and the distortions caused by an operating AUV right next to the magnetometer. The figure below shows that the raw signal is absolute rubbish. So how do we fix that, given the need to measure small disturbances like the one shown in the black filtered line?
Well, a lot of the noise is due to our error: on a team we always inherit legacy decisions that were less than optimal. In this case, someone decided to remove the differential signalling capability of our magnetometer / DSP system and to run the sensor wire in a loop next to the electric motor powering the AUV. Odd, know.
So a decent lowpass filter removes most of that noise, as the blue line above shows. But the triaxial fluxgate magnetometer still needs to properly calibrated. To do this, we built this funky nonmagnetic rig to rotate the AUV within a constant background magnetic field. Yes, this required walking all over campus with a magnetic field gradient sensor to find the most appropriate location (and the help of the trusty undergrad).
When we rotate the AUV in a constant background field, we get some pretty interesting results. It should read about 50,000 nT no matter the orientation (the earth's field isn't changing after all), but it doesn't! The figure below shows the error as a function of orientation within the earth's magnetic field.
A bunch of math later, this problem goes away.
And that brings us back to this image: if I recall, it's simply an error mapping during this field calibration process with the magnitude of the error vector exaggerated.
Great! Now we've got a fleet of robot subs that can do our bidding, namely measuring magnetic fields of ships. But how do we quantify their performance?
First we model the disturbance they ought to see while navigating by a known magnetic source (a large calibrated bar magnet in this case).
Then we give it a shot and navigate past the magnet.
Then we step things up a notch and use a fleet of AUVs to navigate past the magnet (this is taken from a couple of passes).
Now we can finally reach our end goal of building a magnetic map of the surface vessel, which is moving in the opposite direction as the AUVs. This map shows a fleet of AUV tracks under water as they pass the boat and measure the magnetic field of the bar magnet (positioned at the origin).
Inverting Dipoles
With this magnetic map, we should be able to model them as magnetic dipoles and estimate the strength and location of magnetic sources, right? Nope. Turns out its a mathematically intractable problem. Well, let's call it a day.
Final Results