Calibrate a magnetic sensor

I recently worked on a project that required a magnetic sensor (MPU-9250) be calibrated to get best accuracy. I had some basic understanding on how to calibrate a magnetic sensor, although I’ve not done calibration before. The calibration turned out to be a bit complicated and took a while to understand. I got some help, including method to get best calibration, from the author of the MPU9250 Arduino library, Kris Winer. I thought that if I shared my experience here, others that are planning to calibrate their magnetic sensors may find it useful.

First of all, what is calibration? In a general sense, calibrating a sensor makes the sensor provide the most accurate readings allowed by the sensor’s own precision. As an example, let’s assume for a moment that the earth’s magnetic field and any other stray magnetic fields are shielded and you have a uniform magnetic field generated artificially for the sole purpose of calibration. Let’s say that the field strength is 400 mG (milliGauss), equivalent to 40,000 nT (nanoTesla). Now if you align one axis of your magnetic sensor parallel to the direction of the field, it should read 400mG. If you then carefully rotate your sensor so that the axis is anti-parallel with your field, it will read -400mG. If you didn’t do a good job in either alignments, you will read less values, say 390mG, if you’re off by about 13 degrees, because only a portion of the field, which is a vector, is projected along your magnetic sensor’s axis.

In the diagram above, the thick blue arrows represent the constant magnetic field of 400mG pointing to the right. The thin arrows represent various orientations your sensor could take. If your sensor + axis is also pointing to the right, you get the full 400mG. If your sensor + axis points to the left, you get -400mG. If your sensor + axis makes an angle, it reads a projection of the field, which is less. You can figure out the angle:

The above was assuming that there IS a constant magnetic field and the sensor’s reading IS symmetric along its positive and negative axis, meaning with zero magnetic field, the sensor reads zero. When not calibrated, the sensor reading will NOT be zero under zero field. It could read say 10mG. As a result, you might get say 510mG and -490mG with the field on. You know what that means. There is an offset (bias) of 10mG that should be subtracted from your reading to get the correct reading of +-400mG.

The above was the basis for calibration to remove the offset (bias) on each axis. In order to get the maximal and minimal value, you need to write your code to store max/min out of a stream of live data while you rotate your sensor in space, trying to maximize or minimize the readout. Then repeat two more times for a 3-D magnetic sensor. Since you don’t have a magnetic shield, you are relying on the earth’s magnetic field as the constant field. The earth’s magnetic field is not horizontal, or pointing from north to south. In most areas, the field either has a vertical up component, or a down component. And in most cases the field points from south to north as the rotational north pole (AKA the north pole) is near the magnetic south pole, where field lines go in, not coming out. In my area for example, the earth magnetic field points primarily downwards, only slightly towards north, making an angle over 70 degrees with the horizontal. The magnetic field has very little component in the east direction. The relative strength between East, North, and Downward is about 1:64:195. The angle the magnetic field vector makes with the horizontal is called magnetic inclination, with downward being positive. This is approximately atan(195/64)=72 degrees. The angle the magnetic field vector’s horizontal component makes with the true north is called magnetic declination, with east being positive. This is approximately atan(1/64)=0.9 degrees. The properties of magnetic field varies greatly from place to place and also changes from time to time. To find out the magnetic field in your area, visit noaa.gov:

https://www.ngdc.noaa.gov/geomag-web/#igrfwmm

The following is from my area:

The next calibration is for sensitivity. The sensor either returns an analog voltage or a digital value. How do we convert this return into actual magnetic field in mG? This means finding the relation between the sensor readout and actual physical values. Say the sensor is digital and returns values between 0 and 32767, which represents magnetic field between 0 and 49150mG. Then you can use the conversion vactor 49150/32767=1.5mG/LSB to convert your readout. Here LSB means one digit (least significant bit). For an analog sensor, you will need an x.xx mG/V.

All sensors provide this factor in their spec sheets so you can just use this factor to get the actual magnetic field. But since not all sensors were made identical, some sensors should use larger or smaller values than the spec’s factor. Some manufacturers test their sensors at factory and store a correction factor for each axis in the sensor for better accuracy. For example, the MPU-9250 sensor (the magnetic sensor is AK8963) has digital magnetic field sensor output. One of the sensors I got has the following factory trims:

X-Axis sensitivity 1.18

Y-Axis sensitivity 1.19

Z-Axis sensitivity 1.14

So instead of a straight 1.5mG/LSB, the x-axis has 1.5*1.18=1.77mG/LSB. We’ll multiply this factor to the x-axis readout to get x magnetic field in mG. Same for y and z axes.

And yet sometimes these adjustments are still not able to make all 3 axes read the “400mG” value. They are very close to be identical already so we can apply a small correction. We average the maximal readings from all three axes, then divide by the maximal reading of each individual axis to get three factors. If say the x-axis reads slightly higher maximum than y and z axes. Then the avg_max/x_max will be slightly less than 1. We apply this factor to the the final result:

x_field=(1.5mG/LSB)*(x_sensitivity)*(avg_max/x_max)*x_readout

For one of my sensors, this yields 1.5*1.180*0.975*x_readout=1.726*x_readout(mG)

If the sensor you’re using doesn’t have the factory trim, then you’re out of luck unless you have both a magnetic shield and a nice uniform magnetic field inside the shield so you can find out the trim.

The following are steps for the AK8963 magnetic sensor calibration I did, using Kris Winer’s MPU9250 Arduino library:

1. Extract factory sensitivity factor by calling initAK8963().
2. Call readMagData() to extract raw data repeatedly enough to get accurate max/min for all axes.
3. Calculate bias in raw counts by (max+min)/2, such as (510+ (-490))/2=10
4. Combine factory sensitivity factor and Kris’s scale factor described above.
5. Keep these biases and factors in program.

As a testimony to the method that works, here are two graphs.

This graph has three separate plots from raw data that represent mx vs. my, mx vs. mz, and my vs. mz. I rotated my sensor as much as I could for a few minutes before I got bored and couldn’t think of any other ways of rotation. The fact that all three plots are near circular means that the sensor’s three axes have very similar sensitivities. I was simply rotating the sensor around, giving all three axes opportunities to read the whole magnetic field. This means when the x axis reads the whole field, y and z axes read nothing. Some trigonometry can show that the result is a series or circles making a disc. But the discs were not centered as I expected, because the z axis had a very large bias (this means the blue is mx vs. my). After my bias calibration, here is what I got:

Now all three plots are centered at zero pretty well visually, although I didn’t multiple the factory sensitivity or the final factor from Kris’s calculation. This shows that bias calibration is the most crucial. If your sensor doesn’t have stored factory sensitivity factors, getting it calibrated for bias alone will go a long way.

FYI, this is my sensor board inside an enclosure. I found it much easier to hold and rotate when it’s in a box. The cable became much less of an issue when I was rotating the box. The black square board is my SDI-12 USB adapter. The purple board is the sensor board. I customized the SDI-12 USB adapter by gluing the sensor board to it and connecting it to the I2C bus on the adapter.