Q&D Magnetometer Calibrations

The Ideal Magnetometer

From an ideal three axis magnetometer with readings X, Y and Z from orthogonal axis, we can compute the Radius R of a sphere. For easy coding let us represent the three components X, Y, and Z in a vector M=[X, Y, and Z]. This M[0] is the X axis reading, M[1] is the Y axis reading and M[2] is the Z axis reading. The radius R = Sqrt(M[0]^2+M[1]^2+M[2]^2).
For an ideal magnetometer the radius R is a constant for a given external magnetic field.
In practice each axis of the magnetometer will not be centered and may have a different gain from the other two axis. Centering consist of finding an offset value to subtract from the raw readings for each axis. Gain adjustment finds a value that makes the output of each axis equal when positioned in the same magnetic field.

Coding note

I’m using a LSM9DS1 IMU chip connected to a Pico. Since there is recent interest in the Puck magnetometer, I will try to point out where there are differences and give my best guess as to how to use this technique with a Puck.

How the calibrations are implemented

We start with a raw reading from the magnetometer. Mr[i], where Mr is the raw reading vector containing raw values for the X, Y and Z, axis. To get the calibrated reading in vector Mc, the following equation is used:
Mc[i]=( Mr[i] – Moffest[i] ) * Scale * Mgain[i],
Where Mc[i] is the calibrated vector component,
Mr[i] is the raw vector component,
Scale is used to convert ADC count to engineering units such as Gauss. (Can omit for Puck),
Mgain[i] is the gain factor for the vector component,
and i is the component index 0...2.
The raw magnetometer readings from the LSM9DS1 IMU are in ADC counts and the Scale (there are 4 different ones) is the full scale engineering units divided by 32768.
For example 4 Gauss/ 32768 = 0.0001220703125 = Scale.

The min/max Method

function minmax(){
 this.min=[0,0,0];
 this.max=[0,0,0];
 this.avg=[0,0,0];
 this.R=0;
 this.amp=[0,0,0];
 this.gain=[1,1,1];
}

minmax.prototype.process=function(A){
  var i,S=[0,0,0];
  this.R=0;
  for(i=0;i<3;i++){
   if(A[i]>this.max[i])this.max[i]=A[i];
   if(A[i]<this.min[i])this.min[i]=A[i];
   this.avg[i]=(this.min[i]+this.max[i])/2;
   this.amp[i]=(this.max[i]-this.min[i])/2;
  }
  for(i=0;i<2;i++){
   this.gain[i]=this.amp[2]/this.amp[i];
   S[i]=4/32768*this.gain[i];
  }
  console.log("A= ",A);
  console.log("max= ",this.max);
  console.log("min= ",this.min);
  console.log("avg= ",this.avg);
  console.log("amp= ",this.amp);
  console.log("Gain= ",this.gain);
  console.log("S= ",S);
};

For the LSM9DS1 I used the minmax class in a loop that can be stopped using a menu system.

    case "4"://read and display data
     menulevel=10;sst="";
     readall(W);
     nn=setInterval(function () {
       readall(W);
       count++;
       if(count>1000)clearInterval(nn);
      }, 100);
    break;if(count>1000)clearInterval(nn);
xxxx
function readall(W){
if(W.magAvailable()){
  W.readMag();
  T.process(W.m);
}//endif
}//end readall

Due to budget I don't own a Puck yet, so this code may need some enhancement.
For a Puck the Puck.on('mag', function() { ... }); would be used something like this:

var T=new minmax[]; 
var M=[0,0,0];
var Moffset=[0,0,0];
var Mgain=[1,1,1];

function onMag(p) {
  M[0]=(p.x-Moffset[0])*Mgain[0];
  M[1]=(p.y-Moffset[1])*Mgain[1];
  M[2]=(p.z-Moffset[2])*Mgain[2];
T.process(M);
}

Running the code

The idea is to run the code and then point each end of each axis towards the magnetic pole. For my location in North America it is North and about 60 degrees below the horizon due to magnetic dip. This process is continued until the readings for each axis stop changing.
At the start: (readings are in raw ADC counts)

A=  [ 2145, 2153, -1557 ]
max=  [ 2145, 2201, 0 ]
min=  [ 0, 0, -1581 ]
avg=  [ 1072.5, 1100.5, -790.5 ]
amp=  [ 1072.5, 1100.5, 790.5 ]
Gain=  [ 0.73706293706, 0.71830985915, 1 ]
S=  [ 0.00008997350, 0.00008768430, 0 ]

After readings stop changing:

A=  [ 1883, 1919, -1572 ]
max=  [ 6327, 3363, 4486 ]
min=  [ 0, -3755, -2141 ]
avg=  [ 3163.5, -196, 1172.5 ]
amp=  [ 3163.5, 3559, 3313.5 ]
Gain=  [ 1.04741583688, 0.93101994942, 1 ]
S=  [ 0.00012785837, 0.00011364989, 0 ]

At this point for the LSM9DS1, I used a different program to write the offsets (avg)to ROM. For the Puck copy the offsets (avg) to the Moffset[].

To evaluate the calibration data were collected using code like this:

function readall(W){
var avg=  [ 3163.5, -196, 1172.5 ];
var Gain=  [ 1.04741583688, 0.93101994942, 1];
var R1,R2,R3;
var raw=[0,0,0];
var Roff=[0,0,0];
var Rcal=[0,0,0];
var i;
if(W.magAvailable()){
  W.readMag();
//  T.process(W.m);
for(i=0;i<3;i++){
  raw[i]=W.m[i];
  Roff[i]=raw[i]-avg[i];
  Rcal[i]=Roff[i]*Gain[i];
  R1=Math.sqrt(raw[0]*raw[0]+raw[1]*raw[1]+raw[2]*raw[2]);
  R2=Math.sqrt(Roff[0]*Roff[0]+Roff[1]*Roff[1]+Roff[2]*Roff[2]);
  R3=Math.sqrt(Rcal[0]*Rcal[0]+Rcal[1]*Rcal[1]+Rcal[2]*Rcal[2]);
}//next i
console.log(R1,R2,R3);
}//endif
}//end readall

The magnetometer was pointed in many different orientations as data were collected. R1 is the radius from raw data, R2 is the radius from raw data - offset, and R3 is the radius from the gain times the raw data - offset. Excel was used to perform descriptive statistics on the radius values R1, R2, and R3.

Result of the QD calibration of the LSM9DS1 magnetometer using the 8 Gauss scale.

The calibration results:

8gcal.txt
A=  [ 1055, 1059, -774 ]
max=  [ 2787, 2318, 2211 ]
min=  [ -282, -2189, -1154 ]
avg=  [ 1252.5, 64.5, 528.5 ]
amp=  [ 1534.5, 2253.5, 1682.5 ]
Gain=  [ 1.09644835451, 0.74661637452, 1 ]
S=  [ 0.00013384379, 0.00009113969, 0 ]

Statistical results of using the calibrations

For the 8 Gauss range the use of the Gain term reduced the variance in the data.

R1 uses raw readings. R1= sqrt( X1^2 + Y1^2 +Z1^2)
R1 uses raw readings - offset
R2 uses (raw -offset) * gain
.

Magnetometer, Turntable, Wireless, Plot Circle, Calibrate

The hardware

A magnetically agnostic turntable is used to spin a three axis magnetometer. The magnetometer readings are read by a Pico (or equivalent) and transmitted wirelessly to a web page (served by the Pico). Puck?

The webpage has the following elements:

• A slider bar that controls the radius of a circle drawn on the page.
  
• Radio buttons to select the magnetometer axis pair to plot X-Y, X-Z, Y-Z.
  
• Three slider bars for the axis offset values and boxes that display the values.
  
• Three slider bars for the axis gain values and boxes that display the values.
  
• A control to limit the size of the data buffer
  
  

As the data from the magnetometer are acquired the selected axis pair are plotted as an asteroid belt around the origin of the graph. The offset sliders are adjusted to center the asteroids. The cursor circle and the gain sliders are adjusted to visually best fit the data to a circle. The values in the gain and offset boxes are then used for the magnetometer calibration values. It is conceivable that local distortions in the magnetic field could be detected and visualized with such a system.

In Depth Magnetometer Calibration Using Excel and Solver

( Best fit so far!)

The mathematical model

Given raw magnetometer readings X, Y , and Z,
For each reading calculate:
Let Xa= X-Xoffset, Ya=Y-Yoffset, and Za=Z-Zoffset, and
The calibrated values X1, Y1, Z1 are given by:
X1=Xa*gainXX + Ya*gainXY + Za*gainXZ,
Y1=Xa*gainYX + Ya*gainYY + Za*gainYZ,
Z1=Xa*gainZX + Ya*gainZY + Za*gainZZ.
Let R1= sqrt( X1^2+Y1^2+Z1^2), and
Error = R1-Rtarget, and Error Squared = Error^2
Take the sum of the Error Squared for all the samples = SES.
Set the X, Y, and Z offsets =0,
Set gainXX, gainYY and gainZZ =1, and the other 6 gains =0;
Use solver to minimize SES while changing the offsets, and all of the gains except gainZZ

Results

Magcal 4 Gauss 5 Hz 11Jan2017
error = 4129.637996

(Back to the drawing board because the X and Y gains are too small)

http://diydrones.com/forum/topics/magnetometer-soft-and-hard-iron-calibration

(Found the error in the previous post, a copy and paste in Excel)

In Depth Magnetometer Calibration Using Excel and Solver

The mathematical model

Given raw magnetometer readings X, Y , and Z,
For each reading calculate:
Let Xa= X-Xoffset, Ya=Y-Yoffset, and Za=Z-Zoffset, and
The calibrated values X1, Y1, Z1 are given by:
X1=Xa*gainXX + Ya*gainXY + Za*gainXZ,
Y1=Xa*gainYX + Ya*gainYY + Za*gainYZ,
Z1=Xa*gainZX + Ya*gainZY + Za*gainZZ.
Let R1= sqrt( X1^2+Y1^2+Z1^2), and
Error = R1-Rtarget, and Error Squared = Error^2
Take the sum of the Error Squared for all the samples = SES.
Set the X, Y, and Z offsets =0,
Set gainXX, gainYY and gainZZ =1, and the other 6 gains =0;
Use solver to minimize SES while changing the offsets, and all of the gains except gainZZ

Results

Magcal 4 Gauss 5 Hz 11Jan2017

http://diydrones.com/forum/topics/magnetometer-soft-and-hard-iron-calibration

Used a long cable to move magnetometer away from the table and computer with improved results.
8 Gauss range
11Jan2017
LSM9DS1 long cable

See attached spreadsheet in ods format.
Let me know if it doesn't open OK.
I suppressed graphs to save space, if you're curious do some plots.

1 Attachment

• 8gauss.ods