Ellipsoid fitting using python numpy to calibrate magnetometers

1. output you raw data from sensor and name it mag_out.txt in format x,y,z (uT)

2. change the "MField" value (line 42) in calibrate.py according to your sensor value (calculation available at begining of calibrate.py)

3. run script and get "Hard Iron Bias" and "Soft Iron bias" matrixes (and c++ according code)

   // Taken from calibrate.py or magcal
    float hard_iron_bias_x =  41.45884154873271 ;
    float hard_iron_bias_y =  -87.79628696573607 ;
    float hard_iron_bias_z =  569.4171225039286 ;
   
   
    double soft_iron_bias_xx =  0.5823136909144911 ;
    double soft_iron_bias_xy =  0.007124620314368133 ;
    double soft_iron_bias_xz =  -0.024442807568982334 ;
   
   
    double soft_iron_bias_yx =  0.00712462031436818 ;
    double soft_iron_bias_yy =  0.5906868599676302 ;
    double soft_iron_bias_yz =  0.005356720947343228 ;
   
   
    double soft_iron_bias_zx =  -0.024442807568982372 ;
    double soft_iron_bias_zy =  0.005356720947343263 ;
    double soft_iron_bias_zz =  0.7210550285247264 ;
    
    // get values x,y,z and subtract the hard iron offset
    float xm_off = id(hmc5883l_x).state - hard_iron_bias_x;
    float ym_off = id(hmc5883l_y).state - hard_iron_bias_y;
    float zm_off = id(hmc5883l_z).state - hard_iron_bias_z;
    
    // multiply by the inverse soft iron offset 
    float xm_cal = xm_off *  soft_iron_bias_xx + ym_off *  soft_iron_bias_yx  + zm_off *  soft_iron_bias_zx;
    float ym_cal = xm_off *  soft_iron_bias_xy + ym_off *  soft_iron_bias_yy + zm_off *  soft_iron_bias_zy;
    //not needed : float zm_cal = xm_off *  soft_iron_bias_xz + ym_off *  soft_iron_bias_yz  + zm_off *  soft_iron_bias_zz;
    
    //float heading = atan2(ym_cal, xm_cal);
    float heading = atan2(0 - xm_cal, ym_cal);
    
    //heading += id(magnetic_declination); 
    
    if(id(enable_magnetometer_serial_output) == true){
    ESP_LOGD("main", "%.1f,%.1f,%.1f", id(hmc5883l_x).state, id(hmc5883l_y).state, id(hmc5883l_z).state);
    }
    // Correct for when signs are reversed.
    if (heading < 0) {
    heading += 2*PI;
    }
    // Check for wrap due to addition of declination.
    if (heading > 2*PI) {
    //heading -= 2*PI;
    }
    float headingDegrees = heading * 180/M_PI; // Convert radians to degrees.
    return headingDegrees;
   

If you run esphome, a sample code is included to output raw data and get corrected values.

If you want a sample or a working demo, look at https://github.com/nliaudat/weatherstation

calibrate.py requires numpy,scipy and optional matplotlib to plot the graph

John zhang12300 for issuing the bug

jremington for fixing the bug

    -  https://teslabs.com/articles/magnetometer-calibration/      
    -  https://www.best-microcontroller-projects.com/hmc5883l.html