1. AHRS calibration and performance study V. Kulikovskiy

2. Yaw, pitch, roll calculations. Pitch = atan2(Ax, sqrt(Ay 2 +Az 2 ); Roll = atan2(-Ay, -Az); Yaw= atan2( (-Hy*cos(Roll) + Hz*sin(Roll) ), Hx*cos(Pitch) + Hy*sin(Pitch)*sin(Roll) + Hz*sin(Pitch)*cos(Roll)) Accelerometer and magnetometer offsets should be correctly calculated!

3. Magnetometer calculations Rotation of the XYZ-magnetometer in the uniform field should produce a sphere in the (Hx,Hy,Hz) coordinate system if magnetometers are perfectly calibrated. In case of the presence of hard magnetic materials (have the field independent on the external field) the sphere is shifted. In case of the presence of softmagnetic materials (field dependent on the external field) the sphere is deformed - ellipsoid.

4. Rotation in 6 planes (work with S. Viola)

5. Hard iron correction Easy One of the ways – rotate in XY plain – fit the circle and the center of the circle is the Hx_offset, Hy_offset – Rotate in any vertical plane (YZ, XZ or similar) fit circle and find Hz_offset (Hx_cal)=(Hx - Hx_offset) (Hy_cal)=(Hy - Hy_offset) (Hz_cal)=(Hz - Hz_offset)

6. Soft iron correction Do 3D rotation (more points you have better is). Rotate in each plain should be OK (XY up/down, YZ, ZX). Fit with ellipsoid. Find “W -1 ” matrix which “decompresses” ellipsoid to the sphere. (Hx_cal)= (Hx - Hx_offset) (Hy_cal)= (Hy - Hy_offset) (Hz_cal)= (Hz - Hz_offset) W -1

7. Tests with bare CLB Found matrix was almost I. The correction used changes angle by <1 deg. 0.911,0.025,0.022, 0.025,0.969,-0.024 0.022,-0.024,1.134 Ellipsoid fit finds worse values for the offsets than simple circle fits?! (not enough data points? Magnetometer data worsening due to fast rotations?)

8. AHRS calibrations 18 DOMs of the first line calibration. Offset are really different from one DOM to another. CLB shows similar offsets variation.

9. Is this important to calibrate each AHRS? Yes Simulation: not calibrated board (offsets 0,0) with true offsets 0.014 G, 0.037 G)

10. AHRS performance When the CLB is in the fixed position, RMS (yaw) is ~0.6 deg.

11. AHRS performance Find groups of data with tolerance +-10 deg from known directions. Find median for each group. Refine groups with tolerance +-3 deg from median. Find new median. Find mean offset (best estimate of unknown North direction). Find variance and the worst offset respect to the mean.

12. AHRS performance Estimated accuracy <3 deg. Variance Worst shift

13. AHRS performance upside down The same calibration used (AHRS on the top). Estimated accuracy <4 deg? More statistics is needed. Variance Worst shift RMS

14. Offline codes to perform yaw, pitch, roll calculations are studied (note in progress). They can be used for existing AHRS integrated in the DOMs and new accelerometer+magnetometer sensor (if changed). Implementation in the DB? AHRS code was debugged and now AHRS calculations correspond to the offline calculations. There were bugs in application of magnetometers calibration and roll calculation. Calculations are correct and the precision is the matter of good calibration. Tests in future: – Calculation of Yaw for different tilts with Hz calibration/without. Preliminary tests with one board shows effect less than 1 deg for tilts <20 deg and effect of 3 degrees for 30 degrees pitch. Simulation in progress. – Check of the Hx, Hy calibration inside the DOM and comparison with the bare CLB calibration. Effect on the Yaw calculation. – More precise accelerometers calibration?! For now fixed offsets are written (from the one board placed horizontally) – effect of the the proper offset seems to be order of 1 deg. All this study is important for ANY tilt/compass (don’t believe that commercial chip should be calibrated).