Software Gimbals for your compass

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Software Gimbals

Comparison of theoretical and actual accelerometer readings

N	Troll	Tpitch	Tyaw	Aroll	Apitch	Ayaw
0	0.00001	0	1	-0.003021269	-0.041954586	0.999114951
1	-1	0	0.00001	-0.997628186	-0.025433701	0.063961937
2	0.00001	0	-1	-0.045201791	0.000406194	-0.998977794
3	1	0.00001	1	0.993574107	-0.033400851	-0.108142854

T = Theory, A= Accelerometer data
Notice the signs match.

Comparison of theoretical and actual magnetometer readings

N	Troll	Tpitch	Tyaw	Mroll	Mpitch	Myaw
0	0.866	0.5	1.732	0.167571285	0.470716976	-0.866224793
1	-1.732	0.5	0.866	-0.865231458	0.404036655	-0.296865129
2	-0.866	0.5	-1.732	-0.163571745	0.52435959	0.835638262
3	1.732	0.5	-0.866	0.735023669	0.362766964	0.572835348

T=Theory, M= Magnetometer data
Notice that the Z axis signs don’t’match.

Results using the sign change on the Z-axis data on data.

Data are from a LSM9DS1 IMU.

N	Aroll	Apitch	Ayaw	Kroll	Kpitch	Mroll	Mpitch	Myaw	M1roll	M1pitch	M1yaw	tilt	heading	dip
0	-0.003	-0.042	0.999	-0.997	0.072	0.168	0.471	0.866	0.170	0.507	0.845	2.411	288.565	57.694
1	-0.998	-0.025	0.064	-0.025	1.000	-0.865	0.404	0.297	0.231	0.432	0.872	86.333	298.100	60.679
2	-0.045	0.000	-0.999	0.009	1.000	-0.164	0.524	-0.836	0.135	0.522	0.842	-2.591	284.511	57.393
3	0.994	-0.033	-0.108	-0.034	-0.999	0.735	0.363	-0.573	0.504	0.371	0.780	-83.792	323.682	51.273

A= Accelerometer Data
K= Rotation Axis from Rodrigues Rotation Formula
M= Magnetometer Data
M1= Transformed Magnetometer Data
Tilt= angle from Rodrigues
Heading and Dip angles in degrees calculated from transformed magnetometer data.

Conclusion

This data set shows the transformation of real world accelerometer and magnetometer data to achieve the target of a software gimbaled compass. It is a limited data set and needs further testing to confirm the results. (This stuff is like a Rubic’s cube!)