IMU calibration

1. A method of calibrating an inertial measurement unit, the inertial measurement unit comprising at least two magnetometers, and at least two accelerometers, the method comprising:

presuming at least one of the following: (1) a vector angle and a vector length of each of the at least two magnetometers have identical values; (2) each of a plurality of magnetometer vectors is one in magnitude; (3) an angle between a calibrated magnetometer vector and a calibrated accelerometer vector should not change; (4) a radius of the at least two magnetometers, post calibration, is equal to one; and (5) quaternions calculated using different ones of the at least two magnetometers are equal;

collecting data from the inertial measurement unit, while stationary as a first step;

collecting data from the inertial measurement unit while repositioning the inertial measurement unit as a second step;

calibrating the at least two magnetometers using the data collected during the first step and the second step; and

calibrating of the at least two accelerometers using the data collected during the first step and the second step.

2. The method of claim 1 , wherein at least two of the following are presumed: (1) a vector angle and a vector length of each of the at least two magnetometers have identical values; (2) each of a plurality of magnetometer vectors is one in magnitude; (3) an angle between a calibrated magnetometer vector and a calibrated accelerometer vector should not change; (4) a radius of the at least two magnetometers, post calibration, is equal to one; and (5) quaternions calculated using different ones of the at least two magnetometers are equal.

3. The method of claim 1 , wherein at least three of the following are presumed: (1) a vector angle and a vector length of each of the at least two magnetometers have identical values; (2) each of a plurality of magnetometer vectors is one in magnitude; (3) an angle between a calibrated magnetometer vector and a calibrated accelerometer vector should not change; (4) a radius of the at least two magnetometers, post calibration, is equal to one; and (5) quaternions calculated using different ones of the at least two magnetometers are equal.

4. The method of claim 1 , wherein at least four of the following are presumed: (1) a vector angle and a vector length of each of the at least two magnetometers have identical values; (2) each of a plurality of magnetometer vectors is one in magnitude; (3) an angle between a calibrated magnetometer vector and a calibrated accelerometer vector should not change; (4) a radius of the at least two magnetometers, post calibration, is equal to one; and (5) quaternions calculated using different ones of the at least two magnetometers are equal.

5. The method of claim 1 , wherein all five of the following are presumed: (1) a vector angle and a vector length of each of the at least two magnetometers have identical values; (2) each of a plurality of magnetometer vectors is one in magnitude; (3) an angle between a calibrated magnetometer vector and a calibrated accelerometer vector should not change; (4) a radius of the at least two magnetometers, post calibration, is equal to one; and (5) quaternions calculated using different ones of the at least two magnetometers are equal.

6. The method of any one of claims 1 - 5 , wherein presuming the vector angle and the vector length of the at least two magnetometers have identical values, the method further comprising:

calculating a magnitude of vector angle differences weighted using angular derivation between the vector angles to form a cost function;

calculating a threshold using the cost function; and

establishing a presence of a magnetic anomaly based upon the threshold.

7. The method of any one of claims 1 - 5 , wherein presuming each of the plurality of magnetometer vectors is one in magnitude, the method further comprising:

calculating magnetic strength as a mean of combined magnetic strengths from the at least two magnetometers;

establishing a tolerance for the calculated magnetic strength to create a magnetic strength range; and

establishing a presence of a magnetic anomaly based upon the magnetic strength range.

8. The method of any one of claims 1 - 5 , wherein presuming the angle between the calibrated magnetometer vector and the calibrated accelerometer vector should not change, the method further comprising:

calculating angular derivation between a magnetometer vector and a accelerometer vector;

establishing a tolerance for the calculated angular derivation to create an angular derivation range; and

establishing a presence of a magnetic anomaly based upon the angular derivation range.

9. The method of any one of claims 1 - 5 , wherein presuming the radius of the at least two magnetometers, post calibration, is equal to one, the method further comprising:

estimating a radius of a magnetic field using an ellipsoid estimation function and data from the at least two magnetometers;

establishing a tolerance for the estimated radius of the magnetic field to create a magnetic field radii range; and

establishing a presence of a magnetic anomaly based upon the magnetic field radii range.

10. The method of any one of claims 1 - 5 , wherein presuming quaternions calculated using different ones of the at least two magnetometers are equal, the method further comprising:

calculating an orientation of the inertial measurement unit in quaternion for each of the at least two magnetometers using outputs from the at least two magnetometers;

determining a quaternion output discrepancies threshold using the calculated orientations of the inertial measurement unit in quaternion;

calculating an angle between the calculated orientations of the inertial measurement unit in quaternion;

establishing a tolerance for the calculated angle to create a quaternion angle range; and

establishing a presence of a magnetic anomaly based upon the quaternion angle range.

11. A method of calibrating at least two magnetometers of an inertial measurement unit, while the inertial measurement unit is near an operating room of a medical facility comprising a local environment, the inertial measurement unit including at least two accelerometers, the method comprising:

collecting data from the at least two magnetometers of the inertial measurement unit while the inertial measurement unit is rigidly attached to a ferromagnetic object and the ferromagnetic object is repositioned in the local environment;

calculating magnetic distortion from the data collected from the at least two magnetometers during repositioning the ferromagnetic object in the local environment;

applying the magnetic distortion to a reference dataset, the reference dataset comprising uniformly distributed vectors around a sphere, to create a first distorted dataset;

applying an initial magnetic distortion to the reference dataset, the initial magnetic distortion being from a prior calibration of the at least two magnetometers when not rigidly attached to the ferromagnetic object, to create a second distorted dataset; and

calibrating the at least two magnetometers to account for ferromagnetic distortion using a recursive optimization algorithm applied to both the first and second distorted datasets to extract the ferromagnetic distortion.

12. The method of claim 11 , wherein the reference dataset comprises thousands of random three dimensional unit vectors drawn from a vin-Mises Fisher distribution around a sphere; and wherein application of the initial magnetic distortion and the magnetic distortion are applied in reverse to the reference dataset.

13. The method of claim 11 , wherein the prior calibration of the at least two magnetometers includes:

presuming at least one of the following: (1) a vector angle and a vector length of each of the at least two magnetometers have identical values; (2) each of a plurality of magnetometer vectors is one in magnitude; (3) an angle between a calibrated magnetometer vector and a calibrated accelerometer vector should not change; (4) a radius of the at least two magnetometers, post calibration, is equal to one; and (5) quaternions calculated using different ones of the at least two magnetometers are equal;

collecting data from the inertial measurement unit, while stationary as a first step;

collecting data from the inertial measurement unit while repositioning the inertial measurement unit as a second step;

calibrating the at least two magnetometers using the data collected during the first step and the second step; and

calibrating of the at least two accelerometers using the data collected during the first step and the second step.

14. The method of claim 11 , wherein collecting data from the at least two magnetometers of the inertial measurement unit while the inertial measurement unit is rigidly attached to the ferromagnetic object and repositioned includes repositioning the ferromagnetic object for at least one revolution around each Cartesian axis.

15. The method of claim 11 , wherein calibrating the at least two magnetometers to account for ferromagnetic distortion includes centering the data collected from the at least two magnetometers.

16. The method of claim 15 , wherein calibrating the at least two magnetometers to account for ferromagnetic distortion includes at least one of using a point correspondence transformation equation and using a geometric scaling and compensation equation.

17. The method of claim 11 , wherein calibrating the at least two magnetometers to account for ferromagnetic distortion includes applying adjusted hard and soft iron compensation parameters.