Tracking system calibration using object position and orientation

1. A computer implemented method of calibrating a tracking system, comprising:

receiving positional data of a tracked object from an optical sensor by a computing device;

computing a first angle of the object with respect to an optical axis of the optical sensor based on the received positional data;

receiving inertial data corresponding to the object by the computing device;

based on the inertial data, determining a second angle of an orientation of the object with respect to a plane normal to gravity; and

in response to a calibrate command from a user, determining a pitch of the optical sensor based on both the computed first angle and the determined second angle.

2. The method of claim 1 , wherein the second angle is computed from the inertial data by the computing device.

3. The method of claim 1 , wherein the calibrate command is received while the user holds the object at a momentarily fixed position or orientation.

4. The method of claim 1 , wherein the first angle is computed based on a focal length of the optical sensor and a vertical distance between the object and the optical axis in an image taken by the optical sensor.

5. The method of claim 4 , further comprising:

computing a relative yaw between the optical sensor and the object based on the focal length, the determined pitch of the optical sensor and a horizontal distance between the object and the optical axis in the image.

6. The method of claim 1 , further comprising:

computing a relative yaw between the optical sensor and the object concurrent to computing the pitch of the optical sensor, wherein the pitch and the yaw are computed by:

determining a first three dimensional vector that points from the optical axis to a center of the object in a reference frame of the optical sensor;

determining a second three dimensional vector that points from the optical axis to the center of the object in a world reference frame that has an axis aligned with gravity;

computing a three dimensional rotation between the first vector and the second vector; and

decomposing the three dimensional rotation into a first two dimensional rotation that represents the pitch of the optical sensor and a second two dimensional rotation that represents the relative yaw between the optical sensor and the object.

7. A computer readable storage medium including instructions that, when executed by a processing system, cause the processing system to perform a method comprising:

receiving positional data of a tracked object from an optical sensor by a computing device;

computing a first angle of the object with respect to an optical axis of the optical sensor based on the received positional data;

receiving inertial data corresponding to the object by the computing device;

based on the inertial data, determining a second angle of an orientation of the object with respect to a plane normal to gravity; and

in response to a calibrate command from a user, determining a pitch of the optical sensor based on both the computed first angle and the computed second angle.

8. The computer readable storage medium of claim 7 , wherein the second angle is computed from the inertial data by the computing device.

9. The computer readable storage medium of claim 7 , wherein the calibrate command is received while the user holds the object at a momentarily fixed position or orientation.

10. The computer readable storage medium of claim 7 , wherein the first angle is computed based on a focal length of the optical sensor and a vertical distance between the object and the optical axis in an image taken by the optical sensor.

11. The computer readable storage medium of claim 10 , the method further comprising:

computing a relative yaw between the optical sensor and the object based on the focal length, the determined pitch of the optical sensor and a horizontal distance between the object and the optical axis in the image.

12. The computer readable storage medium of claim 7 , the method further comprising:

computing a relative yaw between the optical sensor and the object concurrent to computing the pitch of the optical sensor, wherein the pitch and the yaw are computed by:

determining a first three dimensional vector that points from the optical axis to a center of the object in a reference frame of the optical sensor;

determining a second three dimensional vector that points from the optical axis to the center of the object in a world reference frame that has an axis aligned with gravity;

computing a three dimensional rotation between the first vector and the second vector; and

decomposing the three dimensional rotation into a first two dimensional rotation that represents the pitch of the optical sensor and a second two dimensional rotation that represents the relative yaw between the optical sensor and the object.

13. A tracking system, comprising:

a tracked object that includes one or more inertial sensors, the tracked object to gather inertial data, and to transmit the inertial data to a computing device;

the optical sensor, to gather positional data of the tracked object as the object is pointed approximately toward the optical sensor, and to transmit the positional data to the computing device; and

the computing device, to receive the inertial data and the positional data, to compute a first angle of the object with respect to an optical axis of the optical sensor based on the received positional data, to compute a second angle of an orientation of the object with respect to a plane normal to gravity from the inertial data, and in response to a calibrate command from a user, to determine a pitch of the optical sensor based on both the computed first angle and the computed second angle.

14. The tracking system of claim 13 , wherein the calibrate command is received while the user holds the object at a momentarily fixed position or orientation.

15. The tracking system of claim 13 , wherein the computing device to compute the first angle based on a focal length of the optical sensor and a vertical distance between the object and the optical axis in an image taken by the optical sensor.

16. The tracking system of claim 15 , the computing device further to compute a relative yaw between the optical sensor and the object based on the focal length, the computed pitch and a horizontal distance between the object and the optical axis in the image.

17. The tracking system of claim 13 , the computing device further to compute a relative yaw between the optical sensor and the object concurrent to computing the pitch of the optical sensor, wherein the pitch and the yaw are computed by:

determining a first three dimensional vector that points from the optical axis to a center of the object in a reference frame of the optical sensor;

determining a second three dimensional vector that points from the optical axis to the center of the object in a world reference frame that has an axis aligned with gravity;

computing a three dimensional rotation between the first vector and the second vector; and

decomposing the three dimensional rotation into a first two dimensional rotation that represents the pitch of the optical sensor and a second two dimensional rotation that represents the relative yaw between the optical sensor and the object.

18. The method of claim 4 , wherein the first angle is computed based on a ratio of the vertical distance to the focal length, wherein the first angle is computed as an arctangent of the ratio.