Method for aligning a mobile device surface with the coordinate system of a sensor

1. A method for calibrating an accelerometer located within a mobile device, comprising:

receiving a plurality of measurements of acceleration vectors by a processor of the mobile device from the accelerometer, each of the measurements being taken when the mobile device is held stationary at a different orientation with respect to a normal of a plane on which the mobile device lies;

calculating a circle that fits respective tips of the measured acceleration vectors in an accelerometer coordinate system;

calculating an angle of rotation between the accelerometer coordinate system and a surface of the mobile device based on a radius of the circle and a length of the measured acceleration vectors to align the accelerometer coordinate system with the surface of the mobile device, wherein the angle of rotation is calculated in the presence of a bias, wherein the bias is measured by a distance between a center of the circle and an intersection point, at which the normal extending from an origin of the accelerometer coordinate system intersects a second plane containing the circle;

storing the angle of rotation in a memory of the mobile device; and

calibrating subsequent measurements of the accelerometer based at least in part on the stored angle of rotation in the memory; wherein the surface of the mobile device against which the accelerometer coordinate system is calibrated is the surface that faces and is in contact with the plane.

2. The method of claim 1 , wherein the plane is tilted with respect to a horizontal axis.

3. The method of claim 1 , wherein the plane is aligned to a horizontal axis.

4. The method of claim 1 , wherein each of the measurements is taken when the mobile device is held stationary after being rotated by an angle with respect to the normal of the plane.

5. The method of claim 1 , further comprising:

rotating a measured acceleration vector by the angle of rotation to transform the measured acceleration vector from the accelerometer coordinate system to a vector in a surface coordinate system defined by the surface of the mobile device; and

converting the vector in the surface coordinate system to a gyroscope coordinate system based on a rotational transformation between the surface coordinate system and the gyroscope coordinate system.

6. A mobile device comprising:

an accelerometer;

a processor coupled to the accelerometer and a memory, the processor configured to:

receive a plurality of measurements of acceleration from the accelerometer, each of the measurements being taken when the mobile device is held stationary at a different orientation with respect to a normal of a plane on which the mobile device lies;

calculate a circle that fits respective tips of measured acceleration vectors in an accelerometer coordinate system;

calculate an angle of rotation between the accelerometer coordinate system and a surface of the mobile device based on a radius of the circle and a length of the measured acceleration vectors to align the accelerometer coordinate system with the surface of the mobile device, wherein the angle of rotation is calculated in the presence of a bias, wherein the bias is measured by a distance between a center of the circle and an intersection point, at which the normal extending from an origin of the accelerometer coordinate system intersects a second plane containing the circle; and

store the angle of rotation in the memory; and

calibrate subsequent measurements of the accelerometer based at least in part on the stored angle of rotation in the memory; wherein the surface of the mobile device against which the accelerometer coordinate system is calibrated is the surface that faces and is in contact with the plane.

7. The mobile device of claim 6 , wherein each of the measurements is taken when the mobile device is held stationary after being rotated by an angle with respect to the normal of the plane.

8. The mobile device of claim 6 , further comprising:

a gyroscope coupled to the processor;

wherein the processor is further configured to:

rotate a measured acceleration vector by the angle of rotation to transform the measured acceleration vector from the accelerometer coordinate system to a vector in a surface coordinate system defined by the surface of the mobile device; and

convert the vector in the surface coordinate system to a gyroscope coordinate system based on a rotational transformation between the surface coordinate system and the gyroscope coordinate system.

9. A non-transitory computer program product implemented at a mobile device for calibrating an accelerometer located within the mobile device, comprising:

a computer-readable medium comprising code for:

receiving a plurality of measurements of acceleration vectors by a processor of the mobile device from the accelerometer, each of the measurements being taken when the mobile device is held stationary at a different orientation with respect to a normal of a plane on which the mobile device lies;

calculating a circle that fits respective tips of measured acceleration vectors in an accelerometer coordinate system;

calculating an angle of rotation between the accelerometer coordinate system and a surface of the mobile device based on a radius of the circle and a length of the measured acceleration vectors to align the accelerometer coordinate system with the surface of the mobile device, wherein the angle of rotation is calculated in the presence of a bias, wherein the bias is measured by a distance between a center of the circle and an intersection point, at which the normal extending from an origin of the accelerometer coordinate system intersects a second plane containing the circle;

storing the angle of rotation in a memory of the mobile device; and

calibrating subsequent measurements of the accelerometer based at least in part on the stored angle of rotation in the memory; wherein the surface of the mobile device against which the accelerometer coordinate system is calibrated is the surface that faces and is in contact with the plane.

10. The non-transitory computer program product of claim 9 , wherein each of the measurements is taken when the mobile device is held stationary after being rotated by an angle with respect to the normal of the plane.

11. The non-transitory computer program product of claim 9 , further comprising code for:

rotating a measured acceleration vector by the angle of rotation to transform the measured acceleration vector from the accelerometer coordinate system to a vector in a surface coordinate system defined by the surface of the mobile device; and

converting the vector in the surface coordinate system to a gyroscope coordinate system based on a rotational transformation between the surface coordinate system and the gyroscope coordinate system.

12. A mobile device comprising:

means for receiving a plurality of measurements of acceleration from an accelerometer, each of the measurements being taken when the mobile device is held stationary at a different orientation with respect to a normal of a plane on which the mobile device lies;

means for calculating a circle that fits respective tips of measured acceleration vectors in an accelerometer coordinate system;

means for calculating an angle of rotation between the accelerometer coordinate system and a surface of the mobile device based on a radius of the circle and a length of the measured acceleration vectors to align the accelerometer coordinate system with the surface of the mobile device, wherein the angle of rotation is calculated in the presence of a bias, wherein the bias is measured by a distance between a center of the circle and an intersection point, at which the normal extending from an origin of the accelerometer coordinate system intersects a second plane containing the circle;

means for storing the angle of rotation in a memory of the mobile device; and

means for calibrating subsequent measurements of the accelerometer based at least in part on the stored angle of rotation in the memory; wherein the surface of the mobile device against which the accelerometer coordinate system is calibrated is the surface that faces and is in contact with the plane.

13. The mobile device of claim 12 , wherein each of the measurements is taken when the mobile device is held stationary after being rotated by an angle with respect to the normal of the plane.

14. The mobile device of claim 12 , wherein means for calculating the angle of rotation further comprises means for calculating the angle of rotation in the presence of a bias, wherein the bias is measured by a distance between a center of the circle and an intersection point, at which the normal extending from an origin of the accelerometer coordinate system intersects a second plane containing the circle.

15. The mobile device of claim 12 , further comprising:

means for rotating a measured acceleration vector by the angle of rotation to transform the measured acceleration vector from the accelerometer coordinate system to a vector in a surface coordinate system defined by the surface of the mobile device; and

means for converting the vector in the surface coordinate system to a gyroscope coordinate system based on a rotational transformation between the surface coordinate system and the gyroscope coordinate system.