Rotatable orientation independent gravity sensor and methods for correcting systematic errors

1. A method to correct for a systematic error of a sensor comprising a plurality of collocated accelerometers configured to measure gravitational acceleration, the method comprising:

rotating the plurality of collocated accelerometers about a first axis, the plurality of collocated accelerometers providing output used for measuring the gravitational acceleration, each accelerometer in the plurality having a direction of sensitivity wherein at least two of the accelerometers in the plurality have different directions of sensitivity;

obtaining a first set of calibration measurements from the plurality of accelerometers from the rotation about the first axis;

determining a first systematic error for each accelerometer in the plurality using the first set of calibration measurements; and

removing the first systematic error from sensor measurements to correct for the systematic error.

2. The method of claim 1 , further comprising:

rotating the sensor about a second axis;

obtaining a second set of calibration measurements from the plurality of accelerometers from the rotation about the second axis;

determining a second systematic error for each accelerometer in the plurality using the first set of calibration measurements; and

removing the second systematic error from the future measurements.

3. The method of claim 2 , wherein the first axis is a longitudinal axis of a logging instrument comprising the sensor.

4. The method of claim 3 , wherein the second axis is orthogonal to the first axis.

5. The method of claim 1 , wherein the first set of calibration measurements comprises a series of measurements performed by at least one accelerometer in the plurality of collocated accelerometers.

6. The method of claim 1 , wherein the sensor is rotated 360 degrees about the first axis.

7. The method of claim 6 , wherein the first set of calibration measurements correlates to a sine curve.

8. The method of claim 1 , wherein each accelerometer has a direction of sensitivity and a first acceleromenter in the plurality has a first direction of sensitivity and a second accelerometer in the plurality has a second direction of sensitivity that is different from the first direction of sensitivity.

9. The method of claim 1 , wherein the systematic error is at least one of an offset bias and an error proportional to a value output by an accelerometer in the plurality.

10. The method of claim 1 , wherein the systematic error is due to misalignment of an accelerometer in the plurality.

11. The method of claim 1 , wherein removing comprises:

subtracting the associated first systematic error from a measurement performed by each accelerometer.

12. The method of claim 1 , wherein removing comprises:

averaging the first systematic errors to determine an average systematic error; and

subtracting the average systematic error from a composite response that combines measurements performed by the accelerometers in the plurality.

13. The method of claim 1 , wherein the method is implemented by computer executable instructions stored on a non-transitory computer readable medium.

14. A sensor for measuring gravitational acceleration and correcting for systematic error, sensor comprising:

a plurality of collocated accelerometers providing output used for measuring the gravitational acceleration, each accelerometer in the plurality having a direction of sensitivity wherein at least two of the accelerometers in the plurality have different directions of sensitivity;

a rotational device configured to rotate the plurality of collocated accelerometers about a first axis; and

a processing system in communication with the plurality of collocated accelerometers, wherein the processing system is configured to:

obtain a first set of calibration measurements from the plurality of accelerometers from rotation of the plurality about the first axis;

determine a first systematic error for each accelerometer in the plurality using the first set of calibration measurements; and

removing the first systematic error from sensor measurements to correct for the systematic error.

15. The sensor of claim 14 , wherein the first axis is a longitudinal axis of a logging instrument comprising the sensor.

16. The sensor of claim 14 , wherein the rotational device is further configured to rotate the plurality of accelerometers about a second axis.

17. The sensor of claim 16 , wherein the processing system is further configured to:

obtain a second set of calibration measurements from the plurality of accelerometers from rotation of the plurality about the second axis;

determine a second systematic error for each accelerometer in the plurality using the second set of calibration measurements; and

removing the second systematic error from sensor measurements.

18. The sensor of claim 17 , wherein the second axis is orthogonal to the first axis.

19. The sensor of claim 14 , wherein the rotational device comprises a gimbal.

20. An apparatus for measuring gravitational acceleration in a borehole and correcting for systematic error, the apparatus comprising:

a logging instrument;

a plurality of collocated accelerometers disposed at the logging instrument, the plurality providing output used for measuring the gravitational acceleration, each accelerometer in the plurality having a direction of sensitivity wherein at least two of the accelerometers in the plurality have different directions of sensitivity;

a rotational device configured to rotate the plurality of collocated accelerometers about a first axis; and

a processing system in communication with the plurality of collocated accelerometers, wherein the processing system is configured to:

obtain a set of calibration measurements from the plurality of accelerometers from rotation of the plurality about the first axis;

determine a systematic error for each accelerometer in the plurality using the set of calibration measurements; and

remove the first systematic error from sensor measurements to correct for the systematic error.