Extracting inertial information from nonlinear periodic signals

• US 9,989,553 B2
• Filed: 05/20/2016
• Issued: 06/05/2018
• Est. Priority Date: 05/20/2015
• Status: Active Grant

• Current Assignee: Nxtant Incorporated
• Original Assignee: Lumedyne Technologies Incorporated (Alphabet Inc.)
• Inventors: Waters, Richard Lee, Fralick, Mark Steven, Tally, IV, Charles Harold, Jacobs, John David
• Primary Examiner(s): McCall, Eric S
• Assistant Examiner(s): Keramet-Amircola, Mohammed E
• Application Number:
  US15/160,098
• Publication Number:
  US 20160341762A1
• Time in Patent Office: 746 Days
• Field of Search: 73 138
• CPC Class Codes: B81B 2201/0235 Accelerometers
• CPC Class Codes: B81B 2203/051 Translation according to an axis parallel to the substrate
• CPC Class Codes: G01C 19/04 Details
• CPC Class Codes: G01D 5/2415 adapted for encoders
• CPC Class Codes: G01P 15/0802 Details
• CPC Class Codes: G01P 15/093 by photoelectric pick-up
• CPC Class Codes: G01P 15/097 by vibratory elements
• CPC Class Codes: G01P 15/125 by capacitive pick-up
• CPC Class Codes: G01P 15/13 by measuring the force required to restore a proofmass subjected to inertial forces to a null position
• CPC Class Codes: G01P 2015/0814 for translational movement of the mass, e.g. shuttle type
• CPC Class Codes: G01P 2015/0865 using integrated signal processing circuitry
• CPC Class Codes: G01P 21/00 Testing or calibrating of apparatus or devices covered by the preceding groups

Abstract

Systems and methods are described herein for extracting inertial information from nonlinear periodic signals. A system for determining an inertial parameter can include circuitry configured for receiving first and second analog signals from first and second sensors, each sensor responsive to motion of a proof mass. The system can include circuitry configured for determining a difference between the first and second analog signals, determining a plurality of timestamps corresponding to times at which the difference crosses a threshold, and determining a plurality of time intervals based on the timestamp. The system can include circuitry configured for determining a result of applying a trigonometric function to a quantity, the quantity based on the plurality of time intervals and determining the inertial parameter based on the result.

Claims

1. A method for determining an inertial parameter, comprising:

receiving first and second analog signals from first and second sensors, each sensor responsive to motion of a proof mass;

determining a difference between the first and second analog signals;

determining a plurality of timestamps corresponding to times at which the difference crosses a threshold;

determining a plurality of time intervals based on the timestamp;

determining a result of applying a trigonometric function to a quantity, the quantity based on the plurality of time intervals; and

determining the inertial parameter based on the result.

2. The method of claim 1, wherein the first and second sensors are first and second electrodes, respectively, each interacting with the proof mass.

3. The method of claim 2, wherein the first and second electrodes electrostatically interact with the proof mass.

4. The method of claim 1, wherein determining the difference comprises amplifying the difference between the first and second analog signals to an analog voltage.

5. The method of claim 4, wherein determining the timestamps comprises:

converting the analog voltage to a digital representation to generate a first periodic digital signal;

interpolating to generate an upsampled digital signal; and

determining timestamps corresponding to times at which the upsampled digital signal crosses the threshold.

6. The method of claim 4, wherein determining the timestamps comprises:

comparing the analog voltage to a second threshold;

based on determining that the analog voltage has crossed the second threshold, toggling a rectangular-wave signal between a first value and a second value; and

determining the timestamps based on times at which the rectangular-wave signal toggles between the first value and the second value.

7. The method of claim 6, wherein the quantity comprises a phase shift.

8. The method of claim 1, wherein the quantity comprises a first quotient of two of the time intervals.

9. The method of claim 8, further comprising:

determining a second result of applying a second trigonometric function to a second quantity comprising a second quotient of a second two of the time intervals; and

determining a second difference of the result and the second result.

10. The method of claim 9, further comprising:

determining the multiplicative inverse of the second difference;

determining a product of a pitch of the proof mass and the multiplicative inverse; and

determining an estimate of displacement amplitude of the proof mass based on the product;

wherein the inertial parameter is the estimate of displacement amplitude.

11. The method of claim 9, further comprising:

determining a sum of the result and the second result;

determining a third quotient of the sum and the difference;

determining a fourth quotient of a first scale factor and a sum of a third two of the time intervals;

determining a square of the fourth quotient;

determining a product of the third quotient, the square, and a second scale factor; and

determining an acceleration of an inertial device comprising the proof mass;

wherein the inertial parameter comprises the acceleration.

12. The method of claim 11, wherein the second scale factor comprises a pitch of the proof mass.

13. The method of claim 1, wherein the quantity comprises a phase shift.

14. The method of claim 1, wherein each of the plurality of time intervals is a difference between a respective two of the plurality of timestamps.

15. A system for determining an inertial parameter, comprising circuitry configured for:

receiving first and second analog signals from first and second sensors, each sensor responsive to motion of a proof mass;

determining a difference between the first and second analog signals;

determining a plurality of timestamps corresponding to times at which the difference crosses a threshold;

determining a plurality of time intervals based on the timestamp;

determining a result of applying a trigonometric function to a quantity, the quantity based on the plurality of time intervals; and

determining the inertial parameter based on the result.

16. The system of claim 15, wherein the first and second sensors are first and second electrodes, respectively, each interacting with the proof mass.

17. The system of claim 16, wherein the first and second electrodes electrostatically interact with the proof mass.

18. The system of claim 15, wherein determining the difference comprises amplifying the difference between the first and second analog signals to an analog voltage.

19. The system of claim 18, wherein determining the timestamps comprises:

converting the analog voltage to a digital representation to generate a first periodic digital signal; and

interpolating to generate an upsampled digital signal;

determining timestamps corresponding to times at which the upsampled digital signal crosses the threshold.

20. The system of claim 18, wherein determining the timestamps comprises:

comparing the analog voltage to a second threshold;

based on determining that the analog voltage has crossed the second threshold, toggling a rectangular-wave signal between a first value and a second value; and

determining the timestamps based on times at which the rectangular-wave signal toggles between the first value and the second value.

21. The system of claim 20, wherein the quantity comprises a phase shift.

22. The system of claim 15, wherein the quantity comprises a first quotient of two of the time intervals.

23. The system of claim 22, further comprising circuitry configured for:

determining a second result of applying a second trigonometric function to a second quantity comprising a second quotient of a second two of the time intervals; and

determining a second difference of the result and the second result.

24. The system of claim 23, further comprising circuitry configured for:

determining the multiplicative inverse of the second difference;

determining a product of a pitch of the proof mass and the multiplicative inverse; and

determining an estimate of displacement amplitude of the proof mass based on the product;

wherein the inertial parameter is the estimate of displacement amplitude.

25. The system of claim 23, further comprising circuitry configured for:

determining a sum of the result and the second result;

determining a third quotient of the sum and the difference;

determining a fourth quotient of a first scale factor and a sum of a third two of the time intervals;

determining a square of the fourth quotient;

determining a product of the third quotient, the square, and a second scale factor; and

determining an acceleration of an inertial device comprising the proof mass;

wherein the inertial parameter comprises the acceleration.

26. The system of claim 25, wherein the second scale factor comprises a pitch of the proof mass.

27. The system of claim 15, wherein the quantity comprises a phase shift.

28. The system of claim 15, wherein each of the plurality of time intervals is a difference between a respective two of the plurality of timestamps.

29. The system of claim 15, further comprising the proof mass and the first and second sensors.