Methods and systems for calibration and compensation of accelerometers with bias instability

• US 6,826,502 B2
• Filed: 01/25/2002
• Issued: 11/30/2004
• Est. Priority Date: 01/25/2002
• Status: Expired due to Fees

• Current Assignee: Honeywell International Inc.
• Original Assignee: Honeywell International Inc.
• Inventors: Savard, Thomas A.
• Primary Examiner(s): Barlow, John
• Assistant Examiner(s): PRETLOW, DEMETRIUS R
• Application Number:
  US10/056,718
• Publication Number:
  US 20030144808A1
• Time in Patent Office: 1,040 Days
• Field of Search: 702/85, 702/96, 702/104, 702/141, 702/127
• US Class Current: 702/104
• CPC Class Codes: G01P 21/00 Testing or calibrating of apparatus or devices covered by the preceding groups

Abstract

A method for determining compensation coefficients for accelerometers which exhibit bias transients is described. The method comprises estimating bias accumulation from measured accelerometer outputs, determining a corrected accelerometer output, and determining the compensation coefficients for the accelerometer.

Claims

1. A method for determining compensation coefficients for accelerometers, said method comprising:

measuring an accelerometer output at a center point of time of a high acceleration load interval, where high acceleration is greater than 1 g;

determining the bias accumulation at the center point of time of the high acceleration interval;

determining a corrected accelerometer output based on the bias accumulation determination; and

determining the compensation coefficients using the corrected accelerometer output.

2. A method according to claim 1 further comprising limiting high acceleration testing dwell cycles to about five seconds, where high acceleration is greater than 1 g.

3. A method according to claim 2 further comprising operating the accelerometers at a load of between −

1 g and +1 g for at least five minutes between high acceleration testing dwell cycles.

4. A method according to claim 1 wherein determining the bias accumulation comprises:

measuring accelerometer output at a time prior to a beginning of the high acceleration. interval;

measuring accelerometer output at a time after an end of the high acceleration interval;

subtracting accelerometer output from the time prior to the beginning of the high acceleration interval from accelerometer output at the time after the end of the high acceleration interval; and

multiplying the difference in the measured accelerometer outputs by one half.

5. A method according to claim 4 wherein determining a corrected accelerometer output comprises subtracting the multiplied difference from the measured accelerometer output.

6. A method according to claim 4 wherein the time prior to the beginning of the high acceleration interval and the time after the end of the high acceleration interval are determined using a second derivative of the measured accelerometer output.

7. A method according to claim 1 wherein determining the bias accumulation comprises estimating bias accumulation at a center point of time, a_c, of a high acceleration load interval according to $\frac{1}{2}$

(a

 



(t2)-a

 



(t1)),

where a(t₁) is measured accelerometer output at a time prior to a beginning of the high acceleration load interval, and a(t₂) is measured accelerometer output at a time after an end of the high acceleration load interval, where high acceleration is greater than 1 g.

8. A method according to claim 7 wherein determining a corrected accelerometer output comprises:

measuring accelerometer output at the center point of time; and

correcting accelerometer output according to $a_c=a<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t_c\right)-\frac{1}{2}<br><br>\left(a<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t_2\right)-a<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t_1\right)\right),$

where a(t_c) is measured accelerometer output at the center point of time.

9. A method according to claim 8 wherein determining compensation coefficients comprises calculating calibration coefficients based on accelerometer testing according to $(\frac{r_{p/n}\pm }{}$

drerrorrp/n)

dvload=(w0+w1

T+ac

(w2+w3

T+w4

T2+w5

T3)+w6

ac2),

where dv_load is a change in velocity for an applied load and approximate radius arm r_p/n, a_c is corrected accelerometer output, T is temperature, r_p/n is an approximate radius arm for positive g (p) and negative g (n) orientations, dr_error is an accelerometer sensing element radial error, and w_i are calibration coefficients.

10. A method according to claim 9 further comprising

testing accelerometers at multiple temperatures and multiple loads;

and

determining dr_error and w_i, calibration coefficients using testing results which include and dv_load, a_c, and T from each accelerometer test.

11. A method according to claim 10 further comprising compensating for temperature and accelerometer output error according to dv_load=(w₀+w₁T+dv_out(w₂+w₃T+w₄T²+w₅T³)+w₆dv₂^out), using the values calculated for w_i, to minimize errors, where dv_out is the accelerometer output.

12. A method for compensating for bias instabilities in accelerometers comprising:

removing temperature cycle hysteresis through temperature cycling;

limiting durations of high acceleration load dwell times, wherein high acceleration is an acceleration of more than 1 g; and

determining a corrected accelerometer output to compensate for bias accumulated during the high acceleration load dwell times.

13. A method according to claim 12 wherein limiting durations of high acceleration load dwell times comprises operating the accelerometers at a load of between −

1 g and +1 g for at least five minutes between high acceleration testing dwell cycles.

14. A method according to claim 12 wherein determining a corrected accelerometer output comprises:

measuring an accelerometer output at a center point of time of a high acceleration load dwell; and

estimating the bias accumulation at the center point of time of the high acceleration load dwell.

15. A method according to claim 14 wherein estimating the bias accumulation comprises:

subtracting accelerometer output at a time prior to a beginning of the high acceleration interval from accelerometer output at a time after an end of the high acceleration interval;

multiplying the difference in accelerometer outputs by one half; and

subtracting the multiplied difference from the measured accelerometer output at the center point of time.

16. A method according to claim 15 wherein the time prior to the beginning of the high acceleration interval and the time after the end of the high acceleration interval are determined using a second derivative of the measured accelerometer output.

17. A method of removing bias accumulation from an accelerometer measured output, the output being measured at a center point of time of a high acceleration load interval, high acceleration being a load of more than 1 g, said method comprising:

estimating bias accumulation at the center point of time, t_c, according to $\frac{1}{2}<br><br>\left(a<br><br>\left(t_2\right)-a<br><br>\left(t_1\right)\right),$

where a(t₁) is measured accelerometer output for a 1 g load at a time prior to a beginning of the high acceleration load interval, and a(t₂) is measured accelerometer output for a 1 g load at a time after an end of the high acceleration load interval; and

correcting accelerometer output according to $a_c=a<br><br>\left(t_c\right)-\frac{1}{2}<br><br>\left(a<br><br>\left(t_2\right)-a<br><br>\left(t_1\right)\right),$

where a(t_c) is measured accelerometer output at the center point of time.

18. A system configured to determine compensation coefficients for an accelerometer, said system comprising:

a computer comprising a processor and a memory;

a rate table comprising a chamber;

a rate table controller connected to said computer and configured to run acceleration load profiles on said rate table, the acceleration load profiles stored in said memory of said computer;

a temperature controller connected to said computer and configured to run temperature profiles in said chamber, the temperature profiles stored in said memory of said computer; and

a device configured to measure output of said accelerometer, said device, said computer configured to receive and store output data from said device, said computer configured to estimate bias accumulation from measured accelerometer outputs, determine corrected accelerometer outputs, and determine compensation coefficients using the corrected accelerometer outputs.

19. A system according to claim 18 wherein said computer is configured to limit high acceleration testing dwell cycles for accelerometers to about five seconds, where high acceleration is greater than 1g.

20. A system according to claim 18 wherein said computer is configured to operate the accelerometers at a load of between −

1 g and +1 g for at least five minutes between high acceleration testing dwell cycles.

21. A system according to claim 18 wherein said computer is configured to:

measure an accelerometer output at a center point of time of a high acceleration load interval, where high acceleration is greater than 1 g; and

determine the bias accumulation at the center point of time of the high acceleration load interval.

22. A system according to claims 21 wherein said computer is configured to:

measure accelerometer output at a time prior to a beginning of the high acceleration load interval;

measure accelerometer output at a time after an end of the high acceleration load interval;

subtract measured accelerometer output at the time prior to the beginning of the high acceleration interval from measured accelerometer output at the time after the end of the high acceleration interval;

multiply the difference in accelerometer measured outputs by one half; and

subtract the multiplied difference from the measured accelerometer output at the center point of time of the high acceleration load interval.

23. A system according to claim 21 wherein said computer is configured to determine the time prior to the beginning of the high acceleration interval and the time after the end of the high acceleration interval using a second derivative of measured accelerometer output.

24. A system according to claim 21 wherein said computer is configured to estimate bias accumulation at a center point of time, a_c, of a high acceleration load interval according to $\frac{1}{2}$

(a

(t2)-a

(t1)),

where a(t₁) is measured accelerometer output at a time prior to a beginning of the high acceleration load interval, and a(t₂) is measured accelerometer output at a time after an end of the high acceleration load interval, where high acceleration is greater than 1g.

25. A system according to claim 24 wherein said computer is configured to:

measure accelerometer output at the center point of time; and

correct accelerometer output according to $a_c=a<br><br>\left(t_c\right)-\frac{1}{2}<br><br>\left(a<br><br>\left(t_2\right)-a<br><br>\left(t_1\right)\right),$

where a(t_c) is measured accelerometer output at the center point of time.

26. A system according to claim 25 wherein said computer is configured to calculate calibration coefficients based on accelerometer testing according to $(\frac{r_{p/n}\pm }{}$

drerrorrp/n)

dvload=(w0+w1

T+ac

(w2+w3

T+w4

T2+w5

T3)+w6

ac2),

where dv_load is a change in velocity for an applied load and approximate radius arm r_p/n, a_c is corrected accelerometer output, T is temperature, dr_error is an accelerometer sensing element radial error to be determined using test results, and w_i are calibration coefficients to be determined using test results using specific dv_load, a_c, and T from each test.

27. A computer for removing bias accumulation from accelerometer measured outputs, the outputs being measured at a center point of time of a high acceleration load interval, high acceleration being a load of more than 1 g. said computer configured to:

estimate bias accumulation at the center point of time, t_c, according to $\frac{1}{2}<br><br>\left(a<br><br>\left(t_2\right)-a<br><br>\left(t_1\right)\right),$

where a(t₁) is measured accelerometer output at a time prior to a beginning of the high acceleration load interval, and a(t₂) is measured accelerometer output at a time after an end of the high acceleration load interval; and

correct accelerometer output according to $a_c=a<br><br>\left(t_c\right)-\frac{1}{2}<br><br>\left(a<br><br>\left(t_2\right)-a<br><br>\left(t_1\right)\right),$

where a(t_c) is measured accelerometer output at the center point of time.