ALLAN VARIANCE CALCULATION FOR NONUNIFORMLY SPACED INPUT DATA - DTIC

UNCLASSIFIED Technical Report ARWSE-TR-14011

AD AD-E403 608

ALLAN VARIANCE CALCULATION FOR NONUNIFORMLY SPACED INPUT DATA

Naomi Zirkind

January 2015

U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER

Weapons and Software Engineering Center Picatinny Arsenal, New Jersey

Approved for public release; distribution is unlimited.

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The views, opinions, and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy, or decision, unless so designated by other documentation. The citation in this report of the names of commercial firms or commercially available products or services does not constitute official endorsement by or approval of the U.S. Government. Destroy this report when no longer needed by any method that will prevent disclosure of its contents or reconstruction of the document. Do not return to the originator.

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1. REPORT DATE (DD-MM-YYYY)

January 2015

4. TITLE AND SUBTITLE

2. REPORT TYPE

Final

3. DATES COVERED (From ? To) 5a. CONTRACT NUMBER

ALLAN VARIANCE CALCULATION FOR NONUNIFORMLY SPACED INPUT DATA

5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER

6. AUTHORS

5d. PROJECT NUMBER

Naomi Zirkind

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

U.S. Army ARDEC, WSEC Tactical Effects, Protection & Interactive Technologies Directorate (RDAR-WSH-N) Picatinny Arsenal, NJ 07806-5000

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

U.S. Army ARDEC, ESIC Knowledge & Process Management (RDAR-EIK) Picatinny Arsenal, NJ 07806-5000

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Technical Report ARWSE-TR-14011

Approved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The Allan Variance (AV) characterizes the temporal randomness in sensor output data streams at various times scales. The conventional formula for calculating the AV assumes that the data samples are evenly spaced in time. The problem addressed here is that in some data streams, the data samples are not evenly spaced in time. This report presents a modified approach to AV calculation, which accommodates nonuniformly spaced time samples. The basic concept of the modified approach is that all bins used for averaging have the same time duration, though they may have different numbers of samples. The report presents and documents the Matlab program that was used to implement the modified approach. A key advantage of the approach presented here is that it can accommodate input data streams with arbitrary time spacing between data points. Also, it automatically calculates the range of valid arguments to the AV function, and it calculates and plots the AV only for arguments in that range.

15. SUBJECT TERMS

Allan deviation Nonuniformly spaced time samples Gyroscope Noisy data

16. SECURITY CLASSIFICATION OF:

a. REPORT b. ABSTRACT c. THIS PAGE

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17. LIMITATION OF ABSTRACT

SAR

18. NUMBER OF PAGES

35

19a. NAME OF RESPONSIBLE PERSON

Naomi Zirkind

19b. TELEPHONE NUMBER (Include area

code) (443) 861-1438

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18

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CONTENTS

Summary Introduction Methods, Assumptions, and Procedures

Conventional Allan Variance Equation Pseudocode for Conventional Allan Variance Calculation Procedure for Modified Allan Variance Calculation Matlab Code for Modified Allan Variance Calculation Results and Discussion Conclusions Recommendations References Appendix ? Matlab Code Distribution List

FIGURES 1 VG700CA rate output (ref. 1) 2 Data divided into bins of 1-sec length (ref. 1) 3 Data divided into bins of 10-sec length (ref. 1) 4 Data divided into bins of 500-sec length (ref. 1) 5 AD curve for Crossbow Technology VG700CA gyro (ref. 1) 6 Procedure for calculation of min 7 Calculation of starting and ending indices of bins for =15 8 Clearing all previously stored values of all variables 9 Reading in data for allanarray 10 The creation of sparseallanarray 11 Allanarray broken up into individual arrays

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