**Q:**

How do I measure angle random walk in a MEMS gyroscope?

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**A.**

Angle Random Walk (ARW) can be derived from the Allan Variance of the bias data, at an integration time of 1 second. The Allan Variance method was developed by David Allan, in the 1960s, for the purpose of monitoring stability in atomic clocks, but the method works very well for studying gyroscope bias as well. IEEE-STD-952-1997, Appendix B, provides a lot of detailed information on this method, but the purpose of this discussion is to focus on how to apply this method, using a specific example. Let's start with the ADIS16485, a 6DOF IMU that provides an Allan Variance plot in its datasheet. From this plot, we can see that the Allan Variance is equal to ~18 deg/hour, at an integration time of 1 second. The Allan Variance units are deg/hour, while the ARW units are deg/sqrt(hour). Converting between these two units requires division by 60, which is equal to the square root of 3600 sec/hour.

ADIS16485 ARW = 18 deg/hour x 1/60 = 0.3 deg/sqrt(hour).

**TOOLS**

This example uses (1) ADIS16485AMLZ, (1) EVAL-ADIS, the IMU Evaluation software package (1.1) and a vice for keeping the IMU stable during data collection. The EVAL-ADIS User Guide, UG-287, provides details on how to set the EVAL-ADIS and IMU Evaluation software package for ADIS16485 testing.

**SETUP**

- Set the ADIS16485 up for a decimation rate of 246, which results in an output data rate of 10 samples per second. In the IMU Evaluation software package, click on "Register Access," select "DEC_RATE," enter "F5" in the white entry box, then hit "Write." Note that DEC_RATE = 0x00F5 establishes the decimation rate of 246.
- Set up the Data Capture, with the following settings:
- Scaled data (personal preference)
- 300 data samples (30 time segments, at 10 samples/1 second each)
- Filename/location (personal preference)

- Make sure that the DUT (ADIS16485) cannot move during the data capture process. In this experiment, the DUT was placed in a small vice and placed on top of a desk.

**DATA CAPTURE**

Hit the start button and wait for the data collection process to complete. The Data Capture menu will provide a real-time status update at the bottom of the screen. The following picture show this, along with the Data Capture settings for this test. Click on the image to access a higher-resolution version.

**DATA ANALYSIS**

Once the analysis is complete, open the data file in MS Excel to complete the analysis. Obviously, there are more elegant ways to process this data, for those who can write macros or their own analysis programs, but the attached Excel file (ADIS16485_ARW_DataAnalysisExample.xlsx), provides a manual analysis view, for the purpose of learning each step.

- Produce the average value for 30 "1-second integration time periods." (Column D, E)
- Apply the Allan Variance equation to the set of average values (Cell G34, G35)

**DISCUSSION**

The attached Excel file has the raw data and referenced calculations. The ARW from this experiment is equal to 0.29 deg/sqrt(hour). The bottom line is that this process may take some "trial and error," in order to manage all potential influencers, but hopefully this example is helpful.

Hello everyone! I just wanted to offer one clarification.The relationship that equates Angle Random Walk to the Allan Variance, at an integration time of 1 second, relies on the slope of the Allan Variance curve being equal to -1 (per IEEE-STD-952-1997). For the ADIS16488, this has an impact when we apply this relationship to calculating the Velocity Random Walk (VRW) for the accelerometers. In this case, we used the Allan Variance, at an integration time of 0.1 sec and scaled the result by the square root of 10.

VRW = AVAR(0.1sec)/sqrt((0.1 x 9.81 x 3600)), units = meters/second per sqrt(hours)

I hope that helps!

Best,

NevadaMark