Bias Stability measurement
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Bias Stability Measurement: Allan Variance
Dr. Walter Stockwell
Crossbow Technology, Inc.
http://www.xbow.com
The Crossbow Technology 700 series vertical gyros (VG) and inertial measurement units (IMU) have a
specification for bias stability at constant temperature. What does bias stability mean? Figure 1 shows a
typical output of rate vs. time for a VG700CA unit. Note that the peak-to-peak noise is about 0.38 deg/sec
or about 1400 deg/hr. How can we measure a bias of less than 20 deg/hr?
Bias is a long term average of the data. It is meaningless in terms of a single data point. To measure the
bias, we must first take a long sequence of data, and find the average value. Clearly, in Fig 1, the bias is
about 0.15 deg/sec. Bias stability refers to changes in the bias measurement. For example, what would the
bias be if we took data two hours from now? To measure bias stability, we need to measure the bias many
times and see how the bias changes over time. Even this leaves some open questions: for how long
should we average the data; how many times should we measure the bias to make a valid measurement of
the bias stability?
Figure 1. VG700CA rate output
Fortunately, all of these questions have been worked out already. The Global Positioning System (GPS)
depends on accurate time measurements, and clock stability is an important parameter in determining the
ultimate accuracy of GPS. Dr. David Allan worked out a method of characterizing noise and stability in
clock systems – this method is now called the “Allan Variance.” The Allan Variance (AVAR) is a method
of analyzing a time sequence to pull out the intrinsic noise in the system as a function of the averaging
time. It was developed for clocks, but we can easily adapt it for any other type of output we are interested
in.
Here is the basic idea. Take a long sequence of data and divide it into bins based on an averaging time, τ.
Average the data in each bin. Now take the difference in average between successive bins, square this
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