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LSM9DS1
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LSM9DS1数据手册
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July 2016
DT0064 Rev 1
1/6
www.st.com
Noise analysis and identification in MEMS sensors,
Allan, Time, Hadamard, Overlapping, Modified, Total variance
By Andrea Vitali
Main components
LSM6DS3H
iNEMO inertial module: 3D accelerometer and 3D gyroscope
LSM6DSM/LSM6DSL
iNEMO inertial module: 3D accelerometer and 3D gyroscope
STEVAL-STLKT01V1
SensorTile development kit
Purpose and benefits
This design tip explains how to analyze and identify noise in MEMS sensors. Allan and
Hadamard variance are explained, together with their variations (Overlapping, Modified and
Total). Theoretical variance #1 (Theo1) is also mentioned.
Benefits:
How to characterize MEMS sensors by means of Allan and other variances
The signal and the noise
The basic assumption is that the signal of interest is constant and flat during the
measurement. The sensor output however is the sum of the signal of interest and the
noise. Roughly speaking, the noise should average to zero in the long term.
Many samples are taken during the measurement. Analysis and identification of noise can
help in determining how many samples can be averaged to minimize the variance of the
sensor output.
The problem with the standard variance is that it is not well behaved for increasing length
of the data run. To solve this problem, the Allan variance was developed. The Allan
variance σ
2
is computed as the average of the squared difference between consecutive
“samples” (2-sample variance). “Samples” are computed by averaging over m-samples in
an time interval τ = m*Ts, where Ts=1/Fs is the sampling interval, and Fs is sampling
frequency.
Allan variance and more
The Allan deviation σ(τ) is the square root of the Allan variance σ
2
(τ). The slope of the log-
log plot depends on the noise type. It is the slope which enables noise type identification.
See the table below.

LSM9DS1 数据手册

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