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The characterization and testing of MEMS gyros for GIOVE-A
Conference Paper · August 2006
DOI: 10.2514/6.2006-6044
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AIAA 2006-6044
AIAA Guidance, Navigation, and Control Conference and Exhibit
21 - 24 August 2006, Keystone, Colorado
The Characterization and Testing of MEMS Gyros for
GIOVE-A
A Cropp* and C Collingwood.†
Surrey Satellite Technology Ltd, Guildford, UK
Stephane Dussy‡
ESA/ESTEC, Noordwijk, The Netherlands
This paper describes the characterization and testing of the Systron Donner QRS11
MEMS rate sensors for the GIOVE-A mission. The rate sensing requirements for this
mission exceeded the QRS11 data sheet specifications; hence testing was required to prove
the unit's enhanced performance. This paper describes the test methods used, as well as the
resulting bias and bias instability values measured. Effects such as the bias sensitivity to
temperature, initial bias transient on switch-on, and vacuum effects on bias are measured
and compensated for. The end results are bias and bias instability values that are well within
the values stated in the QRS11 data sheet, and are verified by initial in-orbit results.
I.
Introduction
T
he QRS11 MEMS (Micro Electrical Mechanical System) analogue rate sensor is an inexpensive robust unit with
previous space flight heritage. It has flown on the NASA SAFER EVA backpack experiment, on the ESA
INTEGRAL mission, as part of the NASA Mars Sojourner Rover mission, as well as on a previous Surrey Satellite
Technology Ltd. (SSTL) mission UoSAT-12. It was chosen for GIOVE-A due to cost constraints, and because of
the relatively relaxed mission rate-sensor requirements. The unit was required in the following mission modes:
• DTM (Detumbling): The gyro rate output measures the tip-off rates after launcher separation. In this mode,
the gyros are mission-critical sensors.
• SAM (Sun Acquisition Mode): Before acquiring the Sun, 3-axis gyro rate information is required. After
acquisition, the gyro rates are required to control rate about the Sun vector.
• SAM-C (Sun Acquisition Mode with Coning): Earth searching coning maneuver about un vector, the gyro
rates are required to control rate about the Sun vector.
However, the unit specifications were significantly outside of requirements for maximum bias and bias
instability parameters. Table 1 below gives the GIOVE-A gyro requirements, along with the relevant Systron
Donner specifications, taken from the QRS11 data sheet (correct at time of writing).
Table 1: A comparison of GIOVE-A gyro requirements with QRS11 specifications
Parameter
Rate measurement noise (assumed white
when sampled at 1Hz), also known as
Angle Random Walk (ARW)
Maximum bias at any time
GIOVE-A Requirement
< 0.010 deg/s (1 )
QRS-11 Specifications
< 0.010 deg/s/ Hz (1 )
= ARW of 0.6 deg/ hr
< 0.25 deg/s (hard limit)
Steady-state bias instability (random walk
of gyros)
< 20 deg/hr/ hr (3 )
0.5 deg/s (at 22°C)
+ 0.35 deg/s deviation from 22°C
0.01 deg/s in 100 sec
= 216 deg/hr/ hr
*
Alex Cropp, email a.cropp@sstl.co.uk., tel. +44 1483 803870
Cheryl Collingwood, email c.colligwood@sstl.co.uk, tel. +44 1483 803859
‡
Stephane Dussy, email stephane.dussy@esa.int, tel. +31 715 654018
†
1
American Institute of Aeronautics and Astronautics
Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
This paper briefly describes the tests carried out to
Temp Temp Temp
Temp Temp Temp
demonstrate that the chosen QRS11 units can meet
Gyro Gyro Gyro Pack
Gyro Gyro Gyro Pack
Temp
Temp
X
Y
Z
X
Y
Z
these requirements. The primary tests in Section II are
based on the characterization of bias with temperature,
transient effects, and vacuum effects. Bias instability
AIM 1
AIM 2
tests are included in Section III. A brief note on rate
integration is given in Section IV.
For GIOVE-A, each single-axis gyro provides an
CAN Bus (Primary)
AOCS Interface Module (AIM) with an analogue rate
CAN Bus (Secondary)
and internal temperature signal. A single AIM unit has
Figure 1. AOCS Interface Module Block Diagram
three gyros sensing each axis, with an additional
Each AIM unit has 3 gyros supplying rate and internal
external pack temperature sensor, as shown in
temperature information. In addition, an external
Figure 1. The AIM provides filtering for each signal,
temperature sensor is mounted next each set of three
with a first-order time constant of approximately
gyros. The secondary AIM unit is fully redundant.
100ms. Each analogue signal is converted to raw
telemetry via a 12-bit ADC. Typically, each gyro is
sampled at 10Hz, then averaged each second to provide 1 rate estimate and temperature estimate per gyro per
second.
II.
Bias Characterization
Gyro Bias (TLM)
A. Bias Thermal Calibration
Raw (i.e. uncalibrated) temperature telemetry is compared against raw gyro rate telemetry at fixed temperatures,
while the sensor is at rest. In each case, three gyros and an AIM unit are placed in a thermal chamber, and are
allowed to achieve steady-state temperature. Although the calibrated temperature is unavailable, steady state
temperature can be observed when the average rate of change of temperature telemetry becomes less than the
average telemetry noise. For these test cases, the time required to achieve steady-state temperature was less than 2.5
hours.
The initial temperature range was -10°C to +40°C in 5°C steps. For each fixed temperature, an average gyro rate
telemetry value and an
average
temperature
1980.0
telemetry
value
are
measured. Over the full
1975.0
temperature range, the
various
gyro
and
1970.0
X measured
temperature
telemetry
1965.0
X estimate
points can be fitted to a
Y measured
3rd order polynomial
1960.0
using
least-squares
Y estimate
techniques.
This
Z measured
1955.0
polynomial is then used
Z estimate
1950.0
to estimate the zero-rate
gyro bias telemetry value
1945.0
for any given temperature
telemetry measurement.
1940.0
The use of raw telemetry
0.50
0.70
0.90
1.10
1.30
1.50
values
avoids
the
Temperature (Internal TLM / 2000)
intermediate
and
unnecessary
step
of
Figure 2. Example of measured gyro telemetry with estimated polynomial fitting
having to calibrate and
Points represent individual measurements of gyro rate telemetry and temperature
convert
temperature
telemetry. The far left set of points was added after system assembly & integration thermal
telemetry into °C. In
tests (AIT) took temperatures outside design range down to approximately –25°C.
addition, internal heating
However, as only raw measurements are used, this data point could be added to the model
of the gyros would mean
fitting.
the sensors would be at
different
temperatures
2
American Institute of Aeronautics and Astronautics
from the thermal chamber, making accuarte
calibration of temperature difficult.
During these tests, hysteresis effects were
observed, and hence the units were taken from 10°C up to +40°C and back down again to -10°C
in 5°C steps. All the resulting measurement points
were then used in the polynomial fitting.
1980
Raw Gyro Telemetry
1975
1970
1965
1960
1955
1950
0
20
40
60
80
Time (minutes)
100
120
140
Figure 3(a). Example of raw gyro rate initial transients.
These measurements were taken from 3 gyros immediately after
switch-on. As can be seen, in the first hour, the rates change
noticeably, despite the fact that throughout this test the sensors
were stationary. It is believed this is due to internal heating.
Without correction, these transients can lead to bias errors on
the order of 0.05 deg/s.
2250
Raw Internal Temperature Telemetry
2200
2150
2100
2050
2000
1950
1900
1850
1800
1750
0
20
40
60
80
Time (minutes)
100
120
140
B. Initial Transients
Immediately after the sensors had been
powered, a change in the gyro rate output was
observed. Internal gyro temperature telemetry
seemed to indicate the unit was self-heating.
Figure 3(a) shows a typical example of gyro rate
telemetry taken from 3 gyros. These gyros had
been left in a thermal chamber set at constant
temperature for several hours before being
switched on.
During DTM mode of GIOVE-A, there was a
6-hour critical period when the satellite needed to
reduce initial tip-off rates using rate
measurements from the gyros. If the gyros had to
be switched on and left for 1 or more hours before
being used to allow initial transients to disappear,
this would have taken a significant proportion of
the available time, and reduced margin to an
unacceptable amount. Errors due to transients
alone have been seen to reach 0.05 deg/s.
As can be seen in Figure 3(b), the internal
sensor temperature increased just after switch-on.
As the units had been at constant temperature
before being powered, this increase was assumed
to be due to internal heating. In addition, it was
assumed that the internal heating was causing the
transients observed in the rate output. Hence,
applying the bias thermal calibration model to the
initial transients should remove most of the effect.
Figure 4 below shows the calibrated bias error
based on the raw sequence from Figure 3(a). In
addition to removing the initial transient effects, a
total bias error of less than 0.015 deg/s is
demonstrated, much less than the quoted 0.5
deg/s.
Figure 3(b). Example of gyro internal temperature
measurements during transients
These measurements were taken at the same time as the
measurements in Figure 3(a). These show the observed
increase in internal temperature immediately after switch-on,
followed by a gradual attainment of steady-state temperature.
C. Vacuum Effects
As part of the AIM + gyro Thermal Vacuum
Tests (TVT), the sensors were placed in a vacuum
at controlled temperatures. Due to gyro
requirements for long-duration testing, no vacuum
testing had been carried out. A vacuum
environment was not expected to cause any
change to the unit behavior, as the quartz sensing element is in a hermetic chamber at 1 atmosphere. However, on
testing, an apparent offset in bias of up to 0.1 deg/s was observed. The units were tested after completion of TVT in
ambient conditions, and it was found that this bias offset was removed, and bias values had returned to normal.
From these results it was estimated that each gyro acquired a relatively fixed but unique bias offset when in vacuum.
3
American Institute of Aeronautics and Astronautics
Initial in-orbit results confirm this, although longduration ground tests in vacuum are required to
see if these bias offsets due to vacuum change
with time.
III.
15
10
Bias Instability Characterization
5
mdeg/s
The bias instability specification of these
devices is also considered to be overly
conservative. Although not proven here, it is
estimated that the quoted bias instability figures
given in Table 1 cover the effects of initial
transients discussed above. Bias changes on the
order of 0.06 deg/s over 1 hour are equivalent to a
bias instability of 216 deg/hour (per square-root
hour). Hence, the uncalibrated initial transients
due to expected internal heating may appear to be
a large initial bias drift.
However, if the initial transients are either
removed through calibration or are allowed to
settle, the true bias instability of the unit is much
lower. The bias instability is measured using an
Allan Variance technique, as described below.
0
-5
-10
-15
0
20
40
60
80
Time (minutes)
100
120
140
Figure 4. Example of calibrated bias error
The results in this figure are the bias errors after calibrating
the raw results shown in Figures 3(a) and (b). The bias is
estimated by taking the mean of the calibrated gyro rate
output every minute. As can be seen, the output bias error is
within 15 millidegrees per second (mdeg/s).
A. Bias Instability and Allan Variance
Bias Drift can be modeled as a Random Walk, i.e. the integration of a white noise source. A random walk
process is time varying and highly correlated, and as such it is impractical to try to take the mean or standard
deviation of a sample set. However, the white-noise process that is integrated to form the random walk is easily
characterized by a mean and standard deviation.
For a signal composed of a random walk process with additional white noise added, over a short period of time
the measured variance of the signal will be dependant on
the added white noise. However, over long periods of
10
time, the random walk process will begin to dominate.
Predominantly due to
Allan variance1 is a technique used to extract the
Output Noise
variance of the white noise process driving the random
walk, as well as the variance of the added white noise.
10
Allan Variance is useful for analyzing signals with
2
x
Power Spectral Density (PSD) of the form Sx(f)=Sx0 f(where Sx0 is a constant and f is frequency in Hz). For a
white-noise
source y(t), the PSD is constant for all
10
Predominantly due
frequencies
such that PSD{y(t)} = Sy(f) = Sy0. For a
to Bias Drift
random walk process x(t)= y(t), the PSD of x(t) is given
as Sx(f)=Sx0 f—2.
Time variance (TVAR) is a form of Allan Variance, and
10
for discrete signals is the variance of the double
10
10
10
10
10
Decimation Ratio, n
difference of the mean of a block of data, of varying
length:
Figure 5. Example TVAR
This figure shows an example TVAR plot from a
N 3
synthetic signal. With low decimation ratio n, the
1
2
2
2
measured variance is dominated by added white (output)
(1)
xi
x () =
6(N
2) i = 0
noise. As the decimation ratio increases, the mean of
larger blocks of data reduce the effect of noise, reducing
the measured variance. This decrease continues until the
where N is the length of the total data set, and x k is the
random walk process begins to dominate, where
mean of a non-overlapping block of n samples (where n
variance increases with time and hence block size
is the decimation ratio), and = n 0 is the time duration
(decimation ratio).
of the block of data (where 0 is the sample interval).
-2
-3
-4
-5
0
1
2
3
4
((
4
American Institute of Aeronautics and Astronautics
))
Table 2. PSD and Standard Deviation using Allan Variance (TVAR)
Noise Type
PSD
vs. TVAR
Bias Instability
(Random Walk)
Sw
=
f2
Output Noise
Sv =
Standard Deviation
vs. TVAR
2
x
2
3
2
n
6
2
x
f
2
2
2
B
=
2
x
x
v
n
0
( w2). The relationship between the TVAR variance, PSD,
B=1/2 0).
2
x
w
1990
60 2 60 2
1980
Raw Gyro TLM
= Sw 2
2
and
2000
and decimation ratio
n, the random walk PSD SW/f2 with units
(deg/s)2/Hz can be estimated. The bias instability in
deg/hr/ hr is then given by:
Bias Instability =
2
v
2010
Hence, given a point on the TVAR plot to the
right with TVAR variance
2
0
w
Figure 5 shows an example of the
typical “v” pattern of a TVAR plot,
with reducing effect of added noise
on the left, and increasing effect of
random walk on the right. Away
from the central knee-point where
the two effects balance, taking any
point on the curve will give either
the variance of the added noise ( v2),
or the variance of the white noise
driving the random walk process
are given in Table 2 (where bandwidth
(2)
1970
1960
1950
1940
1930
Estimates of output noise and bias instability
made from TVAR plots tend to be overly
pessimistic from experience. An alternate, more
direct method of estimating the bias instability and
output noise is as follows:
The mean for each consecutive hour of data is
found, and the standard deviation of the differences
in these mean values was used as an estimate of the
bias instability. The mean of the variances of each
10
10
1910
0
10
10
10
-3
-4
-5
-6
-7
-8
10
0
10
1
2
3
10
10
Decimation Ratio, n
10
4
10
20
30
40
50
Time (hours)
60
70
80
90
Figure 6. Example data set for bias instability estimation
An example 90-hour data set from 3 gyros, showing a
relatively stable bias.
2
X
10
1920
10
5
Figure 7. Example TVAR plot from real data
The solid line is the TVAR plot, and the dotted lines are the
estimated output noise and bias instability line fitting. At low
decimation ratios, there are more blocks of data, resulting in
a smoother curve. Conversely, at larger decimation ratios
necessary for estimating bias instability, fewer blocks result
in a plot with more pronounced jitter.
hour of data was taken as an estimate of the output
noise. Such an estimate for output noise would
also include effects of random walk, and would
therefore be conservative.
Figure 6 shows an example 90-hour data set
from 3 gyros, taken at constant temperature after
initial transients had settled. As can be seen
qualitatively from the figure, the gyros
demonstrate a very stable output with low bias
instability. Figure 7 shows the TVAR plot from a
single gyro, along with the estimated output noise
and bias instability lines of best fit.
Table 3 gives the estimates of output noise and
bias stability, based on 90-hour tests on 6 gyros,
using both the Allan variance TVAR method and
the alternate method described above. As
discussed above, the alternate method of
estimating output noise results in an overly
conservative estimate, as the variance of 1-hour
data sets includes both the output noise and to a
lesser extent the bias instability. All direct
estimates of output noise are within the
requirement of 0.01 deg/s. However, the Allan
5
American Institute of Aeronautics and Astronautics
Table 3: Estimates of Gyro Output Noise and Bias Stability
Gyro
Allan
Variance
Noise
(mdeg/s)
13.7
13.2
11.3
13.8
12.6
11.3
1
2
3
4
5
6
Allan
Variance
Bias
Stability
(deg/hr/ hr)
1.4
1.54
1.28
2.94
0.28
3.44
Alternate
Noise
Alternate Bias
Stability
(mdeg/s 1 )
9.76
9.39
7.99
9.72
8.91
7.99
(deg/hr/ hr 1 )
1.42
1.51
1.32
2.42
1.47
2.47
variance estimates of output noise are
all larger than these conservative
estimates.
The bias instability measurements
from both TVAR and the more
simplistic alternate method are all
within 4 deg/hr/ hr. Assuming this is a
1-sigma value, the 3 bias instability
of these units are all less than
12 deg/hour/ hr, which is within
requirements.
IV.
Rate Integration
Given the low values of calibrated
bias and bias instability given above,
these units can be considered for short-duration rate integration modes, where the gyro rate output is integrated to
give an estimate of the attitude with time. For such maneuvers, it is assumed that the gyro bias is estimated to within
some residual error, for example 0.001 deg/s, using some absolute attitude sensor such as a star tracker, at low
satellite inertial rates. A residual bias error of 0.001 deg/s is relatively small compared with the output noise of
0.01 deg/s, but should be achievable with appropriate filtering. Such maneuvers are envisaged to be short-duration,
for example when the primary attitude sensors are temporarily unavailable. As rate is integrated, errors will
propagate and generally increase with time.
Figure 8 gives the expectation of attitude errors due to integrating the initial bias, angle random walk (ARW) and
bias instability. As can be seen, even though the initial bias of 0.001 deg/s is relatively small, this noise term
dominates the estimated angle error for almost 2 hours. This would indicate that performance is determined
primarily by the initial bias estimation, and factors such as gyro bias instability and ARW are secondary
considerations.
degrees
V.
Conclusion
This paper highlights tests carried out with Systron Donner QRS11 gyros for the GIOVE-A mission to achieve
calibrated bias and bias instability errors much
8
smaller than the values given in the official data
sheet. Bias calibration errors after temperature
7
Init. Bias 1e-3 deg/s
ARW 0.6 deg/rt-hr
compensation was less than 0.015 deg/s, and bias
Bias Instab 4 deg/hr/rt-hr
6
instability was less than 4 deg/hour/ hr. Fixed
offset variations in bias was also observed in
5
vacuum.
A brief analysis indicated that the bias
4
instability error is low enough to enable this unit to
3
be used as a low-cost short-term attitude sensor in
rate-integration mode.
2
In addition, in-orbit results have indicated
through
indirect measurements that the gyros
1
performed successfully on GIOVE-A.
0
0
20
40
60
80
100
120
Acknowledgments
Time (minutes)
Figure 8. Comparison of angle estimation error sources
for gyro rate integration
This figure shows the increase in angle error standard
deviation with time due to initial bias error (linearly increases
with time), angle random walk (increases with the square-root
of time) and bias instability (increases with time to the power
1.5). An example initial bias of 0.001 deg/s dominates almost
from the start until almost 2 hours later, even though 0.001
deg/s is a relatively small residual bias.
A.Cropp would like to acknowledge the help of
Graham Baker of BEI technologies Inc. on his
assistance with QRS11 test support and
information.
References
1
D. Allan et.al., “The Science of Time Keeping”,
Hewlett Packard Application Note 1289
6
American Institute of Aeronautics and Astronautics
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