A direct approach for high-quality MEMS based IMU/INS
production

L. Poletti, D. Sendra Sanchis, R. Siryani
SBG Systems
1 Avenue Eiffel
78420 Carrières-sur-Seine
FRANCE

Inertial Sensors and Systems 2020
Braunschweig, Germany
978-1-7281-6848-7/20/$31.00©2020 IEEE

Pxx

Abstract
This paper describes an industrial process for microelectromechanical systems (MEMS)
based inertial measurement unit (IMU) and inertial navigation systems (INS) production.
Producing high accuracy sensor in a limited time and with a robust process is a universal
problem in IMU and INS production. The challenge we face today is finding a calibration
and a performance validation processes which will systematically get the most of eachIMU.
As MEMS based IMU start competing with other technologies based on high-end
gyroscopes, the calibration becomes a critical topic to increase the IMU performance. A
common technique used on high-end technologies as Fiber-optic Gyroscopes (FOG) is tocombine a set of non-specific multi-position observations and a systematic calibration
method as a Kalman filter [1-4]. However, this method requires ultra-low-noise gyroscopeswith excellent bias stability and repeatability to correctly measure Earth rotation rate.
These attributes are hardly found on MEMS. The method also limits the observability of
non-linearities and cross-axis sensitivity errors because of low dynamics.
The calibration method proposed here is based on a direct process [5] combined with highdynamics. High dynamics help discarding noise and bias stability from a proper
measurement. Also, a direct approach allows to master all the process and gives thepossibility to separate and compensate sensors manufacturing and calibration tools
imperfections.
Finally, the performance assessment and acceptance test presented in this paper areused to check the consistency of the direct approach technique by applying high dynamics
after calibration and measuring sensor errors and triads misalignment in a wholetemperature range as shown in Figure 1.
1.

Introduction

SBG systems is an IMU and INS manufacturer, which has developed its knowledges insensor qualification, integration, and calibration for over 13 years. As a MEMS integrator,
SBG systems teams take up the challenge of designing and implementing a robust andfully automatized production workflow.
The production process starts with the assembling of raw material to get IMUs. Then, each
IMU is calibrated on a temperature controlled double axes rate table. Once the calibration
is finished a calibration report is automatically generated for each IMUs and products are[2]

leaved for an aging process. After this process, performance of all IMUs are reevaluatedon the double axes rate table during a performance assessment process. This process
automatically generates a report which sums-up all IMU residual errors and every
validation criterion. If the product passes these criteria it goes through a final acceptancetest which consist in validating electrical and functional features of the product. Once, allthese steps are passed the product becomes a finished product and a final report isprovided for each unit. Every generated report is systematically stored in a data basewhich allows us to follow the accuracy of sensors, production tools, algorithms and global
IMU performance.

Raw materials

Mounting

Calibration

Aging

Performanceassessment

Final
acceptancetests

Finishedproduct

Figure 1. Production workflow

This paper first focuses on the calibration part. Then, it describes production methods toassess sensors performance after calibration. Last, it presents results after calibration.
2.

Calibration

Calibration is one of the most critical topics in IMU and INS production workflow. This
process increases significantly IMU accuracy and consequently INS accuracy. To get themost of an IMU by calibration it is needed to establish both a precise measurement modelof the product and a mechanical tolerance model of the calibration tool. Then, from thosemodels it is possible to suggest an ideal calibration protocol.
2.1.

Measurement model

IMU measurement model can be split into two main categories: sensor measurement
model which regroup every intrinsic sensors errors and triad measurement model which
regroups errors related to clusters of several sensors.
Sensor measurement model can also be divided into two sub-categories deterministic
errors and non-deterministic errors.
Non-deterministic errors cannot be calibrated because of its unpredictable behavior.
Notwithstanding, those errors can be quantified thanks to an Allan variance analysis [6](see Figure 2.).

[3]

Figure 2. Schematic representation of an Allan variance plot

The first error is due to white noise. It can be measured by fitting the – 1/2 slope in thefirst part of the Allan variance plot [7]. For gyroscopes, the white noise is quantified in
𝑑𝑒𝑔

𝑑𝑒𝑔

terms of its power spectral density in 𝑠.√𝐻𝑧 or ℎ𝑜𝑢𝑟.√𝐻𝑧 units and for accelerometers, interms of𝑔√𝐻𝑧𝑚or 𝑠2 .√𝐻𝑧. When the white noise is integrated over time to obtain angularorientation or velocity, it becomes a random walk which is called Angle Random Walk
(ARW) and expressed in deg/√hour units for gyroscopes or Velocity Random Walk (VRW)
expressed in m/s/√hour for accelerometers. The white noise is a random signal with aconstant power spectral density, and it can be averaged to attenuate its impacts on
calibration.
The second error is called bias instability. This is a non-deterministic effect that can bemodeled using flicker noise. It is also a random process and it can be distinguished from awhite noise by a lower frequency spectrum. As this noise is very significant at low
frequencies, removal by averaging samples can be particularly troublesome. Because ofthat, it is often referred to as the true resolution of the sensor. Allan Variance analysis is
usually used to quantify the bias instability by taking the lowest value of the flat profile ofthe curve.
On the contrary, deterministic sensors errors can be calibrated because of its nature.
These regroup biases, scale factor errors, non-linear behavior along measuring rang andspecifically for gyroscopes acceleration sensitivity.
𝑓̃𝑎 = 𝜇𝑎 . 𝑘𝑎 . (𝑓𝑎 + 𝑤𝑎 ) + 𝑏𝑎

(1)𝑓̃𝑔 = 𝜇𝑔 . 𝑘𝑔 . (𝑓𝑔 + 𝑤𝑔 ) + 𝑏𝑔 + 𝐺(𝐴)(2)Equations 1 and 2 define the measurement model of accelerometers and gyroscopes
considering all the deterministic errors. Where the bias 𝑏. is defined as an offset occurring[4]

regardless of sensor input. The Scale factor 𝑘. is defined as a gain proportional to sensor
input. The Non-linear behavior 𝜇. is defined as gain function of sensor input. The
gyroscope acceleration sensitivity 𝐺 is defined as an offset error which occurs whengyroscopes undergo acceleration 𝐴.
Note: 𝑎, 𝑔, and 𝑠 subscript refer to respectively accelerometer, gyroscope, and sensor in
the entire paper.
Every previous error is intrinsic to each sensor. It is also important to consider errors
related to a sensor triad. This group of errors is only composed of deterministic effects sothey can be calibrated and all of them are consequences of design and manufacturing
constraints.
The first triad related error is called cross-axis and it affects accelerometer as well as
gyroscope triads. It is defined as a non-exact orthogonality between sensors of the samekind. It is represented by a misalignment matrix 𝑀𝑠 (see Equation 4).
𝐹̃𝑠 = 𝑀𝑠 . 𝐹𝑠𝑚𝑥𝑥𝑚𝑀𝑠 = [ 𝑦𝑥
𝑚𝑧𝑥

𝑚𝑥𝑦
𝑚𝑦𝑦
𝑚𝑧𝑦

(3)
𝑚𝑥𝑧
𝑚𝑦𝑧 ]
𝑚𝑧𝑧

(4)

Where 𝑚𝑥𝑥 refers to the measurement obtained on 𝑥 sensor when applying a stimulation
along 𝑥 axis, 𝑚𝑥𝑦 refers to the measurement obtained on 𝑥 sensor when applying astimulus along 𝑦 axis, and so on.
The second triad related error is called size-effect and it only affects accelerometers. It isdefined as a residual acceleration which occurs under rotation when accelerometer
centers of measurement are not coincident. Due to obvious physical constraint it is
impossible to make high-end single axis accelerometers point of measurement coincident(see Figure 3). These distances from an ideal center of measurement will generate
centripetal and tangential acceleration which must be cancelled. The error equations 5 and6 are easily obtained from deriving mechanical equation of movement [4].
𝐹̃ = 𝑀. (𝐹 + 𝑆(Ω))

[5]

(5)

𝐶𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙⏞𝑟 . 𝜔 𝜔 − 𝑟 . (𝜔 2 + 𝜔 2 ) + 𝑟 . 𝜔 . 𝜔⏞𝑟𝑥𝑦 . 𝜔𝑧̇ − 𝑟𝑥𝑧 . 𝜔𝑦̇
𝑥𝑧
𝑥 𝑧
𝑥𝑥
𝑧
𝑦
𝑥𝑦
𝑥
𝑦
𝑆(Ω) = [𝑟𝑦𝑧 . 𝜔𝑦 𝜔𝑥 − 𝑟𝑦𝑦 . (𝜔𝑥2 + 𝜔𝑧2 ) + 𝑟𝑦𝑧 . 𝜔𝑦 . 𝜔𝑧 ] + [𝑟𝑦𝑧 . 𝜔𝑥̇ − 𝑟𝑦𝑥 . 𝜔𝑧̇ ]𝑟𝑧𝑥 . 𝜔𝑦̇ − 𝑟𝑧𝑦 . 𝜔𝑥̇
𝑟𝑧𝑦 . 𝜔𝑧 𝜔𝑦 − 𝑟𝑧𝑧 . (𝜔𝑦2 + 𝜔𝑥2 ) + 𝑟𝑧𝑥 . 𝜔𝑧 . 𝜔𝑥

(6)

Where 𝑟.. denotes distance between sensor center of measurement 𝐶. and triad ideal
center along 𝐶𝑠 , 𝜔. denotes rotations around subscripted axis and 𝛺 is the global rotation.

Figure 3. Size effect representation for accelerometer Z axis.

The last triad related error is referred to as triads misalignment. It is defined as a rotation
matrix 𝑅.. between two theoretically parallel sensors triad as shown in Equation 7.
𝑋𝑔
𝑋𝑎
𝑔
𝑌
[ 𝑔 ] = 𝑅𝑎 . [ 𝑌𝑎 ]
𝑍𝑎
𝑍𝑔

(7)

Where 𝑔 and 𝑎 subscript respectively refer to gyroscope and accelerometer.
Finally, it is to be noted that every single error listed above depend on temperature. Figure

4 presents an example of accelerometers bias drift correlated to temperature variation.
Calibration becomes crucial as the temperature-induced drift on bias, scale factor, nonlinearities and cross-axis errors limits the MEMS potential applications in real-world
missions [8].
Moreover, thermal hysteresis is also present on MEMS as the Z accelerometer shows in
Figure 4. This kind of drift has a non-linear dependance on temperature as it possesses
memory and direction dependance [9].

[6]Figure 4. Temperature dependence.

2.2.

Calibration tool error model

Calibrations are usually done thanks to specific tools such as Granite calibration surface
plate, single, double, or even triple axis rate tables. A double axes rate table has beenchosen here for several reasons. Firstly, a granite calibration surface plate is not
appropriate neither for high quality nor for mass production. In fact, the calibration process
handle by a technician is necessary less repeatable than done by a machine. Secondly, asingle axis rate table implies several mounting and demounting operations which is also
not appropriate for mass production and which could reduce calibration accuracy becauseof mechanical tolerances and repeatability. Thirdly, a double axes rate table has enoughdegrees of freedom to stimulate sensors in every direction with only one mounting
operation, consequently it is not needed to have further degrees of freedom. In this sense,a triple axes calibration rate table is over determined. This means that a given stimulation
can be applied by more than one set of calibration tool inputs. Then, this unnecessarily
increases the complexity of mechanical tolerance and consequently the risk of
uncontrolled defects.
In fact, it is important to establish an error model of the double axes rate table for a better
understanding of tools tolerances influence on IMU calibration. To do so, every mechanicalpart of the double axis rate table has been associated to a frame or axis. Firstly, we define
the Earth frame (𝐸). This frame is associated to the earth, 𝑋𝐸 and 𝑌𝐸 axes belong inequator plan and 𝑋𝐸 axis cross the prime meridian as described in [10]. Secondly, wedefine the Navigation frame (𝑁). This frame is associated to the local cardinal points 𝑋𝑁 ,𝑌𝑁 and 𝑍𝑁 are respectively aligned to North, East and Down as shown in Figure 5.

[7]

Figure 5. Earth related frames.

Thirdly, we define the Outer axis (𝑜) and the Inner axis (𝑖). The Outer axis corresponds tothe horizontal axis of the rate table which control the first gimbal. It is aligned by design toEast-West axis. The Inner axis corresponds to the vertical axis of the rate table which
controls the second gimbal. Fourthly, we define the Table frame (𝑇) which is associated tothe plate (or second gimbal) on which IMU are mounted. Fifthly, we define the Body frame(𝐵), which is the theoretical IMU frame. And lastly, we define the Sensors frame (𝑆), whichis associated to each sensor triad.

Figure 6. Picture of (left) a double axes rate table and (right) its associated frames and axes.

Each coupled of frames are linked by a rotation that characterizes either a mechanicaldegree or a mechanical tolerance:-

𝑅𝐸𝑁 characterizes rotation rate observation depending on latitude.

-

𝑅𝑁𝑜 refers to the outer axis initial orientation and horizontal defect and East-West
misalignment.

[8]

-

𝑅𝑖𝑜 characterizes Outer and Inner axis orthogonality defects, Inner axis initialorientation imperfection and Up-down misalignment.

-

𝑅𝑖𝑇 , 𝑅𝑇𝐵 and 𝑅𝐵𝑆 can be regrouped into one rotation 𝑅𝑖𝑆 as all mechanical parts are
assumed to be rigidly attached.

The scheme in Figure 7 sums up every frames and rotation from Earth frame to Sensor
frame.

Figure 7. Frames chain.

This frame chain gives us enough information to model the gravity and earth rotation rate
observation for a given set of mechanical tolerances and a given set of axes inputs.
⃗⃗⃗𝑓𝑎 (𝜃𝑜 , 𝜃𝑖 ) = 𝑅𝑖𝐴 . 𝑅𝑖 (𝜃𝑖 ). 𝑅𝑜𝑖 . 𝑅𝑜 (𝜃𝑜 ). 𝑅𝑁𝑜 . 𝑔⃗⃗⃗⃗⃗𝑁(8)⃗⃗⃗𝑓𝑔 (𝜃𝑜 , 𝜃𝑖 ) = 𝑅𝑖𝐺 . 𝑅𝑖 (𝜃𝑖 ). 𝑅𝑜𝑖 . 𝑅𝑜 (𝜃𝑜 ). 𝑅𝑁𝑜 . 𝑅𝐸𝑁 . ⃗⃗⃗⃗⃗
Ω𝐸(9)

As shown in Equations 8 and 9, 𝜃𝑖 and 𝜃𝑜 respectively refer to calibration tool orientation
input around inner and outer axes.
2.3.

Direct approach

Sensor calibration direct approach consists in estimating each parameter one by one in a
specific order to attenuate the correlation between different errors. The main steps of thisprocess is the non-deterministic error attenuation, sensors calibration and triads
calibration.
Noise is attenuated by averaging measurements over a duration (𝜏) determined for eachsensor through an Allan variance analysis [6]. This duration must respect two criteria: it
must be long enough to get the most precise measurement and it must be short enough to
do not undergo bias instability and rate ramp effects. This value can be observed on an
Allan variance plot as the intersection of random walk slope and bias instability value asshown in Figure 8.

[9]Figure 8. 𝜏 determination using Allan variance plot

Sensor calibration begins with getting rid of the bias 𝑏𝑠 . The basic idea to estimate the bias
is to compute the average value of two opposite measurements (see Equation 10). This is
supposed to get rid of external input such as gravity or earth rotation rate.
1+̃−𝑏̂𝑠 = 2 . [𝑓̃
𝑠 + 𝑓𝑠 ](10)

Where 𝑓̃𝑠 refers to a given sensor measurement and superscript + and - indicate if theassociated stimulation is positive or negative.
It has been proven that the most precise way to estimate accelerometer bias is to selectmeasurement along horizontal plan as those are slightly impact by scale factor andgyroscopes bias can also be directly observed through static measurements taken
orthogonally to earth rotation rate.
For following parameters estimations, earth rotation rate observations must be considered.
There are at least two solutions to cancel earth rotation rate: by post processingorientation and manually subtract it from each measurement, or by carrying out
measurements under specific conditions of orientation to compensate earth rotation rate.
The scale factor 𝑘𝑠 is estimated by stimulating each sensor with two opposite inputs. Thus,
it is possible to cancel the bias by subtracting measurement couple as shown in Equation
11. Generally, gravity is used as accelerometer input and gyroscopes are stimulated by aspecific rotation rate around axis.
1+̂̃−𝑘𝑠 = 2.𝑓 . (𝑓̃𝑠 − 𝑓𝑠 )𝑠𝑡𝑖

Where 𝑓𝑠𝑡𝑖 refers to the stimulus applied to the sensor.

[10]

(11)

For non-linearities 𝜇𝑠 the same process for Scale Factor is extended to the full sensor
measurement range. Therefore, sensor is stimulated with positive and negatives inputs
along its whole range.
𝑓̃ −𝑏̂𝑠(𝑓𝑠𝑡𝑖 ) = 𝑠
𝜇𝑠̂
𝑓

𝑠𝑡𝑖

(12)

The resulting data set is stored to be used by interpolation during real time acquisition.
Considering triads effects, cross-axis errors are estimated by applying a set of opposite
stimulations on sensors along three dimensions. This will make appear residual projectionof stimulations on each axis. As for scale factor estimation, bias effect is cancelled bysubtracting each couple of opposite measurements. And generally, gravity is used as
accelerometer input and gyroscopes are stimulated by a specific rotation rate around axis.
From those observation one can compute each misalignment matrix as shown in Equation
13.
1
+
− )
𝑚𝑠1𝑠2 = 2.𝑓 . (𝑓𝑠̃
− 𝑓𝑠̃
1 𝑠2
1 𝑠2
𝑠𝑡𝑖

(13)

Where 𝑓𝑠1𝑠2 refers to a measurement obtained on 𝑠1 sensor when applying a stimulation
along 𝑠2 axis.
Accelerometer triad to gyroscopes triad alignment is naturally done by fixing orthogonality.
However, this alignment is directly impacted by the calibration tool precision. If theverticality error of the table does not belong in a respectable tolerance accelerometers andgyroscopes will be aligned to two significantly different frame as shown in Figure 9.

Figure 9, Accelerometer and gyroscope misalignment causes by calibration tool defects.

Concerning accelerometer size effect, distances 𝑅𝑥 , 𝑅𝑦 and 𝑅𝑧 between accelerometers
center of measurement from an arbitrary center of IMU are defined by design. From those[11]definitions it is possible to compensate centripetal part of residual accelerations as shownin Equation 14.
𝐶𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙⏞𝑟 . 𝜔 𝜔 − 𝑟 . (𝜔 2 + 𝜔 2 ) + 𝑟 . 𝜔 . 𝜔
𝑟𝑦𝑥
𝑟𝑥𝑥
𝑟𝑧𝑥
𝑥𝑧
𝑥 𝑧
𝑥𝑥
𝑧
𝑦
𝑥𝑦
𝑥
𝑦
2
2
𝑆(Ω) = [𝑟𝑦𝑧 . 𝜔𝑦 𝜔𝑥 − 𝑟𝑦𝑦 . (𝜔𝑥 + 𝜔𝑧 ) + 𝑟𝑦𝑧 . 𝜔𝑦 . 𝜔𝑧 ] , 𝑅𝑥 = [𝑟𝑥𝑦 ] , 𝑅𝑦 = [𝑟𝑦𝑦 ] , 𝑅𝑧 = [𝑟𝑧𝑦 ](14)
𝑟𝑦𝑧
𝑟𝑥𝑧
𝑟𝑧𝑧
𝑟 . 𝜔 𝜔 − 𝑟 . (𝜔 2 + 𝜔 2 ) + 𝑟 . 𝜔 . 𝜔
𝑧𝑦

𝑧

𝑦

𝑧𝑧

𝑦

𝑥

𝑧𝑥

𝑧

𝑥

2.4. Calibration tools specification
Mechanical tolerances of the calibration tool have a huge influence on calibrated IMU
accuracy. Table 1 presents the specification key values of the calibration table used towrite this article. As mechanical tolerance limits calibration performance, this gives an ideaof the minimum precision that can be expected.
Table 1. Double axes rate table key specifications
Parameter

Specification

Units

Inner to outer axis orthogonality<1

arcsecond

Wobble<5arcsecond

Inner axis vertical alignment<2arcsecondOuter axis East-West alignment<2arcsecond

2.5. Calibration results
To prove the consistency of the calibration method a calibration report is automaticallygenerated with the residuals errors for each model computed. To validate the results an
IMU embedding three CRH02-200 MEMS gyroscopes was used. This IMU will be referredto further in the text as IMU-SBG-01.
After computing the calibration model, it is theoretically applied to the measured data toguarantee that all the sensors parameters have been fitted with low errors residuals.
Figure 10 presents the bias, scale factor, and non-linearities residuals from the generated
report.

[12]

Figure 10. Gyroscopes bias, scale factor and non-linearities residual errors after calibration.

Typical values from the technical datasheet manufacturer of these gyroscopes are taken to
be compared to our maximum values in the calibration report in Table 2. The CRH02-200
specifies the following performance on bias, scale factor and non-linearities errors overtemperature.
Table 2: Manufacturer datasheet of CRH02-200 compared to calibration results.
Parameter

Bias overtemperature

Units

°/h

CRH02-200 specifications(Typical values)

IMU-SBG-01 calibration results±3000#1 (X): 1.17

Note: with respect to 25°C
value

#2 (Y): 1.35

(Maximum values)#3 (Z): 2.42
Note: Max residuals for all[13]

temperature range
Scale Factor
Variation Over
Temperature

ppm

±3000

#1 (X): 14.46

Note: with respect to 25°C
value

#2 (Y): 33.89#3 (Z): 25.05
Note: Max residuals for all
temperature range

Scale Factor
Non-Linearity

ppm ofFull Scale±200#1 (X): 45.83#2 (Y): 49.59#3 (Z): 41.81
Note: Value et 20°C

It can be observed that after applying the calibration model the intrinsic errors of thesensor can be significantly reduced. For an ideal sensor, with no drift over time, theseresiduals would be the true performance after calibration. However, it is well known that
sensors parameters can drift and present a low repeatability between power cycles andover time. For this reason, to guarantee the best performance it is important to evaluate
the IMU accuracy after an aging process. This process depends on the IMU grade and it
can last from one day to one month.
3.

Validation

After aging the products undergo two validation processes to ensure establishedspecifications. we want to make sure that products are still compliant to establishedspecifications. Then products will undergo two validation process. The first one assesses
that sensor errors do not drift over time. The second one is a general electrical andfunctional check-up.
3.1. Performance assessment
Performance assessments consist in reevaluating every sensor error and quantifying eachresidue for 3 temperature points.

[14]

Figure 11. Calibration and performance assessment plate.

First, the warmup bias is assessed. Then, random walk and bias instability are quantified
again thanks to an Allan variance study. Residual Start-up bias, Scale factor, nonlinear
behaviors and gyroscope acceleration sensitivity are quantified using methods describedin calibration part. Results from a gyroscope non-linearities measurement can be observedin Figure 12.

Figure 12. Gyro non-linear residuals

Sensor triad validation is divided into two parts. First, we quantify the orthogonality 𝛿𝑠1𝑠2 as
a residual error between a couple of sensors (𝑠1 , 𝑠2 ) as shown in Equation 15.
𝜋⃗⃗⃗⃗⃗⃗𝑠 . ⃗⃗⃗⃗⃗⃗
𝛿𝑠1𝑠2 = acos(𝑀𝑀𝑠2 ) − 2
1

Where 𝑀𝑠1 and 𝑀𝑠2 refer to reevaluated misalignment matrix lines:

[15]

(15)

𝑚𝑠1 𝑠1
𝑀𝑠 = [𝑚𝑠2 𝑠1
𝑚𝑠3 𝑠1𝑚𝑠1 𝑠2𝑚𝑠2 𝑠2
𝑚𝑠3 𝑠2

𝑚𝑠1 𝑠3𝑚𝑠2 𝑠3 ]𝑚𝑠3 𝑠3

= 𝑀𝑠1
= 𝑀𝑠2
= 𝑀𝑠3

(16)

Figure 13. Orthogonality defect residue representation.

Then, misalignment is quantified as a residual rotation relative to the reference surface of
the IMU.
To do so, we estimate the rotation matrix 𝑅 that minimize the error between themisalignment matrix 𝑀 and a given ideally orthogonal triad (𝑋, 𝑌, 𝑍). This consist in finding
the orthogonal matrix 𝑅 with determinant +1 that minimizes the loss function:
𝑋 − 𝑀𝑥 . 𝑅
𝐿(𝑅) ≡ { 𝑌 − 𝑀𝑦 . 𝑅
𝑍 − 𝑀𝑧 . 𝑅(17)

Where 𝑀𝑥 , 𝑀𝑦 and 𝑀𝑧 refer to reevaluated misalignment matrix lines:𝑚𝑥𝑥𝑚𝑀 = [ 𝑦𝑥
𝑚𝑧𝑥

𝑚𝑥𝑦
𝑚𝑦𝑦
𝑚𝑧𝑦

𝑚𝑥𝑧
𝑚𝑦𝑧 ]
𝑚𝑧𝑧

= 𝑀𝑥
= 𝑀𝑦
= 𝑀𝑧

(18)

This process allows detection of defects during production process and ensures the bestproduct quality.
4.2 Final acceptance tests
To guarantee high quality products, once IMUs have passed performance assessment, aseries of electrical and function tests are done.

[16]Those automatized tests aim to control power consumption, sync out frequency,
Inputs/Outputs (CAN bus, serial Comm.) and sensors measurement consistency as:
ground acceleration, earth rotation rate, magnetic field, temperature, atmospheric pressure
consistency. For IMU with high demanding applications ground continuity and insulation
tests are done.
In addition of IMU, for INS other functionalities are systematically tested: GNSS
constellations, GNSS position, (latitude, longitude, altitude) in a known location, GNSS
attitude (Heading, Pitch) for double antenna products.
If the IMU/INS passes every tests it can be stored as a finished product. At the same time,a final report is automatically generated, and all data produced during the entire production
process is stored in a data base. This allows the monitoring of performance, and early
detection of drifts on sensors parameters or manufacturing process. By plotting histograms
IMU specifications are easily defined.
4.

Results

Results have been evaluated on IMU-SBG-01. This IMU is composed of three CRH02-200
gyroscopes and three high-end accelerometers. The following study focuses on
gyroscopes as they present the major challenge on MEMS high-end applications. Results
have been obtained by applying the whole production process on IMU-SBG-01: mounting,calibrating, one week of aging and performance assessing.
An extract of the validation report is presented in Figure 14. It shows composite error
measurement from the IMU one week after calibration.

Figure 14. Overall gyroscopes bias, scale factor and non-linearities error after one week of aging.

Again, these results can be compared to the gyroscopes technical specifications frommanufacturer as shown in Table 3.

[17]

Table 3. Manufacturer datasheet of CRH02-200 compared to performance assessment.
Parameter
Bias overtemperature

Units
°/h

CRH02-200 specifications

IMU-SBG-01 performanceassessment±3000#1 (X): 2.36

Note: with respect to 25°C
value

#2 (Y): 0.85
#3 (Z): -1.78
Note: Max value for all threetemperatures

Scale Factor
Variation Over
Temperature

ppm

±3000

#1 (X): 75.14

Note: with respect to 25°C
value

#2 (Y): 109.95#3 (Z): 64.80
Note: Max value for all threetemperatures

Scale Factor
Non-Linearity

ppm of Full
Scale

±200

#1 (X): 28.56#2 (Y): 25.78#3 (Z): 25.86
Note: RMS value for all threetemperatures

Even if before calibration the CRH02-200 presents great performance for a MEMS
gyroscope, it can be observed that the direct calibration method improves the gyroscopes
specifications. Bias or non-linearities specifications are divided by 10 and scale factor error
is divided by 100. This improvement is crucial for high-end navigation applications and it is
the only way to guarantee an INS accuracy, repeatability, and reliability. In this sense, arigorous screening must be performed during production process to deliver IMUs that meetthe specifications defined during IMU/INS qualification.
5.

Conclusion

By taking care of sensors selection, capitalizing knowledge in mechanical and electronicaldesign, and enhancing production process over years, SBG systems teams have beenable to take the most out of MEMS sensors. This paper focuses on the production
workflow which has been implemented in recent years. It shows the importance of
establishing a robust and meticulous calibration process and particularly the importance tounderstand each IMU errors as well as calibration tools errors. It also demonstrates the
crucial aspect of validating systematically each product to ensure the best quality. The fully
automatized calibration and validation process, presented in this paper, allows SBG[18]

Systems to produce thousands of very high performance IMU and INS every year. The
extensive quality checks combined with rigorous qualifications and aging tests are thekeys to guarantee IMU specifications from unit to unit, over temperature and over the
product lifetime.
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