sensores mems

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Autonomous Systems LabProf. Roland Siegwart

Studies on Mechatronics

Supervised by: Author:Janosh Nikolic Felix RenautMichael Bloesch

MEMS Inertial Sensors

Technology

Autumn Term 2013


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Declaration of Originality

I hereby declare that the written work I have submitted entitled

Studies on Mechatronics : MEMS Inertial Sensor Technology

is original work which I alone have authored and which is written in my own words.1

Author(s)

Felix Renaut

Supervising lecturer

Janosch Nikolic

With the signature I declare that I have been informed regarding normal academiccitation rules and that I have read and understood the information on ’Citationetiquette’ (http://www.ethz.ch/students/exams/plagiarism_s_en.pdf). Thecitation conventions usual to the discipline in question here have been respected.

The above written work may be tested electronically for plagiarism.

Place and date Signature

1

Co-authored work: The signatures of all authors are required. Each signature attests to theoriginality of the entire piece of written work in its final form.

http://www.ethz.ch/students/exams/plagiarism_s_en.pdfhttp://www.ethz.ch/students/exams/plagiarism_s_en.pdf


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Contents

Symbols v

1 Introduction 1

2 Working principles 32.1 MEMS accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Principle of a displacement-based MEMS accelerometer . . . 32.1.2 Capacitive-based displacement accelerometers . . . . . . . . . 42.1.3 Piezoelectric and piezoresistive-based displacement accelerom-

eters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.4 Resonance-based MEMS accelerometers . . . . . . . . . . . . 6

2.2 MEMS gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Principle of a gyroscope . . . . . . . . . . . . . . . . . . . . . 72.2.2 Tuning forks or resonant beam MEMS gyroscopes . . . . . . 72.2.3 Vibrating plate MEMS gyroscopes . . . . . . . . . . . . . . . 8

2.3 Inertial measurement units . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.1 Definition and purpose of an IMU . . . . . . . . . . . . . . . 92.3.2 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Performance and applications 113.1 MEMS inertial sensors error characteristics . . . . . . . . . . . . . . 11

3.1.1 Bias offset and drift . . . . . . . . . . . . . . . . . . . . . . . 113.1.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.3 Stochastic modeling . . . . . . . . . . . . . . . . . . . . . . . 123.1.4 Data filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Comparison with classic inertial sensor performances . . . . . . . . . 153.2.1 Common performance criteria . . . . . . . . . . . . . . . . . . 153.2.2 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.3 Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.4 MEMS IMUs . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Future developments . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.1 Multi-directional MEMS inertial sensors . . . . . . . . . . . . 203.3.2 New applications of MEMS inertial sensors . . . . . . . . . . 20

4 Conclusion 234.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Bibliography 25

iii


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Symbols

Symbols

φ,θ,ψ roll, pitch and yaw angle

constant sensor bias

Ωm 3-axis gyroscope measurement

Indices

x x axis

y y axis

z z axis

Acronyms and AbbreviationsETH Eidgenössische Technische Hochschule

MEMS Micro Electro-Mechanical System

GPS Global Positioning System

IMU Inertial Measurement Unit

PSD Power Spectral Density

ARW Angle Random Walk

LQE Linear Quadratic Estimation

DARPA Defense Advanced Research Projects Agency

v


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Chapter 1

Introduction

Inertial navigation is a technique in which the position and orientation of an object isdetermined through the data given by accelerometers and gyroscopes. The resultsobtained are therefore calculated only from the initial position, orientation andmovement of the object itself, and not compared to an ”external” frame of reference,as it is the case for other navigation systems such as GPS or radars.The first inertial navigation systems were developed for the first long-range rocketsin World War II, since no external reference could be used to determine the positionof those objects in flight. However, the development of inertial navigation mostlytook place during the cold war through the american and the soviet space programs,and the first space missions were only possible due to groundbreaking progress ininertial sensor technology. Inertial sensors are today used in a wide range of objects,from airplanes or the automotive industry to smartphones or running shoes.Most of todays inertial sensors are micro electromechanical systems (MEMS). This

technology was first used for commercial purposes in the 1990’s, and enabled newapplications through high miniaturization and cost reduction. Inertial sensors beganto be used in completely new domains, such as toys. However, this miniaturizationand cost reduction influences the performance of the accelerometers and gyroscopes,which explains why some inertial sensors based on previous technologies are stillused for high-performance purposes.In the following report, the physical working principles of recent MEMS inertialsensors will be explained, and their performance studied. The aim of this studies onmechatronics report is to have a better understanding of these widely used sensorsand of their applications.

1


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Chapter 1. Introduction 2


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Chapter 2

Working principles

In the following, different types of MEMS inertial sensors and the physical propertiesthey rely on are described.

2.1 MEMS accelerometers

2.1.1 Principle of a displacement-based MEMS accelerome-

ter

Most MEMS accelerometers are based on the measurement of the displacement of a proof mass as a result of a change in acceleration. The proof mass is fixed tothe sensor platform by a mechanical spring-damping system, which usually consistsof small beams [1] . The acceleration of the proof mass can be calculated using

Newton’s second law ΣF = mẍ and is equal to the acceleration of the object plusa relative part. This relative part is the result of a change in acceleration of theobject. For a single direction and without any rotation of the object, we get :

m(a(t) + ẍr(t)) = −dẋr(t)− kxr(t) (2.1)where xr is the displacement of the proof mass with a known mass m relativelyto the object, i.e. if the object is taken as frame of reference, a the unknownacceleration of the object in a desired frame of reference (e.g. the earth), k thespring constant and d the damping constant of the mechanical system.

Figure 2.1: Mechanical model of a displacement-based accelerometer

For the measurements, the system is assumed to be in a steady-state, which meansthat the displacement is constant, i.e. ẍr = ẋr = 0. This leads to the followinglinear relationship between the desired acceleration and the displacement of theproof mass :

3


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Chapter 2. Working principles 4

a(t) = − km

xr(t) (2.2)

In many applications, the acceleration is the only desired parameter. However, fornavigation purposes, the position and velocity can also be determined through inte-gration when knowing the initial velocity and position 1. In almost all sensors, theproof mass is only able to move in one direction, which means three different lin-ear accelerometers have to be combined to measure a three-dimensional movement.There are several ways of measuring the displacement of the proof mass. How-

ever, the most current ones are capacitors, piezoelectric crystals and piezoresistivematerials.

2.1.2 Capacitive-based displacement accelerometers

Capacitive-based accelerometers are using the fact that the capacitance of a givenplate capacitor is inversely proportional to the distance between the plates [2,

p. 182ff.] :

C plate(d) = 0rA

d (2.3)

If this distance changes due to a movement of the proof mass, the capacitancechanges and the change in the electrical potential between the electrodes can bemeasured. In order to augment the sensor’s sensitivity and to reduce the noise,many capacitors can be combined linearly to create the output signal. Both in-planeaccelerometers, in which the proof mass moves in the plane of the device and out-of-plane accelerometers, in which the proof mass can rotate perpendicularly to theplane of the device on which the electrodes are put on, can use this physical property.An example of in-plane and out-of-plane capacitive-based MEMS accelerometers isshown in Fig. 2.1.2 .

1given a constant orientation of the sensor, i.e. for a stable-platform IMU. In the case of

strap-down IMUs, the orientation of the object is also needed, since the direction of the measuredacceleration can vary in time. For more information, please refer to section 2.3.2.


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5 2.1. MEMS accelerometers

Figure 2.2: Typical structure of in-plane (left) and out-of-plane (right) capacitive-based MEMS accelerometers. On the left, the measured acceleration is parallel tothe plane of the device, whereas on the right, it is perpendicular to it (from [3]).

Figure 2.3: Functioning principle of in-plane (left) and out-of-plane (right)capacitive-based MEMS accelerometers, from [4].

2.1.3 Piezoelectric and piezoresistive-based displacement ac-

celerometers

A piezoelectric material is a crystal which generates a voltage when mechanicalstress is applied to it. On the opposite, applying an electric field on the crystalgenerates a deformation. This effect is due to the physical disposition of the atomsin piezoelectric crystals, in which a deformation of the crystal separates the electriccharges from one another. Commonly used piezoelectric materials are quartz andPZT (lead zirconate titanate, a ceramic perovskite crystal). For a perfectly uniformpiezoelectric crystal and a given direction of the force applied to the crystal, thecharge difference and hence the output voltage is linear to this force.

∆Qi = dij∆F j (2.4)In the case of an accelerometer, the applied force is the result of the accelerationof the object applied on the proof mass of the sensor, and is given directly usingNewton’s second law. The sensitivity of the sensor is therefore given by the piezo-electric coefficients which are different for each material and each direction. Thisis why having a uniform crystal with as little impurities as possible is essential forthe range and accuracy of the accelerometer. Many different dispositions of thepiezoelectric crystal and the proof mass are possible depending on the applicationdomain of the given accelerometer.

Piezoresistive materials are similar to piezoelectric materials, except that a changein mechanical stress F results in a change of the materials resistivity. The resultingresistivity is also linear with the applied force for a given direction and material,and can be determined by measuring the electric voltage U for a constant electriccurrent I and using Ohm’s Law :


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U = R(F ) · I (2.5)

Piezoelectric and piezoresistive-based accelerometers usually have a higher robust-ness and range than capacitive-based accelerometers but are less precise and aretherefore often used in high-shock applications.

2.1.4 Resonance-based MEMS accelerometers

Many mechanical systems such as pendulums, or basically any system mountedon springs, have a periodical movement. The amplitude of this movement is maxi-mized for certain excitation frequencies, called resonance frequencies. An interestingproperty around the resonance frequency is that a small variation in the excitationfrequency results in a high change in amplitude, as shown in Fig. 2.4.

Figure 2.4: Amplitude as a function of frequency for a general vibration movement.ω1 is the resonance frequency, ω the excitation frequency (from [4]).

This physical property can be of great use for sensors : by exciting a mechanicalstructure at its resonant frequency through an actuator, a small change in thefrequency, for example due to an additional force on the structure, results in agreat change in amplitude of the vibrating structure. If this amplitude change canbe measured accurately, a sensor with high sensitivity can be obtained.Likewise to displacement-based accelerometers, the change of frequency can be mea-

sured capacitively or with the use of a piezoelectric crystal. The actuator, whichenables the proof-mass to vibrate, usually uses the same physical property thanthe sensor used to measure this change of frequency, e.g. a piezoelectric crystal ora capacitor powered by alternative current with a certain frequency. Resonance-based accelerometers usually are more precise, but more cost-effective than simpledisplacement-based accelerometers due to the additional presence of an actuator.

2.2 MEMS gyroscopes

2.2.1 Principle of a gyroscope

Mechanical gyroscopes are based on the Coriolis effect, which is a phenomenonobserved when an object is moving with a certain velocity in a rotating frame of reference. To an observer in this frame of reference, the object seems to change its


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7 2.2. MEMS gyroscopes

trajectory. The apparent force on the object is called Coriolis force, and is propor-tional to the rotation speed of the frame of reference. Its direction is perpendicularto the rotation direction of the reference frame and to the velocity of the moving

object.

−→F Coriolis = 2mobject(

−→v × −→Ω ) (2.6)

By measuring the effect of this force on a proof mass which is moving at a knownvelocity, the rotational speed of the frame of reference, i.e. the one of the objectthe sensor is placed on, can be determined.

2.2.2 Tuning forks or resonant beam MEMS gyroscopes

Since the proof mass has to be in constant motion for the Coriolis effect to appear,MEMS gyroscopes are mostly based on resonant structures. Those structures haveto be put in motion using an actuator, which can be for instance a piezoelectriccrystal put under a varying electric tension or two electrodes which are alternativelyswitched on and off. Usually, the physical principle used for the actuator is the sameas the one used to measure a change in frequency of the proof-mass.

A quite simple example of a resonant structure used for MEMS gyroscopes is whatis called a tuning fork, which is lately nothing more than the combination of two

beams of same length and material on a common shaft, which is excited at theirresonance frequency, resulting in a type of balanced oscillator where the two beamsoscillate 180◦ out-of-phase. Compared to a single beam, this structure is more en-ergy efficient and more accurate. When a rotation of the system occurs in a directionperpendicular to the vibration direction of the beams, the resulting Coriolis forcechanges the frequency of the vibration, which can be detected using a piezoelectricor piezoresistive material on the common shaft. An example of a MEMS tuningfork gyroscope is Systron Donner’s quartz gyroscope shown in Fig. 2.6 which wasvery successful in the 1990’s as a low-cost yaw-rate sensor [3] .

Figure 2.5: Working principle of a tuning fork MEMS gyroscope, without rotation

(left) and when a rotation of the object occurs (right).


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Figure 2.6: Systron Donner QRS and its characteristic H-formed structure com-posed of two tuning fork-shaped piezoelectric quartz elements. It measures a changeof orientation normal to the plane [3] .

2.2.3 Vibrating plate MEMS gyroscopes

Another structure used for MEMS gyroscopes is a vibrating plate, which can bein round or rectangular shape. The plate is suspended by spring structures suchas folded beams. An actuator makes this structure vibrate at a specific frequencyand phase. This vibration can be in an in-plane direction (x-axis), in which casea rotation normal to the plane (in the z-axis) causes the device to vibrate in theother in-plane direction (y-axis), inducing for example a change of capacitance asdescribed in section 2.1.2. Fig. 2.7 and 2.8 show examples of in plane vibratinggyroscopes [1, 4] .

Figure 2.7: Draper Laboratory’s TFG-2,which consists of two silicon proof mass

plates vibrating in an in plane-directionand 180◦ out of phase. Variation of thevibration direction due to change in orien-tation in the direction normal to the planeis measured capacitively.

Figure 2.8: Bosch’s DRS-MM2 con-sists of an in-plane vibrating disk.

It detects a change in orientationin a perpendicular direction capaci-tively through electrodes placed onthe plane of the device.

There are several other structures possible, such as single vibrating beams or vi-brating disks which have different properties due to their mass distribution and theway the change of frequency is measured. However, the working principle is thesame, which is why it won’t be described in detail here2.

2for more details on e.g. the principle of a resonant ring gyro, please refer to [1, p. 202ff]


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9 2.3. Inertial measurement units

2.3 Inertial measurement units

2.3.1 Definition and purpose of an IMU

An inertial measurement unit (IMU) is a combination of different inertial sen-sors,usually three linear accelerometers and three gyroscopes, which provides a 3dimensional measure of the system’s orientation and motion. Such units are usedfor inertial navigation purposes, e.g. in rockets or satellites, to determine the posi-tion of an object. They are sometimes combined with positioning systems (GPS)to have more precise information.

IMUs based on MEMS sensors are strap-down systems, which means the sensor’sorientation depends of the orientation of the object it is on. Theoretically, all typesof previously shown MEMS inertial sensors can be combined in an IMU. However,to win space, most MEMS IMUs designs combine two in-plane accelerometers andgyroscopes (x- and y-axis) with an out-of-plane accelerometer and gyroscope (z-

axis), which permits to place all sensors on a single chip.

2.3.2 Algorithms

As opposed to stable platform inertial navigation systems, in strap-down inertialnavigation technology, the output signal of the gyroscope, i.e. the orientation of theobject, has to be implemented into the accelerometer algorithm since the directionof the acceleration must be updated if the object changes its orientation [1]. Bothalgorithms can be seen in Fig. 2.9 and 2.10.

Figure 2.9: Model of stable platform inertial navigation algorithm, from [5].

Figure 2.10: Model of strap-down inertial navigation algorithm, from [5].


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The implementation of the gyroscopes output signal into the algorithm results inadding the gyroscope error to the one of the accelerometer. This specific problem of strap-down inertial systems may decrease the accuracy of the inertial measurement

unit significantly compared to a similar stable platform system, since the largesterrors in MEMS inertial technology are usually originated by the gyroscope, asshown in section 3.2.3.


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Chapter 3

Performance and applications

3.1 MEMS inertial sensors error characteristics

The total bias of a sensor is usually defined as the average output signal that hasno correlation with the input signal, i. e. the acceleration or rotation, for specificoperation conditions and a specific time [6]. It is generally expressed in degreeper hour (deg/h) for a gyroscope and in meter per second square (m/s2) or g(1g ≈ 9.80665m/s2) for an accelerometer. Additionally to the bias comes noise,which can change the output value and add an additional error to the sensor.

3.1.1 Bias offset and drift

The bias offset of a sensor is defined as the value of the output signal when theinput signal is zero. For an accelerometer, it would therefore be the accelerationgiven by the sensor when it is not actually moving; for a gyroscope, the angularrotation given when the sensor is not undergoing any rotation.

Basically, a change in any physical property such as pressure, temperature or heightcan induce such a bias. Nevertheless, for MEMS inertial sensors, temperature vari-ation, wether it is due to the environment or to the heating of the sensor itself, isthe main cause of bias. Because of the many physical properties depending on thetemperature, the bias caused by temperature fluctuation is almost always nonlinearto the temperature change itself, which means it is difficult to correct. However,many IMUs 1 contain temperature sensors which are used to correct those biasdirectly [5].

The problem of inertial sensors is that the input signals are time integrated, ascan be seen in Figure 2.10 : a constant bias of therefore causes an error whichgrows linearly with time for a gyroscope, i.e. θf (t) = t and quadratically for an ac-celerometer, i.e. xf (t) =

1

2t2 [5] . This means for a 100µg bias in an accelerometer,

the error in position results in 0.05m after 10 seconds and 500 m after 1000 seconds2. The bias of a gyroscope creates an even more important position error, sinceit creates second order errors in velocity and third order errors in position whencombined with the accelerometer. This means that for e.g. a 0.2deg/h gyroscopebias, the final error in position is 0.0016m after 10 seconds, and grows to 1600mafter 1000 seconds [6] . The error due to the accumulation of small bias over timeis called bias drift.

1e.g. the Xsens Mti or the ADIS 16488 from Analog Devices (see table 3.4).2

calculation for 1000s : xf (1000) = 1/2 ·

100 ·

10 ·

10−6

·

10002

= 0.05m where g = 10m/s2

isassumed

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Chapter 3. Performance and applications 12

3.1.2 Noise

Noise is an additional signal that interferes with the output signal of the sensor.

It may come from other sensors or from the sensor itself, but it is present in anysensor and difficult to characterize. Since it is not systematic, noise can not beremoved from the data directly and a stochastic modeling of the noise is necessarybeforehand. Integrating a white noise with a constant standard deviation σ0 onetime, i.e. as it is the case for the output of the gyroscope or for the velocity, givesa zero-mean random walk with a standard deviation that grows proportionally tothe square root of time, and integrating it twice, as it is the case for the positionerror resulting of the accelerometer noise, gives a second-order zero-mean randomwalk with a standard deviation linear to t3/2 [5] .Fig. 3.1 shows a measurement made on 1000 identical gyroscopes by the companycrossbow for the same noisy signal. Those sensors have an angle random walk(ARW) 3 of 0.99 deg/

√ sec. The resulting distribution, after 1000 seconds, should

therefore have a standard deviation of 31.5 degrees, which appears to be the casehere.

-150 -100 -50 0 50 100 1500

50

100

150

200

250

300

Endpoint (deg)

Figure 3.1: Random walk of 1000 identical gyroscopes as a function of time. On theright, the final distribution, i.e. after 1000s, of the output values of the gyroscopesis given (reprinted from [7]).

3.1.3 Stochastic modeling

To study the noise influence of a sensor and therefore being able to categorize itsperformances, stochastic modeling techniques have to be used. In this section, thetwo most important stochastic modeling techniques and their purpose are brieflydepicted. For more information about stochastic modeling techniques applied to

inertial sensors, please refer to [8].

PSD

The power spectral density (PSD) is the most common tool used to analyze data,especially periodic signals. It gives the periodicity of an output signal for differentfrequencies. The two-sided PSD S (ω) corresponds to the Fourrier transform of thecovariance K (τ ) [8] :

S (ω) =

+∞−∞

K (τ )e−jωτ dτ (3.1)

3the angle random walk is a currently given value for gyroscopes It is simply defined as thestandard deviation of the gyroscope output for a white noise input, i.e. a first order random walk

after 1 second and corresponds to the proportionality factor between this standard deviation andthe square root of time


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13 3.1. MEMS inertial sensors error characteristics

A useful property of the PSD is that for a white noise input, the output powerspectral density can give directly the transfer function of the system. The PSD of a random process usually gives linear log-log slopes corresponding to the powers of

frequencies. This means the different random processes such as noise or bias driftare represented through straight lines, wich have different slopes [6] [8].

Figure 3.2: Slopes and appearance frequencies of various random processes for ahypothetical gyro in single-sided PSD form, from [8].

These characteristics can be used to analyze random processes, for instance the biasinstability or the angle random walk of a gyroscope. The resulting PSD obtained asa function of the frequency is usually averaged using frequency averaging techniques,which enable a clear visible slope. An example of such an analysis is shown inFig. 3.3, which shows e.g. an angle random walk of about 0.0015deg /

√ h [6].

Figure 3.3: PSD output for a real MEMS gyro after frequency averaging techniques,

from [6].


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Allan Variance

Allan Variance is a procedure first defined to analyze the rendering of high precisionoscillators [9]. It has later on been applied more generally for the study of oscillatorstability, and can be used quite efficiently to determine the stability and randomdrift characterization of MEMS inertial sensors [10]. The allan variance σ2Ω(τ )describes the frequency stability of a random process, i.e. the variance of the changeof frequency value between two observations done over a certain sample period τ . Itcan be calculated from the PSD estimation with the formula given in equation 3.2,but there is no inverse formula [8].

σ2Ω(τ ) = 4

∞

0

S Ω(f )sin4(πfτ )

(πfτ )2 df (3.2)

Similarly to PSD, allan variance is used to analyze different random processes of inertial sensors by using the different slopes in a log-log scaled plot, as shown inFig. 3.4.

GBGGG+

GBGG+

GBG+

GB+

GBG+ GB+ + +G +GG +GGG

! "#$

" " !

$ " % & # $

' #

( ) * + + ,

- # ()((.$ #

/ # ( ) ( ( . $

#

0 # () ( ( ( .

$ # 1 & 2

Figure 3.4: Slopes of various random processes for a hypothetical gyro in an Allanvariance plot from [8].

3.1.4 Data filtering

The Kalman filter4 is a mathematical algorithm providing an optimized output fora noisy input signal by using a predictive model. The predictive control system isa copy of the studied system, which estimates how the answer should be withoutthe noise or error created by the actual sensor. Using aiding sensors which giveadditional information to the system, it provides a more observable system thanthe original. By averaging the output value of the real control system and thepredictive control system, an optimal signal can be obtained [6, p. 43ff.].

4also called linear quadratic estimation (LQE)


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15 3.2. Comparison with classic inertial sensor performances

Figure 3.5: Schematic plot of a, inertial navigation algorithm for an IMU using aKalman filter, from [6].

The aiding sensors used for the Kalman filter can be temperature and pressuresensors, but also magnetometers or vision-based navigation algorithm, which use achange of the environment to determine their position. Another often used solutionis the combination of IMUs with a geostationary positioning system (GPS) to obtainmore precise information on the position and orientation of the studied system [11].

3.2 Comparison with classic inertial sensor perfor-mances

3.2.1 Common performance criteria

In the following common performance parameters used to describe and comparesensors, and more specifically inertial sensors, are defined.

Range

The range of a sensor is defined as the set of all the possible output values. For anaccelerometer, it would therefore be defined as the acceleration values that can be

measured with this sensor with the given accuracy.

Accuracy

The accuracy of a sensor is defined as the degree of closeness of the measured valueto the real value. It varies from one sensor to another due to drift or noise, and isinversely proportional to the maximal error or bias 5 of the sensor.

Resolution

The resolution of a sensor corresponds to the smallest measurable input signal.Usually, a signal can’t be measured when the noise to signal ratio approaches 1, i.e.when the sensor can’t distinct it from noise.

5see section 3.1


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Bandwidth

The bandwith of a sensor is a signal processing term which refers to the range of

the frequencies that can be measured (usually in Hz or rad/s).

Sensitivity

The sensitivity of a system is generally defined as the ratio between the output signaland the input signal. The higher the sensitivity, the easier a change in the inputsignal (which can result from a change in acceleration or orientation) is measured.However, increasing the sensitivity of a sensor usually decreases its accuracy, sincethe errors are increased as well.

Selectivity

The selectivity of a sensor is its capacity to differentiate the wanted signal from

other present signal. It can be defined as the ratio of the sensor sensitivity for twodifferent signals.

Nonlinearity

The nonlinearity of a sensor is the actual maximal variation of a constant sensitivityover time for the total range or scale.

Bias stability/instability

Bias stability can be defined as the potential of the sensor error to stay within acertain range for a certain time. It is an essential value for inertial sensors, since theintegration steps necessary in the signal processing of these sensors can lead to high

bias instability. Likewise to rate noise density, bias stability/instability is modeledusing stochastic modeling techniques which are described in section 3.1.3.

Repeatability

Repeatability is the potential of the sensor to respond in an identical way, i.e. withthe same output, to a same input signal given the same conditions.

Grades

Inertial sensors are sometimes ”graded” depending on their performances. Thosegrades are corresponding to the possible application domain corresponding to theperformance of the sensor. Table 3.1 shows the grades corresponding to different

in-run bias of inertial sensors.

Application Grade Commercial Tactical Navigation Strategic

Gyroscope > 1deg/s ∼ 1deg/h 0.01deg/h ∼ 0.001deg/hAccelerometer > 50mg ∼ 1mg 25µg ∼ 1µg

Table 3.1: Grades of inertial sensors, from [3].

3.2.2 Accelerometers

One of the main arguments of MEMS accelerometers is the different range thereare able to calculate an acceleration for. This enables their use in many differentapplication domains, as shown in Fig. 3.6.


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Figure 3.6: Application domains of accelerometers, from [4].

Recent MEMS accelerometers have an excellent price/performance ratio, and theirperformances can be in the same range than accelerometers based on previous tech-nologies, which is why many high-precision IMUs contain MEMS accelerometers.Table 3.2 shows the performances of 2 MEMS accelerometers based on differentprinciples.

Kistler miniature Piezobeam R8640A

Analog Devices ADXL335

PrinciplePiezoelectric ceramic beam cre-ates voltage when vibrating dueto acceleration

Capacitors measure linear dis-placement of proof-mass

Prize (USD) not given (low cost) 77Output signal type Analog Analog

Measured Directions 1 3

Size 10.5mm3 4 × 4 × 1.45 mmWeight (grams) 3.5 not given

Range (g) 3 versions available : ±5, ±10,

±50 ±3.6

Bandwith 0.5 to 3000 Hz for 5 and 10g

range, 0.5 to 5000 Hz for 50g0.5 to 1600 Hz for x- and y-axis,5 Hz to 550 Hz for z-axis

Sensitivity1.000 V/g for 5g range, 0.500V/g for 10 g range, 0.100 V/g for50g range

0.300 V/g

Sensitivity changedue to Temperature(%/◦C )

±0.12 for 5g version, ±0,16 for10g and 50g

±0.01

Nonlinearity (% of Full-scale-output)

±1 ±0.3

Shock survival limit 7 000g 10 000g

Offset at 0g none (no operating current) 1.5V on all 3 axis

Noise Density beforefiltering (g/

√ Hz)

not given 150·10−6 for x-, y-axis, 300·10−6

for z-axis

Table 3.2: Comparison of values given by the constructor for 2 different MEMS

Accelerometers (data taken directly from the datasheets of the constructors)


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3.2.3 Gyroscopes

Even though the precision of MEMS gyroscopes has been improved in the lastyears with the help of batch production techniques and new gyroscope designs,they remain the biggest problem of MEMS inertial sensing technology and the mainreason why previous technologies such as fiber-optic gyroscopes (FOG) or ring lasergyroscopes (RLG) are still vastly used in domains where high-precision sensors arenecessary. Today’s best MEMS gyroscopes attain a bias stability in the range of 1◦/h, which corresponds to a tactical grade.

Analog DevicesADXRS453

ST Microelectron-ics A3G4250D

KVH DSP-3400

Technology 1 MEMS gyro 3 MEMS gyros, 1

Temperature sensor

1 Fiber Optic Gyro-

scope (FOG)Prize (USD) 70 not given (< 250) not given (> 2000)

Size 350mm3 4 x 4 x 1.1mm 88.9 x 58.42 x 42.54

mmRange (◦/sec) from ±300 to ±400 ±245 ±375Sensitivity(◦/sec/LSB)

0.0125 0.00875 not given

Nonlinearity 0.05 %Full scale

and range 0.2 %Full scale

0.15%Full-scale andrange

Temperature Sensitiv-ity

not given ±0.03◦/s/◦C


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Invensense MPU6000

YEI 3-Space Sensor Analog Devices

ADIS 16488

Prize (USD) 15 250 1700

Size 4 × 4 × 0.9mm 35 × 50 × 15mm 47 × 44 × 14 mmWeight (grams) not given 17 not given

Number of Sensors (A: accelerometer, G: gy-ros, T : temperature,M: magnetometer, P:pressure)

3A, 3G, 1T 3A, 3G, 1T, 3M 3A, 3G, 1T, 3M, 1P

Accelerometer Range(g)

±2, ±4, ±8, ±16selectable

±2, ±4, ±8 se-lectable

±18

Gyroscope Range

(◦

/sec)

±250, ±500,±1000, ±2000selectable

±250,±500,±2000selectable

from ±450 to ±480

Accelerometer Sensi-tivity (g/LSB)

from 6.10 ·10−5for ±2g range to4.88 ·10−4 for ±16grange

from 2.4 ·10−4 for±2g range to 9.6·10−4 for ±8g range

1.221·10−8

Gyroscope Sensitivity(◦/sec/LSB)

from 0.00763 for±250◦/sec to 0.061for ±2000◦/sec

from 0.00875 for±250◦/sec to 0.070for ±2000◦/sec

3.052 ·10−7

Accelerometer NoiseDensity before filtering(g/√

Hz)

4·10−4 at 10Hz 9.9·10−5 at 10Hz 6.7·10−5 at 25Hz

Gyroscope Noise Den-sity before filtering(◦/sec/√ Hz)

0.005 at 10Hz 0.03 at 10Hz 0.0066 at 25Hz

Gyroscope Bias Stabil-ity

not given 11◦/h average at

25◦C 6.25 ◦/h

Signal processing Programmable low-

pass filters Kalman filtering Kalman filtering

Applications

Motion Con-trol, ImmersiveSimmulations,

Image Stabiliza-tion, PedestrianNavigation, Toys

Robotics, Mo-tion capture,Positioning andstabilization, Per-sonnel navigationand tracking,

Unmanned ve-hicle navigation,Healthcare mon-itoring, Motioncontrol, Immersivesimulations

Platform stabiliza-tion, Navigation,Personnel track-

ing, Instrument,Robotics

Table 3.4: Comparison of values given by the constructor for 3 different MEMSIMUs (data taken directly from the datasheets of the constructors)


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3.3 Future developments

3.3.1 Multi-directional MEMS inertial sensors

A promising breakthrough in MEMS inertial sensing technology would be the useof multi-directional MEMS inertial sensors, which have the particularity to measurean acceleration or rotation in several directions at once. This would not only en-able even more miniaturization, but also more precise sensors since it would makethe combination of different signals from different sensors to know the direction of acceleration or rotation obsolete.An example of such a multi-directional MEMS inertial sensor would be the levi-tating disk accelerometer, which is currently under research at the University of Southampton [12] and Berkeley Sensor and Actuator Center. A physical model of this accelerometer is shown in Fig. 3.7.

Figure 3.7: Physical model of a levitating-disk accelerometer, based on [12].

The proof-mass of the levitating disk is a micro-machined disk which is levitatingbetween two parts composed each of 4 or more electrodes using electrostatic forces.

The displacement of the proof mass is measured capacitively through a comparisonof the tension over each capacitor. This technology has several advantages overprevious technologies : It enables a measurement of the acceleration in all threedirections and two angles (yaw and pitch) with only one proof mass. It also sup-presses the mechanical spring system to which the proof mass is usually fixed, whichwas a cause of errors of the sensor since the spring constant varied with time andphysical properties such as temperature or pressure. Here, the spring constant islinked to the electrostatic forces that levitate the disk, and can be varied dependingon the application of the sensor [12].Several other types of multi-directional inertial sensors are currently under researchin different companies or universities, such as a levitating sphere concept at BallSemiconductor, Tokinec, Inc., Japan, or a levitating spinning disk similar to themodel described above as a basis for a new type of MEMS gyroscope, which wasdeveloped in the DARPA Navigation Grade Integrated Micro Gyroscope initiative[3, p. 18f].

3.3.2 New applications of MEMS inertial sensors

The never-ending miniaturization of MEMS inertial sensors has opened the pos-sibility for new applications. One often given example is smart ammunition : abullet equipped with a MEMS inertial IMU could calculate its position, compare itto the one of its target, and redirect itself using e.g. small fins on the back of thebullet. Such possibilities are currently under research in several companies for theweapon industry6, the most important problem being the shock resistance of the

6

e.g. at Honeywell, which specializes in producing high-precision inertial sensors for militaryand aeronautical use


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21 3.3. Future developments

IMU necessary for its survival to the firing of the bullet. Another example of newpossible applications is microrobotics. Robots small enough to be implemented insomeone’s body have been build7, and if adding an IMU to these robots to enable

precise navigation is not imaginable today, it might be in the upcoming years.

7e.g. at the IRIS Lab at ETHZ


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Chapter 4

Conclusion

4.1 ConclusionMEMS Inertial sensors have been a real breakthrough compared to previous inertialsensing technologies in matters of size and price. Although they function withrelatively simple physical principles, they can enable measurements of accelerationand angular rotation quite precisely. The miniaturization and low cost of inertialsensors created by the MEMS technology has opened new possibilities and industrialapplications, such as their utilization in toys and smartphones, in small robots ormotion capture. New applications are envisaged in the future in different fields,from micro-sized robots to smart ammunition.However, there still are several drawbacks in MEMS inertial sensor performance,especially for MEMS gyroscopes : Their low selectivity, for instance their highsensitivity to temperature or pressure, combined with the integration necessary fora strap-down technology, can lead to high bias drift and create important errorsin position after a certain time. Furthermore, the precision of micromachiningprocesses is limited, which can induce flaws in the basic structure of the sensor. Allthese errors lead to the point that today’s MEMS IMUs still are not comparablein matters of performance to previous technologies, especially due to the MEMSgyroscopes.Nevertheless, one should not forget that MEMS inertial sensing technology is afairly recent technology, and that increasing the performance and design of MEMSIMUs remains a very active development area. Another important point is thatthe size and price of such an IMU enables their combination with other positiontracking devices, such as GPS, magnetometers or vision-based tracking, which sig-nificantly reduce the errors of a inertial measurement navigation system and make

high-precision navigation based on MEMS sensors a reality.

4.2 Acknowledgements

I would like to express my very great appreciation to the tutors of this project,Janosch Nikolic and Michael Bloesch, who answered all my questions and showedgreat support during all the semester. I also would like to thank the whole ASLlab for enabling me to do this work in ideal conditions, and the ETH library forproviding a calm place to work.

23


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Chapter 4. Conclusion 24


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Bibliography

[1] D. Titterton, J. Weston: Strapdown Inertial Navigation Technology . TheAmerican Institute of Aeronautics and Astronautics, second edition, 2004.

[2] S. Beeby, G. Ensell, M. Kraft, N. White MEMS Mechanical Sensors

Artech House - MEMS Series, pp. 173-208, 2004.[3] N. M. Barbour: Inertial Navigation Sensors . Nato Report, C. S. Draper

Laboratory, Cambridge, USA,

[4] C. Hierold: Microsystems Technology Lecture, chapters : Transduction Tech-niques, Micro Resonators and Resonant Microsensors . At ETHZ, Zurich 2012.

[5] O. J. Woodman: An Introduction to inertial navigation . University of Cam-bridge’s Computer Laboratory Technical Report, Cambridge 2007.

[6] H. Hou: Modeling inertial sensors errors using Allan variance . M.S. the-sis, MMSS Res. Group, Dept. Geomatics Eng., Univ. Calgary, Calgary, AB,Canada, UCGE Rep. 20201, Sep. 2004.

[7] W. Stockwell: Angle Random Walk . Crossbow Technology Inc.,http://www.xbow.com.

[8] IEEE Standard Specification Format Guide and Test Procedure for Single-Axis Interferometric Fiber Optic Gyros

[9] D. W. Allan: Statistics of Atomic Frequency Standards . Proceedings of theIEEE, Vol. 54, No. 2, February 1966.

[10] N. El-Sheimy, H. Hou, X. Niu: Analysis and Modeling of Inertial Sensors using Allan Variance . IEEE transactions on instrumentation and measurement,vol. 57, NO. 1, 2008

[11] A. Kealy, G. Roberts, G. Retscher: Evaluating the performance of low cost MEMS inertial sensors for seamless indoor/outdoor navigation . IEEE Po-sition Location and Navigation Symposium, May 2010.

[12] R. Houlihan, M. Kraft: Modeling of an accelerometer based on a levitated proof mass . Microelectronics Centre, University of Southampton, UK, June2002.

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