IN DEGREE PROJECT MECHANICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2018

Development of a crash detection device and sensor position estimation

KAYAN PHUONG

SEID SALEH

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

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Master of Science Thesis MMK 2018: ITM-EX 2018:664

Development of crash detection and sensor position estimation

Kayan Phuong

Seid Saleh

Approved

2018-10-18

Examiner

Martin Edin Grimheden

Supervisor

De-Jiu Chen

Commissioner

Evam System

Contact person

Florian Curinga

Abstract The purpose of this thesis was to design a device that could estimate the position and velocity of

a vehicle as well as record the data in the event of a crash using off-the-shelf components. To

achieve this, the device has to be able to detect crashes. The device utilised measured

acceleration and velocity difference during a time window of 100 ms to determine whether a

frontal crash has occurred. To estimate the state of the vehicle a Kalman filter was implemented.

The amount of false positive errors, i.e. scenarios where the device incorrectly detects a crash

when no crash has occurred, was analysed to determine its relation to different parameters.

Depending on the sensor location, recorded accelerations will result in different crash profiles.

Therefore, for the recorded crash accelerations to be of use, the sensor-to-vehicle position was

estimated with a novel algorithm. The position of the centre of gravity when the vehicle is loaded

and stationary is considered to be known while the sensor position is considered to be unknown.

The estimation algorithm works by comparing velocities at the centre of gravity and sensor

location and using the principle of relative velocities to establish the distance between the two

points. The distance estimation is applied during constant turning in roundabouts in both

physical tests and in simulated tests. The sensor-to-vehicle position was evaluated by comparing

the mean and the standard deviation of the estimated distance during the manoeuvre.

The construction of the device was successful in the sense that it is able to estimate the position

and velocity during normal driving. If a crash occurred the device was able to detect it and

started recording with a higher frequency than prior to the crash. However, at low velocities and

at locations where the GPS-signal was obstructed the position estimation was not optimal.

The false positive analysis showed that in normal driving conditions, there will be no false

positive errors if the acceleration threshold is set to greater than 1g with a velocity difference

threshold corresponding to an average acceleration of 25% of the acceleration threshold. In the

case when a harsh stop is performed, the abovementioned thresholds would still falsely detect a

crash.

The sensor-to-vehicle position estimation in the physical real world test prove to be too

inaccurate for the uses of crash recording. The simulated tests arrived at the same conclusion.

However, tests with an additional GPS at the sensor location showed that pure longitudinal

displacement could be estimated to a satisfactory degree but not pure lateral. Problems in the

methodology and the limitations were analysed and discussed.

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Examensarbete MMK 2018: ITM-EX 2018:664

Utveckling av kraschdetektor och algoritm för sensorpositions estimering

Kayan Phuong

Seid Saleh

Godkänt

2018-10-18

Examinator

Martin Edin Grimheden

Handledare

De-Jiu Chen

Uppdragsgivare

EVAM System

Kontaktperson

Florian Curinga

Sammanfattning Syftet med detta examensarbete var att konstruera en prototyp som kan estimera positionen och

hastigheten av ett fordon samt att spara datan vid krock med hjälp av lättåtkomlig utrustning. För

att kunna åstadkomma detta behöver prototypen även kunna detektera krockar. För att bestämma

om en frontalkrock har skett eller ej, använder prototypen uppmätta accelerationer samt

hastighetskillnaden under de senaste 100 ms. Om dessa värden överskrider förbestämda gränser

anses en krock ha inträffats. För att estimera position och hastighet så används ett Kalman filter.

Mängden av falskt positiv fel, d.v.s. tillfällen där prototypen anser att en krock har inträffat men i

själva verket har det inte skett någon, analyseras för att bestämma hur mängden beror på de

ovannämnda gränserna.

Beroende på vart sensorn är positionerad i bilen kommer accelerations profilerna vara olika. För

att använda accelerationerna som samlas in vid en krasch föreslås en ny algoritm. Fordonets

tyngdpunkt när det är lastat och stillastående antas vara känd medan sensors position är okänd.

Algoritmen jämför hastigheterna i fordonets tyngdpunkt och sensorposition och estimerar

avståndet mellan de två punkterna genom principen för relativa hastigheter.

Slutprototypen klarar av att estimera position och hastighet samt detektera krock och spara datan

med en högre frekvens än innan krock. Positionsestimeringen gav resultat som överensstämmer

väl med vad som förväntades. Vid låga hastigheter och i områden där GPS-signalen är

begränsad, såsom i områden med höga hus eller i tunnlar, så varierar resultaten.

Analysen av mängden falskt positiva fel visar att vid normalt körbeteende så kommer prototypen

inte ge falska utslag om accelerations gränsen sätts till 1g och genomsnittliga accelerationen sätt

till 25% av accelerationsgränsen. Vid hårda inbromsningar så skulle dessa gränser fortfarande ge

ett falskt utslag.

Avtåndsestimationen mellan fordonets tyngdpunkt och sensors position visade sig vara

oanvändbar efter fysiska test. De simulerade testen kom till fram samma slutsats men när en

extra GPS sensor lades till i sensorns position kunde avståndet för rena longitudinella

förskjutningar uppskattas tillräckligt noga. Problem i metodiken och de givna begränsningarna

analyseras och diskuteras.

Table of contents

Abstract i

Sammanfattning ii

1 Introduction 11.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Division of work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Background 42.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 State estimation with Kalman filter . . . . . . . . . . . . . . . . . . . . 52.3 Establishing centre of gravity position . . . . . . . . . . . . . . . . . . . 72.4 Sensor displacement relative centre of gravity . . . . . . . . . . . . . . 8

3 System design and implementation 123.1 Crash detection system . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.1 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.3 Functional design . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.4 Test of false positive errors . . . . . . . . . . . . . . . . . . . . . 133.1.5 Crash recording . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Sensor to vehicle placement . . . . . . . . . . . . . . . . . . . . . . . . 143.2.1 Sensor simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.2 Side-slip estimation . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Results and discussion 204.1 Crash detection and recording . . . . . . . . . . . . . . . . . . . . . . . 20

4.1.1 Vehicle position estimation . . . . . . . . . . . . . . . . . . . . . 204.1.2 Crash detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1.3 Crash recording . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 Sensor to vehicle placement . . . . . . . . . . . . . . . . . . . . . . . . 284.2.1 Physical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2.2 Simulated tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Conclusion 39

6 Future work 41

References 42

Appendix A 1

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1 Introduction

During operation, emergency vehicles are usually moving through the traffic with ahigher speed than its surroundings. This increases the risk of accidents. Other aggres-sive driving behaviours, such as swerving, rapid acceleration and harsh braking, alsoincrease the risk of accidents. Furthermore, aggressive driving leads to increased fuelconsumption by 10-40 %[1] which negatively impacts the environment.

Through training and real-time feedback driver behaviour can be improved. A studyof driver feedback[2] shows that by providing drivers with real-time feedback of thedriving performance leads to a reduction of unnecessary braking events. The authorsfurthermore suggest that this in turn leads to an overall 8 % reduction in safety in-cidents, which includes crashes, traffic violations and such. Therefore, good driverbehaviour is desirable for a small environmental impact as well as to improve safety.

Unfortunately, accidents occur on the roads every day. Emergency vehicles are noexception and are also involved in accidents. When a severe crash occurs, time is ofthe essence. As time goes by, survival rate decreases. Therefore, it would be desirableif emergency personnel would be alerted automatically when a crash is detected. Iforientation and acceleration data is recorded before, during and after the crash itcould be used for various purposes such as crash reconstruction and analysing thedriver behaviour prior to the crash.

The NHTSA estimates that by 2010 85 % of newly manufactured vehicles would bequipped with some kind of Event Data Recorder[3], or more commonly spoken knownas a ”black box”. These do, however, only collect data in the event of a crash or whenthe airbag is deployed or after a critical event. A cheap alternative would be to use asoftware program and utilise the sensors in smart phones. Unfortunately smart phonescannot measure high accelerations due to hardware limitations.

Furthermore, placement of the sensor for acceleration and velocity recording is im-portant. The crash profiles and crash detection algorithms are different depending onsensor placement and car dynamics. One solution is to try to map the sensor positionrelative to a known point such as the centre of gravity (CoG).

1.1 Problem statement

To be able to accurately reconstruct a crash it is important to know how the sensor ispositioned in relation to the CoG of the vehicle. This resulted in two main foci. One ofthem was the development of a sensor device using off-the-shelf components for crashdetection and recording. The other one was to explore the feasibility of placing thesensor at an arbitrary position, and be able to determine the sensor position relativeto the CoG of the vehicle.

When testing the crash detection device, it would be good to test it for both falsepositive and false negative errors. However, only false positive errors were tested for.The reason for not investigating false negative errors was because of it would requiremultiple cars to be involved in actual crashes. False positive errors on the other handare relatively easy to test and optimise for since they do not involve actual crashes.

This resulted in the following research questions presented below:

• How does the amount of false positive errors relate to parameters set in the crashdetection algorithm?

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• What accuracy does a position estimation algorithm have based on IMU and GPSsensor fusion using a Kalman filter?

• Using off-the-shelf IMU and GPS sensors, with what accuracy can the distance fromcentre of gravity to device location be estimated using a specific driving manoeuvre?With an additional simulated GPS sensor, how does the estimation improve? Is thedistance estimation accurate enough for the uses for crash recording?

These points are evaluated with the use of crash detection, crash recording and driverbehaviour in mind. No vehicle characteristics or any external sensors are available, onlyone GPS sensor and IMU for physical testing. Thus, certain maneuvers that excite thedifferences between GPS data and IMU data must be made for conclusions about thesystem to be drawn. These manoeuvres are identified and evaluated in simulations andwith real life testing. A combined error distance in the lateral and longitudinal vehicleplane of ±0.1 m is suggested as it has a small effect on the crash recorded pulse[4] anda negligible effect on navigation.

1.2 Purpose and definitions

The purpose of this thesis is to develop a device using off-the-shelf components. Thisdevice seeks to be able to collect data which can describe the vehicle behaviour, suchas the vehicle accelerations, velocities, position and attitude. The device should beable to record data both during normal driving conditions as well as detect crashesand record the data from the crash. The data collection after a crash should have ahigher acquisition rate. The reason for using off-the-shelf components is that they arecheap and easily acquirable for everyone. The goal is to see whether they are goodenough for the abovementioned purpose.

To analyse the performance of the device, there are two main ways the device mightfail. In one case it might fail to detect a real crash and in the other it might incorrectlydetect a crash when no crash has occurred. The first scenario corresponds to a falsenegative error while the latter corresponds to a false positive error.

The device should be able to be placed anywhere in the vehicle and still record aninformative crash pulse. For this goal to be reached the CoG in the vehicle and thesensors position relative to the CoG needs to be known. This is a challenge as onlyinformation about the vehicle total distance between rear and front axles, front and reartrack width and vehicle height is given. Estimation of vehicle CoG using the given basicvehicle geometric properties is explored in the literature study and ultimately provedto be beyond what is possible today. A novel sensor-to-vehicle position estimationalgorithm is proposed and tested using a highly dynamic manoeuvre for the purposeof estimating the distance between CoG and sensor device.

The manoeuvre to be performed for sensor-to-vehicle position estimation is a straightdrive into a left turn with a constant velocity and steering wheel angle (circle drive).The circle drive manoeuvre, or constant turning manoeuvre, is performed by the driverwho is tasked with turning the vehicle at a constant speed of 20 m/s with a constantsteering wheel angle of 180° counterclockwise in a roundabout. In the physical testsdeviations in steering angle were not be observed. Additionally, the side-slip and thevelocity at the IMU location are observable in simulated tests. The radius of the circlecreated is 15 m.

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1.3 Scope

In this thesis, only frontal crashes were considered for both crash detection and theanalysis of false positive errors. What the sensor-to-vehicle position estimation error(and therefore the error in recorded acceleration) is allowed to be to optimally estimatecrash severity, passenger injury or other uses over large sets of data is out of this thesisscope. No new sensor compensation algorithm is proposed instead the circle of constantacceleration, an established sensor compensation method, is used as a basis. Thesensor-to-vehicle position estimation is proposed with it the intention to be used forcrash acceleration recording. The crash detection, crash recording and vehicle velocityand position estimation is not integrated with the sensor-to-vehicle estimation.

The device does not seek to determine the CoG of the vehicle, but rather the relativeposition from the sensors to the CoG when the vehicle is loaded and stationary. Es-tablishing the distance between the vehicle’s CoG and the sensors position when theCoG is being moved (for example during harshbraking or high speed turns with largeroll degrees) requires the device to track the CoG, which is beyond this scope thesis.

1.4 Methodology

Literature studies were conducted to review works that is similar and related to thisthesis, which is described in section 2.1. With the knowledge acquired from the lit-erature review, a prototype and methods for estimating the sensor-to-vehicle positionwere developed.

The prototype of the sensor device was placed in an actual vehicle to collect data,which was analysed to determine how the amount of false positive errors dependedon certain parameters. The methods for estimating the sensor-to-vehicle position wastested with an physical vehicle and with a state of the art vehicle simulator.

1.5 Division of work

Kayan Phuong has written the software for the sensor device and was also responsiblefor the state estimation of the vehicle, crash detection and analysis of false positiveerrors.

Seid Saleh was responsible for developing and testing the sensor-to-vehicle position-ing algorithm.

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2 Background

This section covers the literature review of previous work done by others as well assome background theory.

2.1 Literature review

In the study [5], the authors successfully combined IMU and GPS signals in order tomore accurately determine the position of a vehicle. This study was set in a place withhigh-rise buildings and overpasses. This causes the GPS signals to be less reliable. Theauthors in the study managed to accomplish a position estimation error of less than2 m in 50% of the time in their tests. This can be compared to a position estimationerror of more than 6 m 50% of the time if only GPS signals were used.

To determine the position of a vehicle, it is good to use a filter for sensor fusion to getbetter estimations. Some of the most common filters are the Kalman filter and theparticle filter. They both have pros and cons. The Kalman filter is computationallyfast and yields good results assuming the system can be linearised and the noise israther gaussian. The particle filter can yield good results for highly non-linear systemsand for arbitrary noise, however, it can be computationally heavy[6]. In this thesis,Kalman filter will be used since the system can be modelled as a linear system and thenoise is assumed to be gaussian.

There are several methods for detecting crashes. One method is using accelerationthresholds to determine whether a critical event has occurred[7]. Another one is tolook at the velocity difference, ∆V , over a short period of time[8]. In some air-bagdeployment algorithms, these two approaches are combined to determine when a crashhas occurred or not. The combination of these two approaches gives less false positiveof crash detection. For air-bag deployment, the thresholds[8] are different for differentkind of cars. However, the thresholds are of the same order of magnitude.

In today’s society where most people own a smartphone and carry it with them, thereare some discussions on the feasibility of using their sensors to detect or record acrash[9][10]. However, the accelerometer range of smartphones is limited and willprobably be saturated during a crash. There are still numerous benefits of using asmartphone as the detector, one of the biggest benefits is its portability. However, itsportability is also the source for one of its disadvantages, it may run out of battery. Ifthis happens the device can no longer detect crashes.

Effects of sensor placement on the recorded crash accelerations were shown to be poten-tially large in [4] and therefore sensor-to-vehicle position estimations were evaluated.Limited information was found for sensor-to-vehicle position estimation using an in-tegrated Inertial Measurement Unit (IMU) and a Global Navigation Satellite System(GNSS) and the ones found were of little interest. A computationally heavy methodwas proposed by [11] that would be out of bounds for inexpensive embedded systems.Other sensor-to-vehicle methods were lacking as they could not provide a distancefrom sensor to any reference point to the car, whether the sensor was at the driver orpassenger side[12]. Longitudinal position estimations, i.e along the vehicle’s directionof travel, were lacking in the same way and required multiple sensors[13][14]. Whatall of these methods had in common was exciting car dynamics in way or another todetermine sensor position.

To determine the distance between CoG and IMU, the CoG position must first beestablished. Estimation of CoG only INS and GNSS signals for measurement were

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found [15][16], these methods however required extensive knowledge of the vehiclesparameter beforehand. The bicycle model in a turning case was looked in to as itneeded little information that could not be estimated beforehand[17][18].

2.2 State estimation with Kalman filter

It is convenient to refer to the position of an object relative to a another fix object,such as the earth. However, when measuring acceleration and angular velocities of avehicle it is often given in the coordinate system of the vehicle. It is therefor necessaryto keep track of these two coordinate systems.

To distinguish between the two coordinate frames, two different superscripts were used,earth and car. The vehicle state, x, can be expressed with position, velocity andorientation, see below.

x =

P earthy

P earthx

vearth

α

where P earth

y and P earthx are latitude and longitude, respectively. The vehicle speed is

vearth and the heading of the vehicle is α, where α = 0° corresponds to driving straightnorth and α = 90° corresponds to driving straight east.

The state equations can be expressed as

P earthy = Cvearth cosα (1)

P earthx =

Cvearth sinα

cos(P earthy )

(2)

vearth = acarx (3)

where acarx is the acceleration in x direction in car frame, e.g. the accelerations measuredby an IMU mounted inside a car. C is the conversion from meters to latitude andlongitude. The denominator in equation (2) comes from the fact that the earth isround.

Kalman filter is used to estimate the vehicle states. The predicted Gaussian distributedstate estimate, xk, and covariance estimate, Pk, can be described with the followingequations

xk = Fkxk−1 + Bkuk (4)

Pk = FkPk−1FTk + Qk (5)

where xk−1 is the previous state estimate. The prediction matrix, Fk, is derived fromequations (1)-(3) and control matrix, Bk, are

Fk =

1 0 C∆t cosα 0

0 1C∆t sinα

cos(P earthy )

0

0 0 1 00 0 0 0

(6)

Bk =

0.5C∆t2 cosα 0

0.5C∆t2 sinα

cos(P earthy )

0

∆t 00 1

(7)

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and the control vector uk and the covariance of the process noise, Qk, are

uk =

[axkαk

](8)

Qk = nprocess

1 0 0 00 1 0 00 0 1 00 0 0 1

(9)

where nprocess relates to the noise of the process.

The measurements from the GPS of the state is zk

zk = [P nx P

ny v

n]T (10)

and the uncertainty of the measurements (e.g. sensor noise) is expressed as Rk whichis seen below in the case of independent noise [19] and is modelled as Gaussian noisewhere the standard deviation is taken from the GPS datasheet. This might not be thebest model for the noise it is deemed adequate for this thesis,

Rk = nsensor

1 0 00 1 00 0 1

(11)

where nsensor is the uncertainty of sensor noise.

In order to compare the measurement, zk, with the predicted state, xk, the units andscale of both must match. Therefore the conversation matrix Hk is introduced whichrelates the state to the measurement.

Hk =

1 0 0 00 1 0 00 0 1 0

(12)

With equations (4), (5), (10) and (12) the final state, x′k, and covariance estimate,P′k,can be obtained,

x′k = xk + K′(zk − Hkxk) (13)

P′k = Pk − K′HkPk (14)

K′ = PkHTk (HkPkH

Tk + Rk)−1 (15)

where K is the Kalman gain (K′ = HkK).

In the absence of GPS signal the position is still estimated, however due to lack ofmeasured position it is possible that it would be less accurate. Once the GPS signal isback, it is possible that the measured position is incorrect. However, this will quicklyconverge to the correct position once more GPS signals are retrieved. This will notcause the crash detection to trigger since it uses multiple sensors.

Attitude estimation based on quaternion with Mahony filterFor simple attitude estimation of an object, Euler angles are usually used. However,once pitch is equal to 90°, estimation of the attitude becomes problematic which isdue to a phenomenon called Gimbal Lock[20]. For crash detection and recording itis interesting to know the total orientation of the vehicle therefore it is importantto ensure the attitude can be estimated in any case. Another approach for attitude

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estimation is using quaternion. A quaternion can be represented by a four dimensionalvector of the following form

q =

q1

q2

q3

q4

=

cosθ

2

ux sinθ

2

uy sinθ

2

uz sinθ

2

(16)

where θ is the angular rotation and u =[ux uy uz

]is the unit vector about which the

rotation takes place. A more thorough explanation of Mahony filter is given in [21].

To aid the visualisation of the attitude, the quaternions are converted to Euler angleswhich can be used to obtain the absolute orientation (roll, pitch and yaw) of an object,see following equations

roll = arctan 2

(2

q1q2 + q3q4

q21 − q2

2 − q23 + q2

4

)(17)

pitch = − arcsin(

2(q2q4 − q1q3

))(18)

yaw = arctan 2

(2

q2q3 + q1q4

q21 + q2

2 − q23 − q2

4

). (19)

2.3 Establishing centre of gravity position

Establishing any dynamic relationship between the sensor signal and the CoG withany prior knowledge of the system or the system dynamics is impossible. At best amodel for a land based vehicle can be made by using basic modeling constraints; thevehicle is always in contact with the ground (vertical velocity is zero) and does notmove sideways (the lateral velocity is zero) [22]. This would still require the systemto be viewed as a moving particle and thus give no information about the dynamicsproperties. Additionally, both constraints do not always apply to the vehicle and wouldbe large sources of error.

Furthermore, estimating CoG on an embedded system on land based vehicles is mainlydone with extensive pre-modelling in mind. The used methods for this are vehiclemodel based estimation, suspension based estimations and estimations based on brakedynamics or road grade. All these alternatives require extensive knowledge about thevehicle which is not available and can not be estimated with an unknown position ofan IMU and GPS. However, recent studies have applied GPS and IMU sensors forestimating CoG position in the lateral and longitudinal plane [17]. By assuming thevertical CoG is poised low and the lateral CoG is in the middle, the one track model(more commonly known as the bicycle model) can be used. The steering angle andlateral acceleration is used as model input for calculating the distance from rear axisto CoG.

Where steering angle, δ, is the angle between and vehicle longitudinal axis x and wheeldirection. The side-slip angle, β, is the angle between vehicle velocity V direction andthe vehicle’s longitudinal axis.

The issue here is that the steering angle and side-slip is needed for the CoG positionestimation. The side-slip can be estimated by using a IMU and a GPS but even withmathematically heavy filtering it still output subpar results[23]. The steering angle on

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Figure 1: Steering angle δ and side-slip angle β in the one track model

the other hand cannot be estimated at all without external sensors (e.g steering wheelsensors or camera) or pre-modeling.

The dynamic one track model requires the cornering stiffness, a tyre dependent prop-erty, to estimate the steering angle, while the kinematic one requires the tyre side-slipangle (which can be estimated but requires the distance to the CoG to be known. Inshort, steering angle estimations fall flat as they either need extensive modeling withknowledge about the specific vehicle parameters or additional steering angle sensors[24].All reasons which defeats the original purpose of estimating CoG using the availablemeans.

Another way to approach this problem is to eliminate the lateral forces involved whencalculating the CoG position, which is what was explored in [18]. By only focusing onlongitudinal dynamics the side-slip does not have to be considered for the longitudinalCoG positioning. The position of the CoG in the y- and x- axis can be calculatedwithout taking the lateral forces into account as well as the vehicle side-slip when theAckerman steering angle is applied. The Ackerman steering angle was designed toremove lateral slip from tyres in low velocity, which is the case when the wheels in acar are set in a specific geometric formation. The steering angle however was found tohave to be accurate to ±1° for a 10 % accuracy estimation of longitudinal CoG. Usingthe approximate CoG position for a steering angle approximation can yield errors wellover one magnitude higher than ±1° making this path not worthy pursuing as the CoGposition estimation would be too inaccurate.

To conclude, for any estimation of the CoG position more information is required. Atminimum the steering angle is needed for longitudinal position of the CoG. For thelateral and vertical axes a pre-modeled approach is necessary or additional sensors.For the rest of this thesis the CoG’s position is therefore considered to be known whenthe car is stationary and at rest.

2.4 Sensor displacement relative centre of gravity

Even with a known CoG position both inertial and GNSS sensor are often displaced.This produces what is known as the ”lever arm” effect and can cause significant errorsfor crash detection and crash reconstruction.

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An early study on the lever arm effect in airplanes using a GPS and IMU integratedsystem [26] showed that over time large errors accumulated due to lever arm effect,especially after a highly dynamic manoeuvre. Which causes problems during longerGPS outages. This has later been confirmed to be true for automobiles as well. Theerrors caused by the lever arm can be traced back the angular rotation; if the angularrotation is small than the differences in velocity between two points is also small. Thisis confirmed in [25] where the lever arm effects are dependent on the cars’ manoeuvers.It is therefore of interest to perform highly dynamic manoeuvres (where the angularrates are high) to estimate the effect or length of the lever arm. Lever arm lengthshave been estimated with a setup of multiple carrier phase grade GPS sensors withattitude estimation functionality together with a low grade inertial sensor[27]. Furtherwork using the same equipment grade resulted in an error of less than 1 % in lever armlength estimation in [28]. In the so far mentioned lever arm estimations and lever armerror estimations multiple high-grade GPS systems have been used where the positioncan be determined with centimeter accuracy. The IMU has therefore been used totranslate position changes in the body frame to the navigational frame (local tangentplane), where it is then compared to the GPS position. In this thesis comparisons areinstead suggested to be made in the body frame. The GPS velocity and heading isused together with the basic formula for relative velocity to be compared with the IMUaccelerations.

Displacement issues in crash detection

A review of current crash detection algorithms [29] state that the sensor displacementis a large problem. Using basic crash detection algorithms comparing only accelerationand velocity difference is not always preferable as establishing crash detection thresh-olds requires tuning for each specific vehicle, as seen in [30] where each vehicle hasits own acceleration threshold for airbag release. The sensitivity for a car universalcrash detection algorithm using GPS and IMU sensors can therefore be considerablylow compared to advanced system system activations (e.g airbag release, electric stabil-ity control and anti-lock braking), as evidenced by [31] where after evaluating severalkinematic thresholds for over half a million crash and near crash cases, the sensitivityand specificity still needed to be greatly improved.

For direct frontal crashes, the lever arm effect is not an issue if the angular rates aresmall. The velocity in CoG and sensor point S in the body frame can therefore bedescribed as:

VCoG = Vsensor + SG× ΩS (20)

Where VCoG is the velocity vector at CoG in the body frame, Vsensor the velocity at thesensor position, SG the distance vector between point S and CoG and Ωs the angularrate vector at point S. Note that when the angular rates approach zero differencesbetween VCoG and Vsensor become negligible.

Displacement issues in crash recording

The sensors for recording crash impulses are not always placed in the position of inter-est, such as the driver seat. To correctly estimate the accelerations at another pointwith a known distance from where the accelerations were measured the circle of con-stant acceleration method is used. An example were the circle of constant accelerationis applied is for airbag deployment and crash recording[4]. The base equation for circleof constant acceleration is described as:

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AQ = ACG + r × αQ (21)

Where ACG is the acceleration in the CoG, AQ the acceleration in a point Q on thevehicle, r is the distance vector between CoG and Q. The angular acceleration is αQ

in point Q, as seen in Figure 2.

Figure 2: Acceleration components in point Q (sensor position) with origo at G (CoG)[4].

The equation is later described in a cartesian coordinate system using an impulse, Ft,with a distance, p, from CoG illustrated in Figure 3.

Figure 3: Illustration of impulse Ft with distnace p from CoG[4].

Consider the basic mechanical formula for moment. where MG is the moment at CoGand IG the vehicle’s moment of inertia.

MG = IG · α (22)

With the vehicle radius of gyration, k, known (22) can be written as:

F · p = mk · α (23)

Where F is the force applied by the impulse Ft. Using newtons second law, α can beexpressed as:

α =F · pm · k2

=ACG · pk2

(24)

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After converting equation (24) from polar coordinates to Cartesian:

AQx = αr sin θ =pACoGr sin θ

k2(25)

AQy = ACG − αr cos θ = ACG(1 − pr cos θ

k2) (26)

which finally leads to the magnitude relation between accelerations at CoG and sensorlocation.

A2Q = A2

CG(1 +(pr)2

k2− 2pkr cos θ

k) (27)

While these parameters (k and p) are not available during the crash if a crash investi-gation were to become an actuality, the recorded accelerations at the sensor locationcould be used for estimating accelerations at any other point in the vehicle. Note thatif p is zero, acceleration at the CoG and sensor location are interchangeable. The sameholds true if the angular acceleration is zero.

The acceleration magnitudes differ significantly depending on distance, a displacementof 1 meter can result in a magnitude difference of over 200 % in a crash pulse, showingthat the distance has to be taken into account [4]. The circle of constant accelerationmethod is however, not without faults as a recent test on physical vehicles show thatwhile calculated crash pulse peaks and trend are strongly correlated, the midsection ofa crash impulse can show weaker correlations[32].

Vertical sensor displacement

The circle of constant acceleration method only describes the relation in the longitu-dinal and lateral axis. The vertical displacement does affect breaking velocity and, ifgiven a pronounced roll rate, the lateral velocity[33] by negligible amounts for vehiclepositioning. The equation (20) for relative velocities holds true for a rigid body. Inthe case of constant turning, the car body can be considered rigid and still give goodresults as car deformation and stress are negligible when determining the longitudinaland lateral car velocity. For the braking case however, this does not hold true. Considerthat the vehicle’s CoG does not coincide with the vehicles rotation centre. This can becircumvented when using the vehicle yaw rate as it can be considered the same at anypoint of the vehicle, the roll and pitch rate however, are controlled by the suspensiongeometries in the car. This means that a roll or pitch angle are dependent on wherethey are measured. Thus, errors with modeling the car as rigid to be able to find thevertical displacement is a deeply flawed method and will not be further explored.

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3 System design and implementation

This section presents the system design and implementation of the device that wasused for answering the research questions of this thesis.

3.1 Crash detection system

As mentioned in section 2.1, crash detection was based on the acceleration or speedof the vehicle. Therefore, an accelerometer was required to acquire the accelerationwhich in turn yielded the velocity. The acceleration during normal driving is usuallylower than 2g, where g is the gravitational constant, g = 9.82 m/s2. During a crashthe acceleration can reach values well over 2g[30], which means that the sensor needsto be able to record even higher accelerations in order to not be saturated.

3.1.1 HardwareThe device consisted of an STM32F746 nucleo board that was equipped with three sen-sors. The first sensor was an inertial measurement unit (IMU - BMI160 from Bosch)with 3-axis low-g accelerometer and 3-axis gyropscope. The IMU was used to obtainmore accurate acceleration data during normal driving as well as determining the ori-entation of the vehicle. As mentioned above, there might be large accelerations duringa crash which would saturate the low-g accelerometer in the IMU. The second sensorwas therefore a high-g accelerometer (H3LIS331DL from STMicroelectronics) whichwould not saturate as easily. However, the high-g accelerometer is not as accurate asthe IMU’s accelerometer for low accelerations. The device also included a GPS sensorwhich was used to determine the position and velocity of the vehicle. Lastly, a flashmemory (IS25LP128 from Integrated Silicon Solution, Inc.) was used to store data.

The sampling frequency for IMU and accelerometer was 1 kHz. The data was writtento the flash memory with a frequency of 100 Hz when operating in normal mode. Oncea crash was detected the logging frequency is changed to 1 kHz. For the GPS, thesampling and logging frequency was always 1 Hz.

3.1.2 SoftwareA graphical tool called STM32Cube was used to configure and generate the initialisa-tion C-code for the STM32F746 microcontroller. For this thesis an embedded softwarelibrary, hardware abstract layer (HAL), was used for the peripherals. The used pe-ripherals were serial peripheral interface (SPI) for the IMU, accelerometer and flashmemory, while universal asynchronous receiver-transmitter (UART) was used for theGPS. By combining the C-code generated by the STM32Cube and user code, thefirmware of the device was set. This enabled the sensor device to read the sensors’data and perform calculations to estimate the position, velocity and orientation of thedevice. For compiling and debugging, the IDE SW4STM32 was used.

3.1.3 Functional designAs mentioned, the device measured accelerations, angular velocities, the velocity of thevehicle and its position. The measured data was used in combination with a Kalmanfilter and Mahony filter to determine the position, velocity and attitude in-betweenGPS data points. The data was also analysed in real-time to be able to detect crashes.If a crash occurred, the device entered logging mode to store all the measured data forpost-processing. In post-processing, the data was used to determine the position andattitude of the vehicle after the crash.

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The Kalman filter, described in section 2.2, used the following values for noise param-eters, nprocess = 0.1 and nsensor = 4. The value for the sensor noise was chosen sincethe standard deviation was 2 m. The process noise was difficult to estimate and thevalue of 0.1 was chosen after analysing the data. To verify the results the estimatedposition in-between the GPS data was compared with raw GPS data. The estimatedposition should coincide well with the raw GPS data.

The flow chart for the crash detection algorithm used in this thesis can be seen inFigure 4. The system was always checking whether the acceleration was more than acertain threshold by continuously polling the accelerometer reading. If the accelerationexceeded the threshold, the system entered a so-called stand-by mode. If the velocitydifference, ∆V , during a short time interval exceeded another threshold while thesystem was in the stand-by mode the system flags the event as a crash. The reason forusing two different thresholds and not just one of them was to reduce the false positivecrash detections.

Figure 4: Flowchart of the crash detection algorithm.

To be able to determine a ∆V , a time interval was required. This interval as well assome values for acceleration and ∆V thresholds for crashes in which the airbag wasdeployed can be found in [8]. The time interval used to determine the ∆V was 100 ms.The velocity difference was based on the velocity estimate of the Kalman filter.

Since the intervals depend on vehicle model and manufacturer, the interval has beenset to rather trigger false positive errors than false negative ones. In other words, thesystem should rather trigger at aggressive driving, such as hard breaking or driving fastthrough roundabouts, than not trigger at crashes where is should have been triggered.

3.1.4 Test of false positive errorsWhenever a crash was detected it stayed in the ”crash is detected”-mode until eitherthe acceleration or velocity difference fell below its threshold. This simple methodfor leaving the ”crash is detected”-mode was added for the test setup to convenientlyperform the test drive without the need to reset the device. For other purpose thantesting of false positive errors this is not of importance since once a crash has been

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detected the device has served its purpose.

To test the occurrence of false positive errors and to be able to compare betweendifferent tests which had different duration, the amount of false positive errors wasnormalised by the duration of the test. During the tests, data from all the sensors wereacquired and stored to the flash memory.

The data was then post-processed with different acceleration and ∆V thresholds. Foreach different acceleration thresholds, four different ∆V thresholds were used with anaverage acceleration corresponding to the acceleration thresholds times 1, 0.75, 0.5 and0.25, respectively. With this a relation between the amount of false positive errors andacceleration threshold was determined.

3.1.5 Crash recordingTo test the crash recording, a rubber band was attached to the device, see Figure 5.This allowed for the same energy to be transferred to the device initially. The devicegained speed and collided with a small obstacle which caused it to flip over. Before theimpact, orientation and acceleration data was logged at a frequency of 50 Hz. Afterthe impact the logging frequency was changed to 1 kHz. During crash recording allthe data from the sensors were logged but no calculations were performed. The loggeddata were post-processed for a simple reconstruction of the event.

Figure 5: An illustration of the test-setup of crash recording.

3.2 Sensor to vehicle placement

The information about the vehicle is limited. The GPS supplies the system with aspeed and vehicle changes in heading while the IMU outputs accelerations and rates ofrotation in a local frame parallel to the vehicle frame. The sensor frame SG (unknownorigo) and vehicle body frame FG ( origo placed in CoG) are shown in Figure 6. Notethat while the height is the same the lateral and longitudinal position is unknown.

Where distances from the CoG to the unknown sensor device position (where the IMUis placed) in the x,y and z axes are respectively called SGx, SGy and SGz. The GPSantenna was placed at the CoG on the lateral and longitudinal plane when the vehiclewas loaded and stationary. Locating the sensor box, the IMU:s location, without anyexternal information will therefore require special manoeuvres to be made. As themovement of the CoG cannot be tracked during the maneuver it is assumed to be theGPS location during it in both stimulated and physical tests. Consider the vehicledriving a with a constant velocity and yaw rate in a roundabout with a radius R inFigure 7.

The following holds true if the body is rigid and the principle for relative velocities isapplied:

Vsensor = VCoG + SG× ΩCoG (28)

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Figure 6: Parallel frames for FG and SG.

Figure 7: Illustration of a vehicle driving with a constant velocity and turning with aconstant yaw rate in a roundabout as seen from above.

Where SG is a vector from the sensor frame S to CoG, VCoG the velocity vector at theCoG and ΩCoG the rotational rate vector at CoG. The velocity for each axis is:

Vsensorx = VCoGx + SGyΩz–SGzΩy (29)

Vsensory = VCoGy + SGzΩx–SGxΩz (30)

Vsensorz = SGxΩy–SgyΩx (31)

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Vsensorx , Vsensory , Vsensorz are measured velocities at the IMU position. Roll rate, pitchrate and yaw rate are represented by Ωx, Ωy and Ωz and the magnitude of the velocityat the CoG is measured by the GPS. The lateral and longitudinal velocity at the CoGare then established with the side-slip estimation.

By assuming that the road is flat, vehicle steering angle and speed is constant andthat the vehicle side-slip is kept to a minimum equations (29)-(31) be simplified. If theprevious sentence holds true, both pitch rate and roll rate Ωy, Ωx can be assumed tobe zero the equations of interest can now be written as:

Vsensorx = VCoGx + SGyΩz (32)

Vsensory = VCoGy–SGxΩz (33)

Re-arranging the equations now gives:

SGy =(Vsensorx–VGPSx)

Ωz

(34)

SGx =−Vsensory + VGPSy

Ωz

(35)

Where Vsensorx and Vsensory are estimated velocities at the IMU locations. The velocitiesat CoG are estimated with VGPSx and VGPSy using the side-slip angle β at the CoG.

VGPSy = VGPS sin β (36)

VGPSy = VGPS sin β (37)

For two displacements are observed separately, one where the sensor is displaced in thelongitudinal axis and another case where the displacement is on the lateral axis.

Lateral Displacement

The constant curve manoeuvre described in the problem definition 1.2 was carried out.Estimations for acceleration at the CoG and IMU position can be made according to:

ax = vx − Ωzvy (38)

ay = vy − Ωzvx (39)

Where ax and ay are longitudinal and lateral acceleration respectively, vx and vy arethe derivative of the longitudinal and lateral velocity respectively and Ωzvy and Ωzvyare centripetal accelerations respectively. Note that migration of roll and pitch centrehave not been taken in to account as height does not affect equations (38)-(39). Otherassumptions for equations (38)-(39) to work is that the steering angles remain the samefor all tires and that the tires are always connected to the ground [34]. Substitute theacceleration ax at the IMU sensor position with IMUaccx and the yaw rate Ωz withIMUΩz for equation (38). The longitudinal velocity can now be described as:

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Vsensorx = IMUaccx + IMUΩzVGPSy (40)

Where Vsensory is the lateral velocity at the IMU sensor location. The lateral velocityis identical at the sensor location and CoG when the longitudinal displacement, SGx iszero, see equation (32). The lateral velocity at the sensor location can thus be describesas:

Vsensory = VGPSy (41)

The longitudinal velocity at the sensor location can then be described as:

Vsensorx = Vsensorx0 +

∫(Vsensorx) (42)

Where Vsensorx0 is given by the initial condition velocity of VGPSx . For determining thelever arm length in the lateral axis, the following tests were carried out:

Physical IMU and GPS test: The GPS antenna was placed on the vehicle roof inlongitudinal and lateral estimated CoG position and the IMU sensor displaced laterallywith -0.5 m and 0 m. The vertical CoG position was estimated to be on the vehiclefloor, the lateral CoG position in the lateral middle of the vehicle and longitudinalCoG and the longitudinal CoG position behind the driver’s seat. The equipment forweighing the vehicle for a proper CoG estimation was not available, therefore the CoGestimation error is unknown. However, the velocity relations between two points in thischapter still holds true if one of the points is not the CoG. The longitudinal velocity ofthe two points was compared and a distance calculated according to equation (34). Theinitial velocity Vsensorx0 was given by the GPS velocity before turning. The distanceestimation started when the yaw rate was larger than 17 deg and changed with anangular rate smaller than 0.8 deg /s and was carried out till the end of the manoeuvre.

Both IMU accelerations and angular rates were filtered with a first order Butterworthfilter, F (s), in the laplace-domain.

F (s) =1

s+ 1(43)

Simulated tests: The same test was made in a vehicle simulation in CarMaker withadded sensor disturbances, as described in 3.2.1. An additional IMU was displaced +0.5m laterally as well as an additional simulated GPS sensor at every IMU location. Theadditional GPS sensor was placed at the IMU location and used to compare velocitiesmeasured at the CoG.

Longitudinal displacement

Estimating a longitudinal displacement requires comparison in lateral velocities. Thelateral velocity in equation (39) can be expressed as:

Vsensory = IMUaccy + IMUΩVGPSy (44)

Where IMUaccy is the measured lateral acceleration from the IMU. The lateral ve-locity at CoG (VGPSy) is used as a purely longitudinally displaced IMU retains same

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longitudinal velocity at CoG, this is evident in equation (33). The lateral velocity isthen:

Vsensory = Vsensory0 +

∫Vsensory (45)

Where the initial velocity Vsensory0 is given by the initial conditions from from VGPSy

at the start of the test. The same physical and simulated tests were carried out inthe same fashion for the longitudinal distance estimation tests but with one crucialdifference, the positions of the IMU sensors. The position of the IMU sensors in thephysical tests were -1.61 m and 0 m in the longitudinal axis. In the simulated tests anadditional An additional IMU is added displaced + 1.61 m as well as GPS sensors atevery IMU location. An illustration of IMU placements on the vehicle (not in of scalefor clarity) is seen in Figure 8. Note that the simulated IMUs are shown as well andthat the CoG refers to the vehicles centre of gravity when loaded and stationary.

Figure 8: Illustration of the IMU positions on the vehicle

3.2.1 Sensor simulationBoth the GPS and IMU sensor were simulated in Matlab after collecting physicalsensor data from the IMU. The accelerometer and gyroscope where both modeled withan added bias and a generated white noise to the measured acceleration and angularrotational rate Accbody,Gyrobody:

Accsensor = bacc + Accnoise + Accbody

Gyrosensor = brot +Gyronoise +Gyrobody(46)

Where Accsensor is the measured acceleration vector in the sensor frame and Gyrosensormeasured rotational velocity in the same frame. The noise, Accnoise and Gyronoise, weremodeled as Gaussian white noise with the standard deviation of [0.056, 0.053, 0.055]°/sand [0.013, 0.01, 0.016] respectively in the x, y and z axis.

The bias for the angular rate was expressed as [0.051, 0.05, 0.052] in °/s and the ac-celeration bias as [0.002, 0.007, 0.001] m/s2. However, the biases bacc and brot wereconsidered constant as the test time is shorter than the time constants for the IMUbias drifting and are therefore removed (it is assumed that the biased is identified andremoved in the installation process).

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The GPS speed and heading angle was modeled with an added white noise with thestandard deviation 0.0667 m/s and 1° respectively. The true accelerations, rotationalrates and velocities at the sensor locations and CoG were all imported directly fromCarMaker where they were treated as readings from perfect sensors at the specifiedpoints on the vehicle.

3.2.2 Side-slip estimationThe vehicle’s side-slip could be calculated with the use of a single GPS receiver andIMU. First a suitable reference system was established in relation to the velocity’sdirection from the GPS. This can be done by driving the vehicle straight forward,meaning that the GPS velocity heading will be aligned with the reference axis X, seeFigure 9.

Figure 9: Relationship between side-slip, yaw rate and heading angle as described in[23]

..

The yaw angle, Ψ, is established by integrating the yaw rate, Ωz. Any differencebetween heading angle from the reference (this is refered to as angle as α) system andvehicle yaw are then attributed to the side-slip angle:

β = α− Ψ (47)

With the lack of modeling and external sensors this is the most viable way to estimateside-slip with a single GPS antenna and IMU since the gyroscope reads the same yawrate regardless where it is placed on the vehicle. Note however that only the side-slipat the CoG, where the GPS antenna is placed will be calculated and the side-slip at theIMU is location unknown. An issue with with this method is that it is heavily relianton the number of available satellites and can output intolerable errors [23] that canlead to unreasonable side-slip angles. Furthermore the GPS sample frequency is 1 Hz,limiting the availability of the vehicle heading. This could be less of a problem duringthe constant curve case as the side-slip is almost constant. However, integrating overthe yawrate signal can result in significant errors.

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4 Results and discussion

This sections presents the results and discussion.

4.1 Crash detection and recording

This section presents the results and analysis of the experimental tests regarding thevehicle position estimation, crash detection and recording.

Three tests were performed in order to analyse both the vehicle position and the amountof false positive errors. The tests were done by placing the sensor device in the middleof a vehicle and letting it log data during the entire drive. Data from the sensor devicewas extracted and post-processed in MATLAB to estimate the position of the vehicleas well as determining the amount of false positive errors.

The crash detection algorithm did not take the device’s displacement relative to theCoG of the vehicle into account. Since only frontal crashes were considered, this hada small impact on the results as described in section 2.4.

The main manoeuvres that were performed in the three tests can be seen in Table1. Where firm braking was when the driver applied the brakes in such a way thatthe vehicle stopped slowly but firmly. Harsh braking was defined as when the driverapplied the brakes as hard as possible without the risk of losing control or damagingthe vehicle.

Table 1: Main manoeuvres in the test drives for state estimation and crash detection.

Test Main manoeuvres

1 Roundabouts and firm braking.2 Roundabouts and firm braking.3 Harsh braking

4.1.1 Vehicle position estimationAs mentioned in section 3.1.3, a Kalman filter was used to estimate the position andthe velocity of the vehicle. The position estimation of Test 1 can be seen in Figure 10.The estimated route corresponded well with the actual route taken, which indicatedthat there was no drift in estimated position over time.

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Figure 10: Position estimation of Test 1 using Kalman filter.

Three sections showing a straight section, a curve and a roundabout can be seen inFigures 11-13, respectively. In the straight section there were barely any overlap orgaps but in the curve and roundabouts some can be seen. However, the largest gapsin position estimation using Kalman filter was in the order of one metre and thereforesuperior than position estimation using solely GPS signals.

Figure 11: Close-up of a straight section from Test 1.

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Figure 12: Close-up of a curve from Test 2.

Figure 13: Close-up of a roundabout from Test 3.

There are discrepancies between the GPS-signal and estimated position right beforethe signal was retrieved. This is because the GPS as well the IMU will have measure-ment errors. Therefore, it is not possible to get the estimated position and measuredGPS-position to perfectly coincide no matter how good the filter is. A reason forthe discrepancies, can be due to bad GPS-signal which in turn can be caused by tallbuildings or driving through a tunnel.

The error between the last estimated position before the GPS-signal arrived and themeasured GPS-position was analysed and the error distribution from Test 2 can beseen in Figure 14. There are no obvious tendencies in the error distribution, in otherwords, in longitudinal position error does not indicate anything about the latitudinalposition error. The mean error for each test can be seen in Table 2.

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Figure 14: Error distribution from Test 2.

Table 2: Mean error for the various tests.

Test Mean error [cm]

1 9.62 3.53 3.2

Even if the mean error is low, the estimated position might be bad if the absolute erroris large. Therefore, the absolute error was analysed in terms of how many percent ofthe estimated data points that were within a certain distance from their respectiveGPS-positions, defined as estimation accuracy in this case. As can be seen in Figure15, the estimated position was superior to just using the GPS-signal. The estimationaccuracy for the cases with GPS only was taken as distance between two GPS-positions.This can be thought of as a sort of worst case scenario since if one wants to know theposition right before a new GPS-signal, one might use the previous position. In Table3 the estimation accuracy for 50% and 90% of the time for the three different tests arepresented.

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Figure 15: Estimation accuracy for the respective tests.

Table 3: Estimation accuracy for 50% and 90% of the time.

Estimation accuracy Estimation accuracyfor 50% of the time [m] for 90% of the time [m]

Estimation Test 1 0.79 2.6Estimation Test 2 0.93 2.2Estimation Test 3 1.1 3.0GPS only Test 1 8.5 13GPS only Test 2 7.7 12GPS only Test 3 9.5 18

To put this into comparison with the study [5], they had an estimation accuracy of 2m for 50% of the time. The estimation accuracy presented in this thesis is lower thanthat. However, the terrain that the vehicle was driven in varied significantly betweenthese two studies. Their study was set in an urban region with high-rise buildings andoverpasses while the tests in this thesis were performed where GPS-signals were notsignificantly obstructed. They also estimated the error in a different way. Therefore, itis not possible to say that the results in this thesis is superior to theirs, but they are,at the very least, comparable.

These results show that the position estimation algorithm is sufficient to be used forcrash detection.

4.1.2 Crash detectionThe device is triggered for crash detection when the acceleration and velocity differenceexceeds certain thresholds, as described in section 3.1.4. Due to different paths takenand different driving behaviour in the different test drives, the amount of false positiveerrors per hour varies between the test drives. In Test 3, there were one harsh brakingfrom 40km/h while the other two tests did not include as harsh stops. All tests didhowever include multiple of roundabouts and moderate deaccelerations. In Test 3 thereare false positive errors all the way up until the acceleration threshold reaches roughly3.5g. In Test 1 and 2, the false positive errors reached zero well before an accelerationthreshold of 1g. The amount of false positive errors for Test 1-3 can be seen in Figures16-18, respectively.

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Figure 16: Plot of the amount of false positive errors for different acceleration and ∆Vthresholds of Test 1.

Figure 17: Plot of the amount of false positive errors for different acceleration and ∆Vthresholds of Test 2.

Figure 18: Plot of the amount of false positive errors for different acceleration and ∆Vthresholds of Test 3.

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For certain acceleration thresholds intervals, the amount of false positive errors in-creased as the acceleration threshold increased. Since the crash detection algorithm istriggered when the measured acceleration and velocity difference exceed the threshold,multiple crashes will be detected when the measured acceleration oscillated around thethreshold. This could happen if the vehicle is subjected to constant acceleration. Onone hand, if a lower threshold was used, only one crash would be detected since thesystem would consider the event to be still be ongoing. On the other hand, if a higherthreshold was used, no crashes would be detected since the measured acceleration wouldnever reach the threshold.

The amount of false positive errors in Test 1 and 2 as well as the first part of Test 3suggest that there will be no false positive errors in normal driving if the accelerationthresholds is set to 1 g. Due to harsh braking in Test 3, there are some false positiveerrors above 1 g. This is still a false positive error but was not considered to be normaldriving behaviour. However, sometimes it is necessary to perform one of these harshstops due to some unpredictable event. Therefore, the acceleration threshold shouldbe set to something greater than 1 g. Depending on the choice of ∆V threshold, theacceleration threshold can be chosen differently. With a higher ∆V threshold, a loweracceleration threshold can be chosen to prevent false positive errors. On one hand, ifone chooses a high ∆V threshold, one might not be able to detect severe crashes thatoccur at low velocities. If one would be hit while standing still, one might not reach thenecessary velocity required to trigger the detection. On the other hand, if one choosesa low ∆V threshold, more false positive errors will occur as can be seen in Figure 18.

There is always a trade-off between false positives and false negative errors. Sometimes,devices simply ignore positive results in order to reduce the amount of false positiveserrors. This can obviously increase the amount of false negative errors which happenedin one of Uber’s self-driving cars[35]. One way to reduce the amount of false positivesis to incorporate more sensors in to the detection algorithm. In the study [10], theauthors used microphone in order to measure the sound level. During a crash, thesound levels reach high values, especially in a high speed crash where the airbag isdeployed. The authors also had a function where a video was recorded right after thecrash event. This video was then forwarded to human who determined if it was a falsepositive or not. However, this involved human interactions.

4.1.3 Crash recordingThe crash recording reconstruction gave acceptable results. The idea of the reconstruc-tion is to prove that it is feasible to reconstruct the event. This thesis does not howeverfocus on this and therefore the presented reconstruction is sufficient. The result canbe seen in Figure 19. In the middle column of Figure 19 the z-axis is visible, whichproves the device was tilting to the side about either the x- and/or y-axis. The tiltingpart was due to the collision with the obstacle, which made the device to tilt on to theside.

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Figure 19: Reconstruction of a crash test. The pictures above are taken from a videoof the event while the pictures below are taken from the reconstruction.

The result from the crash recording is as mentioned sufficient since it shows the maincharacteristics of the event. One might argue that the yaw angle might not be veryaccurate. However, an explanation to this might be that the frames correspond to twoslightly different times. Another reason for this might be that the camera was notperfectly positioned. The linear distance which the device travels might not seem tomatch in the pictures but this is due to different scaling of the pictures.

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4.2 Sensor to vehicle placement

This section describes the physical and simulated test results regarding the sensor-to-vehicle position estimation. The distance between the sensor device and the GPSantenna (CoG) as shown in Figure 8 was estimated using a turning manoeuvre wherethe driver tried to keep a constant velocity, 20km/h, and a constant steering wheelangle after driving straight.

The data from three physical tests manoeuvres, as described above, were analysed, eachwith a different IMU displacement from an estimated point (CoG) in the vehicle. Thelogged sensor data was than extracted and used for distance estimation in MATLAB.The displacement in each test can be viewed in Table 4.

Table 4: Distance from estimated CoG at each IMU during physical tests.

IMU number Lateral distance [m] Longitudinal distance [m]IMU 0 0 0IMU 1 -0.5 0IMU 4 0 -1.63

Using the vehicle simulation program CarMaker, a generic lightweight car performed asimilar constant turning manoeuvre after a straight drive. The vehicle simulator wasused to pinpoint the car CoG position. The accelerations, velocities, and angular ratesduring the manouver at the CoG and four additional different points in the vehicle werelogged and exported to MATLAB. MATLAB was then used to simulate five differentIMU and GPS sensors at each of the previously mentioned positions. The distancebetween the GPS sensor placed at the CoG and the IMU sensors was than estimated.The IMU displacements in the simulated tests are presented in Table 5.

Table 5: Distance from CoG at each IMU during simulated tests.

IMU number Lateral distance [m] Longitudinal distance [m]IMU 0 0 0IMU 1 -0.5 0IMU 2 0.5 0IMU 3 0 1.61IMU 4 0 -1.61

In addition to the physical test, the distance between the GPS sensor placed at CoGand another GPS with the same placement as the IMU sensor was estimated.

4.2.1 Physical testsThe sensor-box was installed by strapping it on inside the vehicle with the GPS antennaplaced on the vehicle roof. The orientation of the sensor device was manually alignedwith the vehicle frame. To remove any accelerations caused by the device being tiltedand the sensor bias the average acceleration in the y, x, z were removed (with theexception of the gravity constant in the z axis). The accelerations after the installationprocess can be seen to stay constant around the expected values of zero and 9.82 m/sin Figure 20.

The vehicle angular rate at each physical test, were the name is based on IMU po-sition, is shown in Figure 21. A negative yaw rate is first observed upon entry tothe roundabout followed by an an increase when the driver turns left and finally anoscillating yaw rate when the driver is trying to keep a constant steering wheel angle.While the manoeuvre was performed in the same roundabout the yaw rate varies ineach test. This is due to driver skill, traffic and entry turn into the roundabout. Thisis more notable when comparing the yaw rate measured at the test for IMU 1 where

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Figure 20: Accelerations (m/s2) after installation and calibration.

the constant yaw rate is 10 deg /s higher and oscillating more violently than the yawrates measured during the tests for IMU 1 and IMU 4.

Figure 21: Vehicle angular rate (°/s) at physical tests.

Furthermore, despite the small pitch and roll rates in Figure 21, notable constantaccelerations errors are still likely to occur. If the recorded attitude from the sensordevice differ from the true vehicle attitude or the road is not flat, large accelerationsare recorded by the IMU due to the gravity component. Over longer periods of time,

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these accelerations result in large errors in the velocity estimation.

The estimated longitudinal velocity at the CoG using equation (36) and the sensorlocation using equation (42) at the test for IMU 0 and IMU 1 are presented in Figure22. The estimated longitudinal velocity when the vehicle enters the constant turningphase can be seen to oscillate between 1 - 2 m which is severely higher than the expectedvalue. Furthermore, the velocity at the CoG during the constant turning was lowerthan the expected value of around 20 km/h or 5 - 6 m/s. The estimated longitudinalvelocities are even far worse off. At the test for IMU 0 the velocity difference betweenCoG and sensor is larger than 1 m, which is already larger than what is expected,and then continues to grow. The longitudinal velocity estimation at IMU 0 is clearlyerroneous is it rapidly decreases and becomes negative. The same can be observed atIMU 1, however the velocity difference between estimated longitudinal velocity at CoGand sensor is positive as the estimated velocity at the sensor location is increasing.

Figure 22: Longitudinal velocity (m/s) at CoG and laterally displaced IMU sensors.

Similarly, the lateral velocities estimated at the CoG, using equation (37), and sensorlocation (45) are compared in Figure 23. The estimated lateral at the CoG for IMUoscillates around 2-4m/s during constant turning in the roundabout, which is unrea-sonably high due to the dry road conditions. At the test for IMU 4 the estimatedlateral velocity oscillates around a smaller velocity, 2-3 m/s but is still too large. Theestimated lateral velocity at the test for IMU 0 and IMU 4 show a similar behaviour to

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each other, they increase rapidly over time. Due to this increase the lateral velocitiesat the tests for IMU 0 and IMU 4 become highly unrealistic (larger than 2m/s) beforethe vehicle enters the constant turning phase.

Figure 23: Lateral velocity (m/s) at CoG and laterally displaced IMU sensors.

One source of error for the high unlikely estimated velocities is the side-slip. The side-slip, after being fed through an averaging filter (smoothed) to avoid sharp oscillations,for all IMU test can be viewed in Figure 24 and show that it is certainly so. Theside-slip estimation at each and every IMU test is substantially larger than what isexpected. Under normal driving conditions on a dry road the side-slip in a roundaboutcan be expected to be under 10 deg. The presented side-slips in Figure are all over 20deg. The side-slip does however seem to follow the general expected trend, negativeside-slip when turning into the roundabout, increasing as the driver turns and thanstaying constant with some oscillations as the driver tries to keep a constant steeringwheel angle.

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Figure 24: Estimated side-slip (°).

The vehicle is considered to have entered the state of constant turning when the yawrate is larger than 17° and constant (changes with a rate smaller than 0.8°/s). Thedistance estimation equations (34) and (35) were then applied. The average distanceand standard deviation during the full constant turning manoeuvre (10s) and 1 s afterentry is presented in Table 6.

Table 6: Distance estimation [m] between IMU sensor and CoG during full and short-ened constant turning manoeuvre.

True lateral distance [m]0.5

(IMU 1)0

(IMU 0)Estimated average

lateral distance [m], standard deviation [m]Complete manoeuvre (10s after entry) 11.6, 1.93 -14.7, 2.38Shortened manoeuvre (1s after entry) 9.22, 0.77 5.39, 0.60

True Longitudinal distance [m]1.61

(IMU 3)0

(IMU 0)Estimated average

lateral distance [m], standard deviation [m]Complete manoeuvre(10s after entry) 41.9, 10.4 9.44, 2.65Shortened manoeuvre (1s after entry) 24.6, 2.5 -10, 3.6

The distance estimation cannot be used for sensor compensation during crash record-ing as it is too inaccurate. Whether this is caused by the large side-slip, angularmisalignment or the road not being completely flat cannot be discerned as all theseerror sources are unobservable. They are all, however, substantially larger than thesensor noise. The recorded GPS velocity for each case can be viewed in Appendix A.

Furthermore, using the distance estimation for any kind of sensor-to-vehicle compensa-

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tion for position estimation or velocity estimation is not feasible due to the large errorsvelocity estimations at the sensor location as shown by Figure 22 and Figure 23.

4.2.2 Simulated testsA generic lightweight car was used for modeling the vehicle used in the simulation. Aconstant curve test was carried out where the simulated driver tried to keep a constantsteering wheel angle of 180° and constant velocity of 20 km/h. The steering wheelangle is displayed in Figure 25.

Figure 25: Steering wheel angle (°) during manoeuvre.

Small deviations can be observed from 180° as keeping both a constant steering angleand constant velocity is problematic. The steering angle does however not differentiatefrom 3° from the set value, which is perhaps more than can be asked from a real driver.The driving manoeuvre was carried out on a flat road in a roundabout with a radius of15m. To calculate the distance between GPS receiver at CoG and the sensors location,as described in (34) and (35), the vehicle roll rate and pitch rate must be low duringthe manoeuvre, which is evident in Figure 26.

Figure 26: Vehicle attitude rate (°/s).

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For calculating the lateral displacement from CoG the longitudinal velocities at thesensor position and CoG needs to be estimated. The velocity difference between thelongitudinal velocity at CoG , estimated IMU velocity Vsensorx and estimated longitu-dinal GPS velocity VGPSx are presented in Figure 27.

Figure 27: Longitudinal velocity (m/s) at CoG and laterally displaced IMU sensors.

The estimated longitudinal GPS velocity, VGPSx , follows the expected behavior relativeto the CoG velocity. The estimated velocity using the IMU, Vsensorx , does not. A largevelocity error can be observed in every case and appears to be consistent regardless oflocation. Indeed, this is more clear in the error graphs for Vsensorx and VGPSx in Figure28.

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Figure 28: Estimated longitudinal velocity errors (m/s) for lateral displacement.

For calculating the longitudinal displacement, the lateral velocities at CoG and sensorposition are compared. The velocity difference between the lateral velocity at CoG,estimated IMU velocity, Vsensory , and estimated GPS velocity, VGPSy , can be viewedin Figure 29. Note that Vsensory grows increasingly larger after the vehicle enters thestate of constant turning.

Figure 29: Lateral velocity (m/s) at CoG and longitudinally displaced IMU sensors.

The error for simulated Vsensory and VGPSy is shown in Figure 30. Similarly to the CoGand longitudinal velocity comparisons, the GPS velocity gives expected results whilst

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the velocity estimated with the IMU accelerometer has a consistent error. Thus notallowing its relation to the velocity at CoG to be discerned.

Figure 30: Estimated lateral velocity errors (m/s) for lateral displacement.

The vehicle was considered to have entered the state of constant turning when the yawrate is larger than 17 deg and constant (changes with a rate smaller than 0.8 deg /s,which happens at around the 24 s mark. Equation (34) and (35) were then applieduntil the end of the manoeuvre. The average error, standard deviation and effects ofestimated initial velocities can be observed in Table 7.

Table 7: Distance estimation [m] between IMU sensor and CoG during full constantturning manoeuvre.

True lateral distance [m]

Single GPS receiver at CoG0.5

(IMU 2)0

(IMU 0)-0.5

(IMU 1)

Initial velocities [m/s]Estimated average lateral distance [m],

standard deviation [m]Vx0 =Vx0 -0.64, 0.27 -1.24, 0.27 -1.84, 0.26Vx0 = Vx0+.1 m/s -0.39, 0.27 -0.99, 0.27 -1.59, 0.26Vx0= Vx0 - 0.1 m/s -0.89, 0.27 -1.49, 0.27 -2.09, 0.26Additional GPS receiverat IMU location

0.60, 0.01 0.31, 0.03 -0.60, 0.01

True longitudinal distance [m]

Single GPS receiver at CoG1.61

(IMU 3)0

(IMU 0)-1.61

(IMU 4)

Initial velocities [m/s]Estimated average lateral distance [m],

standard deviation [m]Vy0 = Vy0 -0.67, 0.7 -0.97, 0.7 -2.6, 0.7Vy0 = Vy0+0.1 m/s -0.43, 0.7 -1.22, 0.7 -2.9, 0.7Vy0= Vy0 - 0.1 m/s -0.92, 0.7 -0.72, 0.7 -2.3, 0.7Additional GPS receiverat IMU location

1.63, 0.02 -0.02, 0.04 -1.63, 0.02

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In both the longitudinal and lateral placement estimations, a substantial error can beobserved and with a high standard deviation, larger than the accepted value of 0.1 mwhen using Vsensory and Vsensorx (single GPS receiver). Another problem was the initialvalues effect on the end result as it was larger than the allowed error. The requirementswere not fulfilled and were worse than current sensor-to-vehicle position estimations.With an additional GPS the requirement is still not met for laterally displaced IMUs.The longitudinal position estimations however, show promise as the requirement wasmet. It is important to note that the requirement was only met during ideal conditionsdue to the nature of the simulation.

The road was completely flat, the driver can keep both the steering angle and velocityconstant almost perfectly, the side-slip and side-slip error was small and the sensor boxwas perfectly aligned with the vehicle frame. These factors are unreasonable to expectin reality, the double GPS solution does therefore need real physical tests.

As the estimated IMU velocity error increased over time, shortening the manoeuvrewill give better results. In Table 8 the time window has been shortened to one secondafter entering the constant turning state.

Table 8: Distance estimation [m] between IMU sensor and CoG during the shortenedconstant turning manoeuvre

True lateral distance [m]

Single GPS receiver at CoG0.5

(IMU 2)0

(IMU 0)-0.5

(IMU 1)

Initial velocities [m/s]Estimated average lateral distance [m],

standard deviation [m]Vx0 =Vx0 -0.37, 0.04 -0.97, 0.04 -1.57, 0.04Vx0 = Vx0+ 0.1 m/s 0.12, 0.04 0.72, 0.04 -1.32, 0.04Vx0= Vx0 - 0.1 m/s -0.61, 0.04 -1.21, 0.04 -1.82, 0.04

True longitudinal distance [m]

Single GPS receiver at CoG1.61

(IMU 3)0

(IMU 0)-1.61

(IMU 4)

Initial velocities [m/s]Estimated average lateral distance [m],

standard deviation [m]Vy0 =Vy0 1.90, 0.08 0.26, 0.08 -1.39, 0.08Vy0 = Vy0+0.1 m/s 1.66, 0.08 0.02, 0.08 -1.63, 0.08Vy0= Vy0 - 0.1 m/s -0.92, 0.08 -0.72, 0.08 -1.14 0.08

The lateral distance does still not give any usable information when using a singleGPS receiver, however, the longitudinal distance estimation is greatly improved butstill fails the requirement for the use of crash recording.

Using perfect sensors without added noise or bias the estimated lateral and longitudinalvelocity was compared to the real velocity Vrealx and Vrealy in same axis. The errorsproduced are respectively called Vex and Vey in equation (48) and (49).

Vex = Vrealx − Vsensorx (48)

Vey = Vrealy − Vsensory (49)

The longitudinal velocity error Vex and lateral velocity error Vey are plotted for the fullduration of the test in Figure 31.

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Figure 31: Longitudinal and lateral velocity (m/s) error due to modeling over time atCoG.

By reviewing the base equation for the velocity estimation at the sensor location,equation (40) and equation (44), the error trend can be explained. When the velocitiesand yaw rate are correct the error is bound to come from the acceleration. While theequations hold for estimating lateral and longitudinal acceleration for vehicle modeling(the error is small) [34] it is not suited to be used for vehicle velocity estimation,especially with the margin of error needed for sensor-to-vehicle estimation. Both thelateral and longitudinal acceleration error lead to large errors in estimated vehiclevelocity; the rotation of the IMU position causes a false read of acceleration due togravity that does not coincide with the actual acceleration due to rotation around theroll and pitch centre. Over time this difference become more pronounced and causesthe IMU measured velocity Vsensorx and Vsensory to diverge. Other possible sources oferror might exist but are not of interest since vehicle modeling is not the focus of thisthesis. The error was similar at all the IMU positions.

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5 Conclusion

A device was constructed, which could estimate position and velocity of a vehicle usinga Kalman filter. It was also able to detect frontal crashes by looking at measuredaccelerations and velocity differences in a time period of 100 ms.

The position estimation had an estimation accuracy between 0.8-1.1 m half of the timeand 2.6-3 m 90% of the time for the different tests. The mean errors for the tests werein the order of centimetres which means that the estimation algorithm did most likelynot have a systematic error.

For crash detection, an acceleration threshold of 1g could be utilised to remove mostfalse positive errors in normal driving behaviour. However, harsh manoeuvres couldstill trigger the crash detection and therefore greater thresholds would have to beutilised if no false positive errors are allowed. This might lead to the device failing indetecting a crash (false negative error) which is not desired, especially in applicationswhere the main purpose is to log data during the entire crash. For such an application,the mentioned acceleration threshold of 1g could be used.

The amount of false positive errors was reduced when a larger value of ∆V thresholdwas used. As mentioned in section 4.1.2, a larger ∆V threshold might lead to anundetected crash if the vehicle was stationary. Therefore, if the areas of interest includecollisions including stationary vehicles, a lower ∆V threshold should be considered. Theamount of false positive errors can be further reduced by adding more sensors, such asmicrophones[10] and cameras.

The physical tests suffered large distance estimations as seen in Table 6, which can beexplained by unreasonably large side-slip estimations. Other error sources are possiblemisalignments of sensor frame to vehicle frame and sensor noise, both which are smallwhen compared to any angular misalignment in roll and pitch due to the gravity com-ponent. As both the true side-slip and road angle were unobservable in the tests, noclear conclusion can be taken to why the physical estimations differ so heavily fromthe simulated tests. Note that both the measured accelerations and yaw rate from theIMU needed to be integrated which causes larger errors as well.

The simulated velocity comparisons when using only one GPS (the same setup as thephysical tests) showed similar results. The velocities estimated at the sensor locationdeviate far too much from the real velocities as seen in Figure 28 and Figure 30.Subsequently the sensor-to-vehicle distance estimations become too unreliable, neitherestimated distance for longitudinally displaced sensors or laterally displaced sensors areclose enough to be used for crash recording. This can be seen in Table 7, were both thedistance errors and standard deviation are larger than 0.1 m. As the error grows overtime it was of interest to shorten the time during which the sensor-to-vehicle estimationwas active. While doing so showed improved results the errors in estimated sensorto vehicle distances were still too large as seen in Table 8. However, when using anadditional GPS at the sensor location the simulated results improved even further. Thedistance when the sensor was displaced purely in the longitudinal axis was estimated toa satisfactory degree for three different distances shown in Table 7, where one was zero.Thus establishing that the distance estimation works for smaller longitudinal distances.The results for lateral distance estimations however proved to be more problematic asthe error for estimated distance were larger and did not meet the requirement of an amaximal error 0.1 m at all positions. Note however that the tests was made under idealsimulated conditions and that the simulated results are better than can be expectedin the real world. Furthermore, the constant turn case is troublesome in itself. Thestarting velocity has to be discerned accurately as it effects the end result, see Table 3and Table 4. This could be remedied by repeating the manoeuvre multiple times but

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the error would still be too large as the estimated distance differ greatly from the truedistance. Another issue with the proposed methodology is changed load distribution,road angle or other instances where the lateral and longitudinal position of the CoGis significantly changed. The GPS sensor position is assumed to be at the CoG anddisplacement errors from CoG to GPS sensor would therefore directly affect the endresult on the circle of constant acceleration described in 2.4.

The physical and simulated results are worse than current solutions for lever armestimations (the distance between IMU and GPS). In one example the longitudinal,lateral and vertical distance of 1 m was asserted with a standard deviation error smallerthan 0.01m in each axis [28] however, the equipment used for estimating the lever armdistance was more expensive and multiple GPS sensors were used. Compared to theestimated average distances and standard deviations in Table 6 and 7, the resultsare far off. One study in sensor-to-vehicle estimation [11] using a grid of inexpensivesensors (one GPS and IMU in each position) but with access to more computing powerhad the root-mean square error of 0.5m, which neither the physical nor the one GPSsimulated results could match, see the average error and standard deviation in Table 6and Table 7. The simulated solution with an additional GPS sensor in Table 7 howeverhad better results with an error smaller than 0.11m and standard deviations of 0.01– 0.04 m. These results however were acquired under perfect conditions and are notlikely to be mirrored in physical tests results.

To conclude, the sensor-to-vehicle position estimation was found to not be viable whenonly using one IMU sensor and one GPS sensor placed at CoG in both simulatedand real tests. Even if many of the problems in the physical world were solved (IMUmisalignment in particular) the method is flawed and will not give accurate enoughvelocity estimations under ideal circumstances as shown in Figure 31. In the simulatedtests the sensor-to-vehicle estimation was found satisfactory when an additional GPSwas placed at the sensor location and the device was displaced purely in the longitudinalaxis. When the sensor was displaced laterally under the same conditions this was notthe case.

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6 Future work

It would be a good idea to add a magnetometer to the device to be able to always knowthe relation to the magnetic field. This would improve both the Kalman estimationof position and velocity, crash reconstruction as well as the sensor-to-vehicle positionestimation. However, other external magnetic fields, such as those from electricalcomponents or permanent magnets, might interfere with the magnetometer.

Crash reconstruction could be improved to reconstruct more advanced crashes whichinvolves time segments where the vehicle is airborne. The crash reconstruction couldalso be improved to include deformation of the vehicle.

Better filters for the accelerations and rotations from the IMU could be implementedas the basic Butterworth filter used for the physical tests is rudimentary when testingthe sensor-to-vehicle position estimation. The same manoeuvre could be repeated butwith fully observable reference values for side-slip, velocities and rotation at the IMUposition, preferably with multiple IMU sensors as the same manoeuvre cannot be madetwice reliably. The issues with modeling would still exist but the errors dependenton modeling and the errors dependent on the sensors would be more clear for thenew physical tests. The double GPS setup, showed promise in simulations and wouldtherefore be interesting to investigate through real tests.

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Appendix A: GPS velocities during physical tests

The raw GPS velocities during physical tests. Note that the velocity of the vehiclecould not be kept constant during the full turning manoeuvre.

Figure 32: GPS velocity [m/s] at IMU 0.

Figure 33: GPS velocity [m/s] at IMU 1.

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Figure 34: GPS velocity [m/s] at IMU 4.

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