Indoor Positioning Using Angle of Departure Information874882/FULLTEXT01.pdf · 2.1...

Department of Science and Technology Institutionen för teknik och naturvetenskap Linköping University Linköpings universitet

gnipökrroN 47 106 nedewS ,gnipökrroN 47 106-ES

LiU-ITN-TEK-A--15/061--SE

Indoor Positioning Using Angleof Departure Information

Erica Gunhardson

2015-10-01

LiU-ITN-TEK-A--15/061--SE

Indoor Positioning Using Angleof Departure Information

Examensarbete utfört i Elektroteknikvid Tekniska högskolan vid

Linköpings universitet

Erica Gunhardson

Handledare Adriana SerbanExaminator Qin-Zhong Ye

Norrköping 2015-10-01

Upphovsrätt

Detta dokument hålls tillgängligt på Internet – eller dess framtida ersättare –under en längre tid från publiceringsdatum under förutsättning att inga extra-ordinära omständigheter uppstår.

Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner,skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat förickekommersiell forskning och för undervisning. Överföring av upphovsrättenvid en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning avdokumentet kräver upphovsmannens medgivande. För att garantera äktheten,säkerheten och tillgängligheten finns det lösningar av teknisk och administrativart.

Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman iden omfattning som god sed kräver vid användning av dokumentet på ovanbeskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådanform eller i sådant sammanhang som är kränkande för upphovsmannens litteräraeller konstnärliga anseende eller egenart.

För ytterligare information om Linköping University Electronic Press seförlagets hemsida http://www.ep.liu.se/

Copyright

The publishers will keep this document online on the Internet - or its possiblereplacement - for a considerable time from the date of publication barringexceptional circumstances.

The online availability of the document implies a permanent permission foranyone to read, to download, to print out single copies for your own use and touse it unchanged for any non-commercial research and educational purpose.Subsequent transfers of copyright cannot revoke this permission. All other usesof the document are conditional on the consent of the copyright owner. Thepublisher has taken technical and administrative measures to assure authenticity,security and accessibility.

According to intellectual property law the author has the right to bementioned when his/her work is accessed as described above and to be protectedagainst infringement.

For additional information about the Linköping University Electronic Pressand its procedures for publication and for assurance of document integrity,please refer to its WWW home page: http://www.ep.liu.se/

© Erica Gunhardson

Sammanfattning

I detta examensarbete undersöks möjligheten att kunna använda en positione-ringsmetod som inte enbart förlitar sig på den uppmätta signalstyrkan. Iställetanvänds en metod som bestämmer från vilken vinkel en signal uppkommer ifrån.Den här tekniken kallas för direction-finding. När informationen om signalensvinkel fastställts används den i ett positioningsfilter som uppskattar positionen.Två tillvägagångssätt har använts i den här rapporten, ett där enbart vinkeln an-vänds och ett där både signalstyrka och vinkel används.

Simuleringar där direction-finding algoritmen tillsammans med positionerings-filtret har använts, visar goda resultat. Verklig data behövs för att vidare kunnaanalysera prestandan hos det framtagna positioneringssystemet.

1

Abstract

This master thesis investigates the possibility to use an indoor positioning ap-proach that does not completely rely on the strength of the received signal. In-stead, information from what angle the incoming signal originates is utilized.This technique is called direction-finding. When the angle information is deter-mined, it is used in a position filter. Two approaches for the estimation filter hasbeen conducted, one which relies only on the angle information and one that re-lies both on the received signal strength and the angle information.

Simulations using the direction-finding algorithm together with the estimationfilter generates promising results. Real data are required to further analyze theperformance of the positioning system proposed in this thesis.

3

Acknowledgments

I would like to thank my supervisor at SenionLab, David Törnqvist, for his con-stant support in my work. I would like to thank Per Skoglar from SenionLab forgreat input along the course of the project.

I would also like to give a special thank you to my supervisor at Linköping Uni-versity, Adriana Serban, for her valuable insights, guidance and encouragement.

Another special thank you to Johan Gustafsson who never stops believing in meand supports me no matter what.

Erica GunhardsonLinköping, June 2015

5

Contents

Notation 9

1 Introduction 11.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Direction-Finding Theory 52.1 Direction-Finding Techniques . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Watson-Watt Method . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Doppler Method . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Antenna Constellations . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Direction-Finding Algorithm 113.1 MUSIC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.1 Uniform Linear Array . . . . . . . . . . . . . . . . . . . . . 123.1.2 Single Source Model . . . . . . . . . . . . . . . . . . . . . . 133.1.3 General Model . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 M:1 MUSIC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.1 Uniform Linear Array . . . . . . . . . . . . . . . . . . . . . 183.2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Direction-Finding Simulations 234.1 Algorithm Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Simulation with Pre-Determined Parameters . . . . . . . . . . . . . 234.3 Number of Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 Antenna Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.5 Number of Transmitting Antennas . . . . . . . . . . . . . . . . . . 264.6 Noise Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

7

8 Contents

5 Localization Background 295.1 Bearing-Range Localization . . . . . . . . . . . . . . . . . . . . . . 295.2 Bearing-Only Localization . . . . . . . . . . . . . . . . . . . . . . . 295.3 Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 Localization Simulations 336.1 Setup Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.2 Bearing-Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6.2.1 Bearing-Range Model . . . . . . . . . . . . . . . . . . . . . . 366.2.2 Bearing-Range Simulations . . . . . . . . . . . . . . . . . . 38

6.3 Bearing-Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.3.1 Bearing-Only Model . . . . . . . . . . . . . . . . . . . . . . 426.3.2 Bearing-Only Simulations . . . . . . . . . . . . . . . . . . . 44

6.4 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . 486.4.1 Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.4.2 Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7 Positioning Tag 537.1 Microprocessor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557.2 Sensor Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.2.1 Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . . . 567.2.2 Gyroscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587.2.3 Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . 607.2.4 Pressure Sensor . . . . . . . . . . . . . . . . . . . . . . . . . 627.2.5 Multi sensor solution . . . . . . . . . . . . . . . . . . . . . . 64

8 Conclusion and Future Work 678.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Bibliography 69

Notation

Abbreviations

Abbreviation Description

aoa Angle-of-Arrivalaod Angle-of-Departureble Bluetooth Low Energydf Direction Findingekf Extended Kalman Filteresprit Estimation Parameters via Rotational Invariance Tech-

niquegps Global Positioning Systemips Indoor Positioning Systemkf Kalman Filtermcu MCUmems Micro Electro Mechanical Sensormimo Multiple Input Multiple Outputmiso Multiple Input Single Outputmusic Multiple Signal Classificationod Output Dataodr Output Data Raterf Radio Frequencyrssi Received Signal Strength Indicatorsimo Single Input Multiple Outputsiso Single Input Multiple Outputsnr Signal to Noise Ratiovhf Very High Frequencyhf High Frequency

9

1Introduction

This thesis covers the development of a direction-finding algorithm together witha position filter. The project was carried out as a master thesis on the ElectronicDesign program at Linköping University. The foundation of the thesis was pro-vided by SenionLab AB.

1.1 Background and Motivation

The interest in identifying ones geographical position is ancient and various tech-niques have been used over the years. Modern technology became a part of itwhen the first step towards the Global Positioning System (gps) was made inthe 1950s [9]. While the positioning system for outdoor use has been widely re-searched and developed, the positioning system for indoor use has been laggingbehind. There is no definite standard for indoor positioning today, but the most-frequently used technique is to use the received signal strength [19]. Togetherwith a technique called fingerprinting, in which a radio map over the indoor en-vironment is created, the strength of the signal makes it possible to estimate oneslocation. A disadvantage with this technique is when it is used in larger areaswhere the changes in the received signal strength are too small to be recognizeddue to the weakness of the signal strength.

In the light of this, a localization approach called Direction-Finding (df) will beinvestigated. Instead of measuring the received strength of a signal, the directionfrom which the signal originated will be utilized. With this proposed technique,an estimation filter will be implemented to enable a localization estimate, usingthe result from the df algorithm.

1

2 1 Introduction

1.2 Objectives

The main objective of this thesis has been to investigate and develop a df algo-rithm as a complement with the received signal strength . The main potentialbenefit would be to eliminate the problem of finding ones location in larger ar-eas. As a complement to the result of the algorithm, a position estimate filter hasbeen investigated and used.

1.3 Limitations

A pre-determined hardware design for a beacon device has acted as a designfoundation for the df algorithm. To minimize the current consumption of thebeacon, all intended calculations will be performed within the receiving device.Specifications for the antenna constellation for the receiver is pre-determinedand the microcontroller within the receiver is pre-determined to be the TexasInstruments radio chip CC2650.

Figure 1.1: Block diagram of the system.

Figure 1.1 presents the antenna constellation design for the system. A re-search foundation for the functionality of such device will be presented as a fu-ture work suggestion. Hardware design of the receiving device lies outside thescope of this thesis.

All data are simulated, which limits the results to only be theoretical and arenot validated with real data.

1.4 Approach

The possibility of determining a position based on the Angle of Departure (aod)information is investigated. The technique is called df and requires an array ofantennas, either on the transmitting end, the receiver end or both. Generally, theantenna array is located at the receiving end of the system. A df algorithm willprovide the angle of the signal but this information is not sufficient to determinethe position of a target. To get an estimation of its position, two methods calledbearings-range and bearing-only localization, which is based on the ExtendedKalman Filter (ekf), is investigated.

1.5 Outline of the Thesis 3

Both algorithms are simulated in MATLAB, in separate files to get a better un-derstanding of each method individually.

1.5 Outline of the Thesis

Chapter 2 outlines the theory and background regarding different df methods.It also describes the differences in various antenna constellations.

Chapter 3 provides a deeper understanding of a specific df algorithm called Mul-tiple Signal Classification (music). This algorithm will serve as a foundation fora further development called M:1 music algorithm that suit the specifications ofthis thesis.

Chapter 4 presents simulation of the df algorithm.

Chapter 5 outlines the theory behind the bearings-range and bearing-only local-ization, it also includes the theory of the ekf.

Chapter 6 explains the modeled scenario of the bearing-range, bearing-only andekfmethods, it also includes simulations of these methods.

Chapter 7 provides a research foundation for a receiver device called position-ing tag.

Chapter 8 includes a concluding discussion.

2Direction-Finding Theory

This chapter includes the theory behind different df methods, together with thetheory behind different antenna arrangements.

2.1 Direction-Finding Techniques

df is a method to provide the functionality of Angle of Arrival (aoa) for a re-ceived signal, or the Angle of Depature (aod) of a transmitted signal. Themethoduses a single or multiple transmit antennas and a single or multiple receiving an-tennas to determine the azimuth angle of a distant emitter [23].

The df method has existed for as long as electromagnetic waves have beenknown. Heinrich Hertz discovered the directivity of antennas in 1888.

2.1.1 Watson-Watt Method

One of the first methods of df was the polarisation df, frequently used in theFirst World War. After the war, Sir Watson-Watt developed a non-mechanical dfsystem using crossed loop antennas. These type of system consist of four spatiallydisplacedmonopole or vertical dipole antennas. The angle of the incoming signalis determined by the differences in amplitude of the received waveform. Oneadditional antenna is usually placed in the centre to resolve uncertainties in thebearing, Figure 2.1.

5

6 2 Direction-Finding Theory

Figure 2.1: Typical Watson-Watt antenna arrangement.

The system compares the amplitudes received by each antenna, which are ob-tained as voltages out from the transmitting antenna. The antenna constellationcreates two axes, one in the y-direction that gives the y-axis angle and one in thex-direction that gives the x-axis angle. By changing the spacing of the antennas,the system is capable to operate over a wide range of frequencies.

2.1.2 Doppler Method

In 1941, the Doppler principle of df systems appeared, consisting of a circulararray of antennas. In 1950, airports were equipped with vhf/hf Doppler dfsystems for air traffic control. Doppler df systems use phase differences in thereceived antenna array. Early designs used rotating antenna arrays to obtain theDoppler shift, but more modern designs called Pseudo-Doppler systems use elec-trical methods to simulate the rotation. These systems use the changes in the ve-locity of a signal introduced by the rotating antenna array to induce the Dopplereffect. Pseudo-Doppler df uses four equally spaced antennas positioned on thecircumference on a circle. The antennas are being switched between in order tosimulate the rotation.

Figure 2.2: Typical Doppler antenna arrangement.

If a signal would be incoming from the North, Figure 2.2, the switchingmakesthe East-antenna to rotate away from the source and the West-antenna to rotatetowards the source. There is no Doppler effect on the South-antenna. This showsthat the signal is coming from the North.

2.2 Antenna Constellations 7

2.1.3 Interferometry

From the 1970s, the systems started to be digitalized and due to digital signal pro-cessing advances in the early 1980s, interferometry df systems were developed.Interferometry df systems uses phase differences to determine the angle of thetransmitted signal. This method consists of an antenna array which is equallyspaced in a straight line. Since the frequency of transmission is known, the phasedifferences can be calculated for each of the antennas. By knowing the phasedifferences and the distance between each antenna the angle can be calculated.

Figure 2.3: Typical interferometry antenna arrangement.

A typical interferometry antenna arrangement is shown in Figure 2.3, wherethe arrows represents the incoming signals and the dashed lines represents theadvancing wavefront [22].

2.2 Antenna Constellations

In wireless communication, the constellation of the antenna systems are of im-portance. This is to know how to create a mathematical model of the system.The communication systems can be divided into four main types called single-input single-output (siso) system, single-input multiple-output (simo) system,multiple-inputmultiple-output (mimo) system andmultiple-input single-output(miso) system. A siso system is the most commonly used consisting of one trans-mitting antenna and one receiving antenna, Figure 2.4.

Figure 2.4: siso system.

The simo system consist of one transmitting antenna and N receiving anten-nas, Figure 2.5.

In a simo system, due to the receiving antenna array, it is the aoa that is ofimportance when the phase difference will be determined.

8 2 Direction-Finding Theory

Figure 2.5: simo system.

The miso system consist of M transmitting antennas and one receiving an-tenna, Figure 2.6.

Figure 2.6: miso system.

When the phase difference of amiso system is to be determined, it is the aodthat is of importance. The most complex system is the mimo, which consist of Mtransmitting antennas and N receiving antennas, Figure 2.7.

Figure 2.7: mimo system.

In a mimo system, both the aoa and aod information can be used to deter-mine the phase difference of signals [6]. The transmitting and receiving end canbe categorized depending on the number of rf channels. When each antenna gotone rf channel, its called a multi-channel transmitter, and when there is only onerf channel independent of the number of antennas, its called a single-channeltransmitter. Figure 2.8 illustrates a multi-channel transceiver.

Figure 2.8: An example of a multi-channel transceiver.

2.2 Antenna Constellations 9

Figure 2.9 illustrates the single-channel transceiver.

Figure 2.9: An example of a single-channel transceiver.

This kind of transceiver use some form of switching among the antenna ele-ments or combining them to present the receiver with a single signal [24].

3Direction-Finding Algorithm

A pre-determined hardware design for the beacon and the antenna constellationregarding the receiver are taken into consideration when an existingdf algorithmwill be investigated. Specifications of interest within this project are that the bea-con possess four transmitting antennas which are arranged in an uniform lineararray, and the receiver possess one receiving antenna.

The interferometry df method described in Section 2.1.3 will serve as a designfoundation for the algorithm due to the existents of an antenna array. Within theinterferometry method, various techniques are available. These can be classifiedinto conventional beamforming techniques, subspace-based techniques and max-imum likelihood techniques. The subspace-based technique was chosen afteran evaluation regarding these methods, [31]. Within the subspace-based tech-nique, there are two main approaches which are called Multiple Signal Classifi-cation (music) and Estimation Parameters via Rotational Invariance Techniques(esprit). Here, the music approach was chosen, due to its proven stability andaccurate results, [26].

First, a general case of themusic algorithm will be presented, followed by a mod-ified development called M:1 music Algorithm, which is suited for this specificcase.

11

12 3 Direction-Finding Algorithm

3.1 MUSIC Algorithm

The classicMultiple Signal Classification (music) algorithm is a high performancealgorithm using a number of source signals and an array of receiving antennas.The algorithm achieves its high resolution from the evaluation of an input covari-ance matrix derived from the input data model. The eigenvalues of this covari-ance matrix are determined and partitioned into two sets, the signal and the noisesub-spaces [24]. In general, the music algorithm acts as a simo system, thus thelocation of the antenna array is at the receiving end.

3.1.1 Uniform Linear Array

The following assumptions are being made for a mathematical model: The an-tenna array is located far from the signal sources such that far-field characteris-tics are applied. This means that the wavefront generated by each signal sourcearrives at all the array elements at an equal direction of propagation and the wave-front is planar. Each source is narrow band with the same center frequency, ω0,and the noise is assumed to be Gaussian white noise. The noise at every array ele-ment have a common standard deviation of σn. The number of signal sources areD(d = 0, 1, .., D). The antenna array consists of M(m = 0, 1, .., M) elements andeach element has the same characteristics. The antennas are aligned and equallyspaced. [29]. An illustration of the scenario is displayed in Figure 3.1.

Figure 3.1: D signal sources and M receiving antennas.

Figure 3.2 illustrates the antenna array and one incoming signal. A signal gener-ated by signal source d are approaching the array with an angle θd . The signaltravel distance differs with a factor of ds for each antenna due to the antennaspacing da, Figure 3.2.

3.1 MUSIC Algorithm 13

Figure 3.2: The receiving antenna array.

3.1.2 Single Source Model

To be able to evaluate the spectrum of a received signal, a general mathematicalmodel for the input data is constructed, Equation (3.1). This function is based onthe fact that the signal belongs to the narrow band spectrum.

x(t) =

x0(t)

x1(t)

...

xM (t)

=

e−jζ0

e−jζ1

...

e−jζM

s(t) = a(θ)s(t) (3.1)

where the vector x(t) is called input data vector, a(θ) is called the steering vectorand s(t) is the vector of incident signals derived from the narrow band signalmodel [27]. The a(θ) is a general form of the steering vector which is a function ofthe individual element response. The ζi is the phase shift factor that is the effectof the propagation delay which occurs due to the placement of the antennas. Toget a more realistic model of the input data, Equation (3.1) is rewritten into:

x(t) = a(θ)s(t) + n(t) (3.2)

which can be expressed as

x0(t)

x1(t)

...

xM (t)

=

e−jζ0

e−jζ1

...

e−jζM

s0(t)

s1(t)

. . .

sD(t)

+

n0(t)

n1(t)

...

nM (t)

(3.3)


where the vector n(t) represents the interference and noise components. As illus-trated in Figure 3.2, the incoming plane wave travels a longer distance to reachthe mth antenna element, than it does to reach the first element. The differencein distance between two elements is ds = da sin θ, and the corresponding phaseshift differs between the elements with respect to the first element. Between thefirst and second element, the phase shift is ζ1 = βds, and for the mth element, thephase shift is:

ζm = mβds = mβda sin θ (3.4)

where the β is a propagation factor equal to 2π/λ where λ is the wavelength. Byusing Equation (3.5), the a(θ) vector can be rewritten into:

a(θ) =

1

e−jζ1

...

e−jζM

(3.5)

3.1.3 General Model

The input data model in Equation (3.2) can be extended into a more general caseof multiple transmitting signals [27]:

x(t) = A(Θ)s(t) + n(t) (3.6)

The A(Θ) in Equation (3.6) can be expanded into:

A(Θ) =

1 1 . . . 1

e−jβda sin θ0 e−jβda sin θ1 . . . e−jβda sin θD

......

. . ....

e−jβMda sin θ0 e−jβMda sin θ1 . . . e−jβMda sin θD

(3.7)

To better understand how the A(Θ) matrix is composed, Figure 3.3 illustrateshow the transmitting signals is received by the antenna array.


Figure 3.3: Illustration of the transmitting signals and the receiving array.

Each row of the A(Θ) matrix in Equation (3.7) is derived from how one receiv-ing antenna receives signals from each transmitter. Figure 3.4 illustrates how thefirst (m = 0) receiving antenna receives signals from each transmitter.

Figure 3.4: One receiver receives signals from different transmitters.

Due to the considerable distance between each transmitter, the aoa of eachsignal in Figure 3.4 is unique. Each column of the A(Θ) matrix in Equation (3.7)is derived from how each receiving antenna receives a signal from the same trans-mitter, illustrated in Figure 3.5.


Figure 3.5: One transmitter sending signals for the receiver array to receive.

The signal traveling distance is considerably larger than the antenna spacing,da, which results in the aoa being assumed to be equal. The A(Θ) matrix inEquation (3.7) is usually denoted as:

A(Θ) =[

a(θ0) . . . a(θD)]

(3.8)

For the vector x, the covariance matrix Rxx can be expressed as:

Rx,x = E[xxH ] = E[(As+n)(As+n)H ] = AE[ssH ]AH + E[nnH ] (3.9)

where E[ssH ] = Rss is the signal correlation matrix and E[nnH ] = σ2n I the noise

correlation matrix, rewriting Equation (3.9) to:

Rx,x = ARssAH + σ2

n I (3.10)

The vector space of Rx,x spans one set composed by noise and one set composedby both noise and signal. It is the latter that is interesting for further calculations.In practical applications, the sample covariance R̂xx is usually used [29]:

R̂x,x =1N

N∑

i=1

x(ti )x(ti )H (3.11)

where R̂x,x is the maximum likelihood estimation of Rx,x and N is the number ofsamples obtained at some time instances.

Equation (3.10) has positive eigenvalues that occur D times that correspondto signals and small (close to zero) eigenvalues that occur NN = M −D times, cor-responding to the noise, σ2

n [28]. The eigenvectors of the covariance matrix Rx,x


belong to either of the two orthogonal subspaces, the signal subspace or the noisesubspace. The steering vectors of A(Θ) lie in the signal subspace and the noiseeigenvalues, VN lie in the noise subspace. Due to orthogonality of the two sub-spaces, it is possible to search though all possible array steering vectors to findthose which are orthogonal to the noise eigenvectors. By doing this its possibleto determine the angle of arrival, θ.To get an estimationwith this method, the number of transmittersmust be greaterthan the number of receivers in the antenna array;

M > D (3.12)


3.2 M:1 MUSIC Algorithm

A modified version of the music algorithm, suited for the specifications of thisthesis, is presented in this chapter.

3.2.1 Uniform Linear Array

The considered transmitter contains the antenna array instead of the receivingend of the system, illustrated in Figure 3.6. As described in Section 2.2, it isthe aod that will be determined in this case. The antenna array consists of fourantennas, which are being switched between. When the switch is connected toan antenna, it sends out a signal during a known period of time, illustrated inFigure 3.7. The spacing between the transmitting antennas is da and it is assumedthat the transmitter is at a distance from the receiver so that the aod from eachtransmitter antenna is constant during one switching period.

Figure 3.6: Antenna constellation for the system.

The signals sent from each transmitting antenna are illustrated in Figure 3.7and the four signals form one switching period. The appearance and propertiesof the signals are purely for illustrative purpose.

The receiver receives a combined signal of the four signals, and due to theantenna spacing da on the transmitter, the signals from respectively transmittingantenna gets an unique phase shift. As illustrated in Figure 3.8.

The received signal with respect to the phase can be described as:

x(t) = e−jζ(t)s(t) + n(t) (3.13)

where

ζ(t) = ζ0uT0 (t) + ζ1u

2TT (t) + ζ2u

3T2T (t) + ζ3u

4T3T (t) (3.14)

and ut1t0(t) is a rectangle function defined as:

ut1t0(t) =

1, if t0 < t ≤ t10, otherwise

3.2 M:1 MUSIC Algorithm 19

Figure 3.7: Signals sent from each TX-antenna.

Figure 3.8: Illustrative signal received by the RX-antenna.

In the originalmusic algorithm D represents the number of source signals. Inthe M:1 music algorithm, it represents one switching period which means thatD = 1 for this system. Instead of looking at the number of receiving antennas, Mhere represents the number of transmitting antennas.

3.2.2 Model

The general case of the input data model is equal to the expression in Equa-tion (3.2), except from the notation of a(θ) that is denoted a(ζ) due to the constantDoA. Here, s(t) is a scalar since it is one signal and thus D = 1.

x(t) = a(ζ)s(t) + n(t) (3.15)


which can be expressed as

x(t)

x(t + T )

x(t + 2T )

x(t + 3T )

=

e−jζ0

e−jζ1

e−jζ2

e−jζ3

s(t) +

n(t)

n(t + T )

n(t + 2T )

n(t + 3T )

, 0 ≤ t ≤ T (3.16)

where the noise, n(t) can be rewritten into:

n(t) =

n(t)

n(t + T )

n(t + 2T )

n(t + 3T )

∆=

n0(t)

n1(t)

n2(t)

n3(t)

(3.17)

due to the fact that ni is independent noise. This result in:

x(t)

x(t + T )

x(t + 2T )

x(t + 3T )

=

e−jζ0

e−jζ1

e−jζ2

e−jζ3

s(t) +

n0(t)

n1(t)

n2(t)

n3(t)

, 0 ≤ t ≤ T (3.18)

Between the first and second element the phase shift is ζ1 = βda sin θ and for themth element the phase shift is:

ζm = mβda sin θ (3.19)

where the β is the propagation factor, Equation (3.5).

There are five steps to implement the M:1 music algorithm. The process isdescribed in Algorithm 1.

3.2 M:1 MUSIC Algorithm 21

Algorithm 1M:1 music algorithm

1. Collect N (n = 0, 1, .., N ) input samples to form the array x in Equa-tion (3.15) and estimate the input covariance matrix R̂x,x using Equa-tion (3.11).

2. Determine the eigenvectors of R̂x,x using eigenvalue decomposition:

R̂x,xV = VΛ (3.20)

where Λ = diag[λ0, λ1, .., λM ], λ0 ≤ λ1 ≤, ..,≤ λM are the eigenvalues ofR̂x,x and V = [v0, v1, .., vM ] are the corresponding eigenvectors[27].

3. Evaluate the music function, P(θ):

P(θ) =1

aH (ζ)VNVHNa(ζ)

,−π2≤ θ ≤ π

2(3.21)

where VN = [vD+1, vD+2, .., vM ]. The product VNVHN represents the pro-

jection matrix on the subspace. Orthogonality between a(θ) and VN willminimize the denominator.

4. Find the D maximum peaks of P(θ). This occurs when the denominator isat its minimum. [20] [25]

4Direction-Finding Simulations

This chapter presents the simulation results for the 4:1 music algorithm. Tofully understand the impact of different system design aspects, simulations withvarying values of parameters have been performed. The evaluated parameters isthe number of samples taken for each phase, N , antenna spacing for the beacondevice, da, and the number of transmitting antennas, M .

4.1 Algorithm Simulations

Calculations for this system are intended to be performed in the receiver, as de-scribed in Section 1.3. The microcontroller within the receiver is pre-determinedto be the Texas Instrument CC2650 radio chip. The incoming signal frequencyis 2.45 GHz, and the microcontroller has a sample rate of 200 kbit/s [4], whichindicates a signal downconvertion to a maximum of 100 kHz [18]. It is this fre-quency that are used in the df algorithm. The simualtions are being made withthe software tool MATLAB.

4.2 Simulation with Pre-Determined Parameters

Simulations of the 4:1 music algorithm is presented in Figure 4.1, the parame-ters for these are set to match the pre-determined values. The graph to the leftshows a signal being recognized by the algorithm at -70° and the rightmost graphpresents a signal being recognized at 10°.

23

24 4 Direction-Finding Simulations

Figure 4.1: Simulations with pre-determined parameters.

The number of samples per phase is set to 100, the antenna spacing is λ/4,number of transmitting antennas is 4 and the snr noise level is 20 dB. The noiseis ideal white Gaussian noise. The music function does not estimate the signalpower associated with each recognized angle. Instead, the peaks of P(θ) corre-spond to the true angles of departure.

4.3 Number of Samples

The simulations for varying number of samples per phase are illustrated in Figure4.2. Other conditions remain unchanged. The graph to the left represents a aodof -70° and the right represents a aod of 10°.

Figure 4.2: Varying number of samples.

4.4 Antenna Spacing 25

For the solid line in the figure, the number of samples are 50 which providesthe highest noise floor but requires the least amount of processing data. Thedashed line represents 100 samples and the dash-dotted line represents 300 sam-ples. The number of samples is a software design aspect that can be varied toobtain a suitable result.When the number of samples are varied, the highest number of performed sam-ples provide the best angle detection. But a high number of samples result in ahigh amount of processing data. Figure 4.2 proves that an angle detection is pos-sible with a considerably low number of samples. Which also result in a loweramount of computation resources.

4.4 Antenna Spacing

The simulations for varying antenna spacing are illustrated in Figure 4.3. Otherconditions remain unchanged compared to the basic simulation. The graph tothe left represents a aod of -70° and the right represents a aod of 10°.

Figure 4.3: Varying antenna spacing.

The solid line represents an antenna spacing of λ/4, the dashed line repre-sents an antenna spacing of λ/2 and the dash-dotted line represents a spacing ofλ.Figure 4.3 shows that the antenna spacing is an important hardware design as-pect. When the antenna spacing are half the wavelength or less, the beam widthbecomes narrow. And when the antenna spacing is more than half the wave-length, a false peak will emerge. This phenomenon is created due to the angleof departure condition of −π2 ≤ θ ≤ π

2 . For each aod angle θ there is a corre-sponding phase shift ζ. In order to determine θ uniquely from ζ, a one-to-one-correspondence is desired between them. This results in a phase shift conditionof −π ≤ ζ ≤ π and thus

26 4 Direction-Finding Simulations

da,max =ζmaxλ

2π sin θmax(4.1)

which yields

da ≤λ

2(4.2)

So when da exceeds this value there will be an ambiguity in the detection.

4.5 Number of Transmitting Antennas

The simulations for varying number of transmitting antennas are illustrated inFigure 4.4. Other conditions remain unchanged compared to the basic simulation.The graph to the left represents a aod of -70° and the right represents a aod of10°.

Figure 4.4: Varying number of transmitting antennas.

The solid line represents 2 transmitting antennas, the dashed line represents4 antennas, which conforms with the actual hardware design. The dash-dottedline represents 8 antennas.Figure 4.4 shows that the aod estimation beam width becomes narrower for ahigher amount of antennas. By increasing the number of antennas, the signal getseasier to distinguish but the processing data are also increasing for every addedantenna. This would also be a practical aspect, though every antenna requires acertain amount of spacing on the beacon device.

4.6 Noise Level 27

4.6 Noise Level

The simulations for varying noise level are illustrated in Figure 4.5. Other condi-tions remain unchanged compared to the basic simulation. The graph to the leftrepresents a aod of -70° and the right represents a aod of 10°.

Figure 4.5: Varying noise level.

The solid line in the figure represents a snr of 5 dB, the dashed line representsa snr of 20 dB and the dash-dotted line represents a snr of 35 dB. The snr isdefined as:

snr =Psignal

Pnoise(4.3)

where Psignal is the power of the signal and Pnoise is the power of the backgroundnoise. The noise of the system affects the peak definition, and a high snr valueproves to have less of an impact on the system.

5Localization Background

There are many different techniques to wirelessly locate objects with unknownpositions. This section describes two methods, bearing-range and bearings-only.An estimation algorithm is presented in which these techniques will be used inChapter 6.

5.1 Bearing-Range Localization

When both bearing and range measurements are available for position estimationof a target, it is called bearing-range localization. The bearing measurement arethe aod data calculated in the df algorithm and the range data could be obtainedby using the signal strength of a received signal. To calculate the received signalstrength, Friis transmission formula is utilized:

Pr =PtGtGrλ

2

4πR2(5.1)

where Pt is the power at which the signal was transmitted, λ is the wavelengthand R is the range between the transmitter and receiver. The Gt and Gr are thegains of the transmitter and receiver respectively [7]. With bearing-range mea-surements, one beacon is sufficient to estimate a position of a target.

5.2 Bearing-Only Localization

Bearing-only localization is a technique used to determine the location of a targetby using bearings measurements. The bearings are calculated using:

θ = tan−1(

Ry

Rx

)

(5.2)

29

30 5 Localization Background

where Ry is the y-term range from the beacon to the target, and Rx is the x-termrange from the beacon to the target [5].When the line of bearings are intersecting, it is possible to calculate the positionof the target. With bearing-only measurement, one beacon would be insufficientto determine a position. Here, at least two beacons are required to get the inter-secting point.

5.3 Extended Kalman Filter

To estimate the location of the moving target, an estimation filter called the Ex-tended Kalman Filter (ekf) will be used. The ekf is a non-linear derivation of thelinear Kalman Filter (kf) which optimizes the state estimate by minimizing thestate covariance [30]. A continuously estimation of the state is conducted by us-ing a non-linear motion and measurement model of the system. To linearize thesystem, Taylor expansion is performed around the current state estimate. Statespace models of the motion and measurements are given by:

xt = ft−1(xt−1) + ut (5.3)

yt = ht(xt) + vt (5.4)

where xt is the motion state which contains position and velocity information.This model calculates a prediction of how the state change over time when theprevious state, xt−1, is taken into consideration. Equation (5.4) is the measure-ment model. The ut-vector represents the process noise, which is assumed to bea zero mean Gaussian white noise with covariance Q. Further, the measurementnoise, vt , is assumed to be zero mean Gaussian white noise with covariance R.The filter involves two stages, prediction and measurement update. Equationsfor the prediction stage are:

x̂t|t−1 = ft−1(x̂t−1|t−1) (5.5)

Pt|t−1 = Ft−1Pt−1|t−1FTt−1 +Qt−1 (5.6)

where x̂t|t−1 is the predicted state estimate and Pt|t−1 is the corresponding covari-ance. Equations for the measurement stage of the filter are given by:

Kt = Pt|t−1HTt (HtPt|t−1H

Tt + Rt)

−1 (5.7)

x̂t|t = x̂t|t−1 +Kt(yt − ht(x̂t|t−1)) (5.8)

Pt|t = (I −KtHt)Pt|t−1 (5.9)

where x̂t|t is the state estimation corrected by the measurements and Pt|t is theupdated covariance. By utilize the difference in the received and predicted mea-surements, and the modeled uncertainty, the state prediction from the prediction

5.3 Extended Kalman Filter 31

stage can be corrected. Estimated states are updated to get an estimation closerto the true state.

Further, the Ft and Ht are defined as:

Ht =∂ht(xt)∂xt

∣

∣

∣

∣

∣

xt=x̂t|t−1(5.10)

Ft =∂ft(xt)∂xt

∣

∣

∣

∣

∣

xt=x̂t|t(5.11)

where Ht and Ft are defined as the jacobians of the motion and measurementmodel respectively, Equation (5.3) - (5.4) [21]. The ekf is summarized in Algo-rithm 2.

Algorithm 2 EKF

1. Initialize with x̂0|0 = x0 and P̂0|0 = P0.

2. Predicition update:x̂t|t−1 = ft−1(x̂t−1|t−1)Pt|t−1 = Ft−1Pt−1|t−1F

Tt−1 +Qt−1

3. Measurement update:Kt = Pt|t−1H

Tt (HtPt|t−1H

Tt + Rt)

−1

x̂t|t = x̂t|t−1 +Kt(yt − ht(x̂t|t−1))Pt|t = (I −KtHt)Pt|t−1

4. Set t = t + 1 and repeat from step 2.

6Localization Simulations

To be able to test the ekf, data for both the target trajectory and the measure-ment has to be generated. Environment settings for the beacons will be included.Two simulation models are taken into consideration, one with measurements gen-erated from two beacons and one with measurements generated from three bea-cons. These models is based on the results given by the df algorithm presentedin Chapter 3.2 and the theory introduced in Chapter 5.

6.1 Setup Models

By using the motion model, an actual trajectory is generated, which is repre-sented as the dashed line in Figure 6.1. Initialized data for the actual trajectoryis set to a constant velocity in both x and y-direction. In x-direction,vx,t = 1 m/s, and in y-direction, vy,t = 0 m/s, which result in a horizontal pathwith respect to the x-axis. The general motion model are given as:

xt =

px,t

py,t

vx,t

vy,t

+ ut (6.1)

where px,t and py,t represents the position of the target, and vx,t and vy,t repre-sents the velocity of the target. The ut-vector represents the process noise, whichis assumed to be a zero mean Gaussian white noise with a covariance of 0.5 me-ters. The initial motion model are given as:

33

34 6 Localization Simulations

x0 =

0

0

1

0

+ u0 (6.2)

The first model, Model 1, is simulated using two beacons, and the secondmodel, Model 2, is simulated using three beacons, Figure 6.1. The generatedtrajectory is equal in both Model 1 and Model 2.

6.1 Setup Models 35

Figure 6.1: Model 1 and Model 2.

To generate the measurement data, a measurement vector is utilized whichconsists of positioning data with added noise. The positions of the beacons aredetermined and are represented as the wedges in Figure 6.1. These positions areknown, denoted as (bx1, by1), (bx2, by2) and (bx3, by3) for beacon 1 (b1), beacon2 (b2) and beacon 3 (b3) respectively. The arrows in Figure 6.1 represent thedirection reference for the aod:s. This reference is set to match the aod derivedfrom the df algorithm. It is assumed that the beacons are placed aligned on awall.


6.2 Bearing-Range

The setup model, measurement vectors and simulations of the bearing-rangemethod is presented in this section.

6.2.1 Bearing-Range Model

When bearing-range is used together with the ekf, the measurement parametersfor the system are the aod values and the distance between each beacon and thetarget, Figure 6.2. The positions of the target are denoted as p = (px, py).

Figure 6.2: Measurement parameters for Model 1 and Model 2, using thebearing-range method.

In the ekf, the measurement vector, yt , will consist of four parameters forModel 1, denoted yBR1,t . This is due to the fact that two beacons are used in thiscase, and each beacon results in two statements, one aod value and one distancevalue. Equation (6.3) is the specified measurement vector for this model.

yBR1,t = hBR1(xt) + vt =

d1,t

θ1,t

d2,t

θ2,t

+

vd

vθ

vd

vθ

(6.3)

where hBR1(xt) is given by:

hBR1(xt) =

||p − b1||

tan−1(

py−by1px−bx1

)

||p − b2||

tan−1(

py−by2px−bx2

)

(6.4)

which yields

6.2 Bearing-Range 37

HBR1,t =∂hBR1,t(xt)

∂xt=

px−bx1√(px−bx1)2+(py−by1)2

py−by1√(px−bx1)2+(py−by1)2

0 0

by−py1(bx1−px)2+(by1−py )2

px−bx1(bx1−px)2+(by1−py )2

0 0



0 0



0 0

(6.5)

The measurement vector will consist of six parameters when using Model 2, de-noted yBR2,t . Equation (6.9) is the specified measurement vector for this model.

yBR2,t = hBR2(xt) + vt =

d1,t

θ1,t

d2,t

θ2,t

d3,t

θ3,t

+

vd

vθ

vd

vθ

vd

vθ

(6.6)

where hBR2(xt) is given by:

hBR2(xt) =

||p − b1||

tan−1(

py−by1px−bx1

)

||p − b2||

tan−1(

py−by2px−bx2

)

||p − b3||

tan−1(

py−by3px−bx3

)

(6.7)

which yields

HBR2,t =∂hBR2,t(xt)

∂xt=



0 0



0 0



0 0



0 0



0 0



0 0

(6.8)

The measurement noise, vd and vθ , has a standard deviation of 0.5 meters re-spectively 0.05 radians. These vectors represent the measured target positions inpolar coordinates with respect to each beacon.


6.2.2 Bearing-Range Simulations

Each model is simulated with a varying beacon spacing. This is to distinguishdifferences in the localization estimation. Values of the beacon spacing are 4 and12 meters. In the bearing-range simulation, the noise used for the measurementsare normally distributed pseudorandom numbers. The noise corresponding tothe range has a standard deviation of 0.50 meters and the noise corresponding tothe aod has a standard deviation of 2.86° (0.05 radians). Figure 6.3 presents thesimulations performed for Model 1 with a beacon spacing of 4 meters.

Figure 6.3: Model 1 with a distance of 4 meters between each beacon, usingbearing-range measurements.

The dashed lines represent the actual trajectory, in the figure to the left, thesolid line represent the ekf estimation. To the right, the dots represents the mea-surements.

Figure 6.4: Angle and distance values for Model 1 with a beacon distance of4 meters, using bearing-range measurements.


Figure 6.4 presents the values for the angles and the distances for each bea-con during the tracking with the beacon placement equal the one in Figure 6.3.The measurements are represented by the solid lines and the actual values arerepresented by the dashed lines. The thick lines correspond to the first beacon,b1 in Figure 6.2, and the narrow lines correspond to the second beacon, b2 inFigure 6.2. The measurements i Figure 6.4 are symmetric between beacon 1 andbeacon 2. This is due to the placement of the beacons. Figure 6.5 presents thesimulations performed for Model 1 with a beacon spacing of 12 meters.


Figure 6.6 presents the values for the angles and the distances for each beaconduring the tracking with the beacon placement equal the one in Figure 6.5.



The measurements in Figure6.6 are more stable than the measurements inFigure 6.4, this is because the estimation filter has a longer period of time tostabilize here.Figure 6.7 presents the simulations performed for Model 2 with a beacon spacingof 4 meters.





Figure 6.8 presents the values for the angles and the distances for each beaconduring the tracking with the beacon placement equal the one in Figure 6.7. Mea-surements and true values for the third beacon, b3 in Figure 6.2, are representedby the lines in magenta. The thick and the magenta lines are similar to the graphin Figure 6.6.Figure 6.9 presents the simulations performed for Model 2 with a beacon spacingof 12 meters. Figure 6.3, 6.5, 6.7 and Figure 6.9 shows that the estimation filterhas an initial uncertainty but find the right path quickly. The graphs in thesefigures displays a small instability in between the beacons.


Figure 6.10: Angle and distance values for Model 2 with a beacon distanceof 12 meters, using bearing-range measurements.

Figure 6.10 presents the values for the angles and the distances for each bea-con during the tracking with the beacon placement equal the one in Figure 6.9.


Measurements and true values for the third beacon, b3 in Figure 6.2, are repre-sented by the lines in magenta.

6.3 Bearing-Only

The setupmodel, measurement vectors and simulations of the bearing-onlymethodis presented in this section.

6.3.1 Bearing-Only Model

When the bearing-only method is used together with the ekf, the measurementparameters for the system are the aod values, Figure 6.11.

Figure 6.11: Measurement parameters for Model 1 and Model 2, using thebearing-only method.

In the ekf, the measurement vector will consist of two parameters for Model1, denoted yBO1,t . One aod value for each beacon. Equation (6.9) is the specifiedmeasurement vector for this model.

yBO1,t = hBO1(xt) + vt =

[

θ1,t

θ2,t

]

+ vθ (6.9)

where hBO1(xt) is given by:

hBO1(xt) =

tan−1(

py−by1px−bx1

)

tan−1(

py−by2px−bx2

)

(6.10)

which yields

6.3 Bearing-Only 43

HBO1,t =∂hBO1,t(xt)

∂xt=



0 0



0 0

(6.11)

The measurement vector will consist of six parameters when using Model 2, de-noted yBO2,t . Equation (6.12) is the specified measurement vector for this model.

yBO2,t = hBO2(xt) + vt =

θ1,t

θ2,t

θ3,t

+ vθ (6.12)

where hBO2(xt) is given by:

hBO2(xt) =

tan−1(

py−by1px−bx1

)

tan−1(

py−by2px−bx2

)

tan−1(

py−by3px−bx3

)

(6.13)

which yields

HBO2,t =∂hBO2,t(xt)

∂xt=



0 0



0 0



0 0

(6.14)

The measurement noise, vθ , has a standard deviation of 0.05 radians. These vec-tors represent the measured positions of the target in polar coordinates with re-spect to each beacon. When the polar coordinates are converted to cartesian, thefollowing equation is used:

di = ||p − bi || (6.15)

where i is equal to the beacon of interest.


6.3.2 Bearing-Only Simulations

Each model is simulated with a varying beacon spacing. This is to distinguishdifferences in the localization estimation. Values of the beacon spacing are 4 and12 meters. In the bearing-only simulation, the noise used for the measurementsare normally distributed pseudorandom numbers. The noise corresponding tothe aod has a standard deviation of 2.86° (0.05 radians). Figure 6.12 presentsthe simulations performed for Model 1 with a beacon spacing of 4 meters.

Figure 6.12: Model 1 with a distance of 4 meters between each beacon, usingbearing-only measurements.


Figure 6.13: Angle and distance values for Model 1 with a beacon distanceof 4 meters, using bearing-only measurements.

6.3 Bearing-Only 45

Figure 6.13 presents the values for the angles and the distances for each bea-con during the tracking with the beacon placement equal the one in Figure 6.12.The measurements are represented by the solid lines and the actual values arerepresented by the dashed lines. The thick lines correspond to the first beacon,b1 in Figure 6.2, and the narrow lines correspond to the second beacon, b2 inFigure 6.2. This graph is similar to the leftmost graph in Figure 6.4, just with abigger uncertainty.Figure 6.14 presents the simulations performed for Model 1 with a beacon spac-ing of 12 meters.

Figure 6.14: Model 1 with a distance of 12 meters between each beacon,using bearing-only measurements.




Figure 6.7 presents the simulations performed for Model 2 with a beacon spac-ing of 4 meters.

Figure 6.16: Model 2 with a distance of 4 meters between each beacon, usingbearing-only measurements.

The dashed lines represent the actual trajectory, in the figure to the left, thesolid line represent the ekf estimation. To the right, the dots represents the mea-surements. Figure 6.17 presents the values for the angles and the distances foreach beacon during the tracking with the beacon placement equal the one in Fig-ure 6.16.


Measurements and true values for the third beacon, b3 in Figure 6.2, are rep-resented by the lines in magenta.

Figure 6.18 presents the simulations performed for Model 2 with a beacon

6.3 Bearing-Only 47

spacing of 12 meters. The simulations for the bearing-only estimation presentsa bigger uncertainty in the initial phase than in the bearing-range estimation. InFigure 6.12, 6.14, 6.16 and Figure 6.18, the uncertainty in between the beaconsgets more difficult to distinguish due to this.

Figure 6.18: Model 2 with a distance of 12 meters between each beacon,using bearing-only measurements.




6.4 Monte Carlo Simulations

Monte Carlo diagrams of the estimation error are presented, with a beacon spac-ing of 4 meters as well as 12 meters. The graphs represents the mean error, µ, andthe standard deviation, σ , over time. In every timestep of the position estimation,1000 samples has been collected and then been averaged for the mean value anda standard deviation has been calculated.

Notation and corresponding line representation are consistent throughout thischapter. The mean error for bearing-range estimations are denoted as µBR andcorresponds to the solid thin line. The mean error for bearing-only estimationsare denoted as µBO and corresponds to the solid thick line. Standard deviationsfor the bearing-range estimations are denoted as σBR and corresponds to to thedashed thin line. The standard deviation for the bearing-only estimations aredenoted σBO and corresponds to the dashed thick line.

6.4.1 Model 1

In Model 1, two beacons are utilized. Figure 6.20 presents the mean estimationerror and the standard deviation with a beacon spacing of 4 meters. The graphto the left corresponds to the x-component and the rightmost graph correspondsto the y-component.

Figure 6.20: Monte Carlo diagram of the estimation error for a beacon dis-tance of 4 meters, Model 1.

Figure 6.21 displays the mean estimation error and the standard deviationwith a beacon spacing of 12 meters.

6.4 Monte Carlo Simulations 49


6.4.2 Model 2

Three beacons are utilized in Model 2, which means that these graphs are morecomprehensive and makes it easier to distinguish estimation error patterns. Fig-ure 6.22 presents the mean estimation error and the standard deviation with abeacon spacing of 4 meters. The graph to the left corresponds to the x-componentand the rightmost graph corresponds to the y-component.


Figure 6.21 displays the mean estimation error and the standard deviationwith a beacon spacing of 12 meters.



Simulations for the estimation error indicates that the estimations get moreaccurate with a smaller beacon spacing, Figure 6.20 and Figure 6.22, in which aspacing of 4 meters is utilized. Evaluation of Figure 6.21 and Figure 6.23 displaysa bigger uncertainty in between the beacons, where a beacon spacing of 12 me-ters is used. The error pattern in Figure 6.23 shows that the error for the x-termdecreases when the target is close to a beacon, and that the error for the y-termincreases when the target is close to a beacon. This can be explained by the us-age of a distance error, that does not take the x-and y-term into considerationseparately. Figure 6.24 shows the distance error when the target is close and far,respectively.

Figure 6.24: Error evaluation.

From the figure, the following can be stated:

6.4 Monte Carlo Simulations 51

ex,close < ex,f ar (6.16)

ey,close > ey,f ar (6.17)

This causes a big uncertainty over time when looking at the Monte Carlo di-agram i Figure 6.23, but these errors are canceling each other out. The meanvalues of the estimated errors are the most stable with three beacons and whensmaller beacon distances are utilized.

7Positioning Tag

This chapter will work as a design foundation for a future implementation.

The intended functionality of the receiver is to develop it into a positioning tag.This tag would be placed on an equipment of some sort, i.e on a hospital bed. Thereceived signals are calculated and an estimation of it position is made. If theseestimations are sent to a server, the location of the equipment can be monitored.A suggestion of its design is presented in Figure 7.1.

Figure 7.1: Block diagram of the system.

Besides from the df algorithm and the ekf, the tag should contain at leastone motion sensor to enable a sensor fusion method to complement the positionestimation. The sensor should also work as a motion indicator so that the sleepmode function of the microprocessor could be used. The intended functionalityof the positioning tag is described in Figure 7.2.

53

54 7 Positioning Tag

Figure 7.2: Flowchart of the project.

Starting off with the microprocessor in sleep mode, the motion sensor willsample data to indicate if the device is moving or standing still. To maintaina low current consumption in this state, the sensor should be able to go downto a low power mode. The microprocessor should stay in sleep mode as long asthe sensor does not indicate any motion. When the sensor notices a movementof the device, the microprocessor should waken and start receiving ble-signalsfrom the peripheral, which will be the beacon device. The received signals will beprocessed via the df algorithm which will state from what direction the signalsare coming. To confirm the motion and calculated position, sensor fusion can beused.

If the tag is moving, the receiving part should waken to pick up ble signalsfrom the transmitter, process the signals to calculate its position and heading andthere after send the data to a server via Wi-Fi.

7.1 Microprocessor 55

7.1 Microprocessor

The intended microprocessor for the positioning tag is a CC2650. This processoris provided by Texas Instruments and is a wireless microcontroller unit (mcu)able to target various wireless communications standards, such as Bluetooth Smart[4]. The processor is a low power 2.4 GHz rf device which is able to provide alow-power mode, this leads to a longer lifetime for the used batteries. It is suitedto function with external sensors that collects data while the processor is in low-power mode. This conforms with the workflow described in Figure 7.2.

7.2 Sensor Components

The type of sensors that will be investigated are accelerometers, gyroscopes, mag-netometers and pressure sensors. A few alternatives for each sensor type is pre-sented in the sections below for comparison. Various properties are displayed foreach type but one of the most important properties that is looked at for all sen-sors is the current consumption, this is to keep the over all current consumptionfor the positioning tag as low as possible. All sensors are a part of the micro-electromechanical systems (mems) technology.


7.2.1 Accelerometer

An accelerometer is an electromechanical device thatmeasures acceleration forces.The tilt angle of a device can be measured by the amount of static accelerationdue to gravity, with respect to the earth. The dynamic acceleration can be mea-sured to calculate the direction in which the device is moving.The considered accelerometers in Table 7.1 all have three axes.

Table 7.1: Technical comparison between three accelerometers.

Feature LIS2DHTR KXCJ9-1008 KX022 UnitVoltage Supply 1.71 - 3.60 1.71 - 3.60 1.71 - 3.60 VCurrent Consumption @ 1 Hz 2.0 2.0 1.8 µACurrent Consumption @ 50Hz

11.0 16.0 13.0 µA

Full-Range-Scale ±2/±4/±8/±16 ±2/±4/±8 ±2/±4/±8 gI2C Yes Yes YesMotion Detection/Interrupts Yes – YesManufacturer STmicroelectr-

onicsKionix Kionix

Costs per unit @ qty 1000 0.802 0.969 1.043 USD

For additional features and data, see [13] for the ”LIS2DHTR”, [11] for the”KXCJ9-1008” and [10] for the ”KX022”. In the sub chapters below is the powermodes of the accelerometers discussed.

LIS2DHTR

The LIS2DHTR-accelerometer has four different power modes; high resolutionmode, normal mode, low-power mode and power-down mode. In the high reso-lution mode a 12 bit Output Data (od) is used, in the normal mode a 10 bit odis used and for the low-power mode a 8 bit od is used, in the power-down modeis no sapling performed. For all the power modes where sampling is performed,the full Output Data Range (odr) can be used, but due to the difference in theod-resolution, different odr s are recommended.

Table 7.2: Current consumption for LIS2DHTR.

Power Mode @ ODR = 50 Hz [µA] @ ODR = 1 Hz [µA]High Resolution 11.0 2.0Normal 11.0 2.0Low-Power 6.0 2.0Power-Down 0.51 –

The sensor can be programmed to automatically switch to low power modeupon recognition of a determined event, such as an acceleration value threshold.As soon the acceleration value goes back over the threshold does the device returnback to the present normal mode [13].

7.2 Sensor Components 57

KXCJ9-1008

The KXCJ9-1008-accelerometer has three power modes; full power mode, lowpower mode and disabled. In the full power mode a 12 or 14 bit od is used, forthe low power mode a 8 bit od is used and the sensor does not sample in disabledmode.

Table 7.3: Current consumption for KXCJ9-1008.

Power Mode [µA] [µA]Full Power 135.0 @ ODR = 50 Hz 135.0 @ ODR = 0.781 HzLow Power 16.0 @ ODR = 50 Hz 1.7 @ ODR = 0.781 HzDisabled 0.9 –

The device can be configured to detect acceleration greater than the user-defined threshold for a user-defined amount of time [11].

KX022

The KX022-accelerometer has three power modes; high power mode, low powermode and standby mode. The sensor is not sampling in the standby mode, in thehigh power mode the sample rate is typically between 800-1600 Hz and in thelow power mode the sample rate is typically between 0.78 - 400 Hz.

Table 7.4: Current consumption for KX022.

Power Mode [µA] [µA]High Power 146.0 @ ODR = 800 Hz 146.0 @ ODR = 1600 HzLow Power 13.0 @ ODR = 50 Hz 1.8 @ ODR = 0.781 HzStandby 0.9 –

The device can be configured to detect acceleration on any axis dependingon a user-defined wake-up threshold. The device switches from an inactive stateto an active state. When the event is finished, the device returns to the inactivemode [10].


7.2.2 Gyroscope

A gyroscope is a device thatmeasures angular velocity using Coriolis effect. memsgyroscopes consists of a single mass which is driven to vibrate along a drive axis,when the gyroscope is rotated a secondary vibration is induced. The angular ve-locity can be calculated by measuring this secondary rotation. The consideredgyroscopes in Table 7.5 all have three axes.

Table 7.5: Technical comparison between three gyroscopes.

Feature L3G4200D BMG160 FXAS21002CQR1 UnitVoltage Supply 2.40 - 3.60 2.40 - 3.60 1.95 - 3.60 VCurrent Consump-tion Normal Mode

6.10 5.00 2.70 mA

Full-Range-Scale ±250/±500/±2k

±125/±250/±500/±1k/±2k

±250/±500/±1k/±2k

dps

Noise Density 0.030 0.014 0.025 dps/√Hz

I2C Yes Yes YesMotion detec-tion/interrupts

No Yes Yes

Manufacturer STmicro-electronics

Bosch Sen-sortec

Freescale Semi-conductor

Costs per unit @qty 1000

3.47 2.34 2.37 USD

For additional features and data, see [12] for the ”L3G4200D”, [1] for the”BMG160” and [8] for the ”FXAS21002CQR1”. In the sub chapters below is thepower modes of the gyroscopes discussed.

L3G4200D

The L3G4200D-gyroscope has three power modes; normal mode, sleep mode andpower-down mode. The datasheet of the product does not specify the powermodes any further [12]. The current consumption values in Table 7.6 are notodr specified.

Table 7.6: Current consumption for L3G4200D.

Power Mode [mA]Normal 6.1Sleep 1.5Power-Down 5.0

The device has programmable interrupts, although not for switching betweenpower modes.


BMG160

The BMG160-gyroscope has four power modes; normal mode, fast power-upmode, suspend-mode and deep suspend-mode. In the fast power-up mode is thesensing analog part powered down and no data sampling is being made, in thesuspend-mode the entire analog part is powered down and no data acquisition isbeing performed and in the deep suspend-mode, only the interface section is keptalive and no data acquisition is being made. The current consumption values inTable 7.7 are not odr specified.

Table 7.7: Current consumption for BMG160.

Power Mode [mA]Normal 5.0Fast Power-Up 2.5Suspend 0.025Deep-Suspend < 0.005

The device has motion detection which generates an interrupt when a sensorvalue exceeds a user-defined threshold. The interrupt is cleared when the sensorvalue falls below the threshold. The interrupts are fully functional in normalmode only [1].

FXAS21002CQR1

The FXAS21002CQR1-gyroscope has three power modes; active mode, readymode and standby mode. In the active mode all blocks are enabled and the de-vice is actively measuring the angular rate. In ready mode the drive circuits arerunning but no measurements are being made, and for the standby mode, onlythe interface are kept alive. The current consumption values in Table 7.8 are notodr specified.

Table 7.8: Current consumption for FXAS21002CQR1.

Power Mode [mA]Active 2.7Ready 1.6Standby 0.0028

The device has a detection function which detects an angular rate event thatexceeds a programmed threshold on any one of the enabled axes and triggers aninterrupt. The interrupt is cleared after a user-defined amount of time after theangular rate is below the threshold [8].


7.2.3 Magnetometer

A magnetometer is a device that detects and measures magnetic fields. It de-tects effects on the Lorentz force acting on a current-carrying conductor in themagnetic field. The mechanical motion of the micro-structure are sensed eitherelectronically or optically. In Table 7.9 are two magnetometers compared.

Table 7.9: Technical comparison between two magnetometers.

Feature LIS3MDL MAG3110 UnitVoltage Supply 1.90 - 3.60 1.95 - 3.60 VCurrent Consumption @20 Hz

270.0 275.0 µA

Current Consumption LowPower Mode @ 20 Hz

40.0 2.00 µA

Magnetic-Full-Scale ±400/±800/±1200/±1600

±1000 µT

Noise 0.32 - 0.41 0.25 - 0.40 µTI2C Yes YesManufacturer STmicro- elec-

tronicsFreescaleSemiconduc-tor

Costs per unit @ qty 1000 0.838 0.680 USD

For additional features and data, see [14] for the ”LIS3MDL” and [16] for the”MAG3110”. In the sub chapters below is the power modes of the magnetometersdiscussed.

LIS3MDL

The LIS3MDL-magnetometer has three powermodes; ultra-high resolutionmode,low-power mode and power down mode.

Table 7.10: Current consumption for LIS3MDL.

Power Mode [µA]Ultra High Resolution 270.0 @ ODR = 20 HzLow-Power 40.0 @ ODR = 20 HzPower-Down 1.0

The datasheet of the device does not specify the power modes any further[14].


MAG3110

The MAG3110-magnetometer has two power modes; active mode and standbymode. In the active mode, the device performs periodic measurements with anODR of 0.63 - 80 Hz. The standby mode can be defined to either not sample atall or to exit the standby mode and perform one measurement cycle that is basedon the programmed odr and then re-enter the standby mode [16].

Table 7.11: Current consumption for MAG3110.

Power Mode [µA]Active 8.6 @ ODR = 0.63 HzActive 275.0 @ ODR = 20 HzStandby 2.0


7.2.4 Pressure Sensor

Pressure sensors are based on the principle of a membrane bending caused bythe pressure in a liquid or gas. A conductive screened layer is placed on themembrane that follows its bending properties. This makes it possible to measureeither the distance between the conductive and a resistive layer, or the resistanceof the conductive layers which changes with the bending. A pressure sensor canbe used to navigate the altitude of a device. In Table 7.12 are two pressure sensorsare compared.

Table 7.12: Technical comparison between two pressure sensors.

Feature LPS25HB BMP280 UnitVoltage Supply 1.70 - 3.60 1.71 - 3.60 VCurrent Consumption High Res-olution

4.5 - 25.0 24.8 µA

Current Consumption Low Res-olution

4.0 2.8 µA

Current Consumption Power-Down Mode

0.5 0.2 µA

Pressure Range 260 - 1260 300 - 1100 hPaNoise 0.010 - 0.030 0.013 hPaI2C Yes YesManufacturer STmicroelectronics Bosch SensortecCosts per unit @ qty 1000 2.02 1.73 USD

For additional features and data, see [15] for the ”LPS25HB” and [2] for the”BMP280”. In the sub chapters below are the power modes of the pressure sen-sors discussed.

LPS25HB

The LPS25HB-pressure sensor has four power modes; low-resolution mode, nor-mal mode, high-resolution mode and power down mode.

Table 7.13: Current consumption for LPS25HB.

Power Mode [µA]Low Resolution 4.0 @ ODR = 1 HzNormal 4.5 @ ODR = 1 HzHigh Resolution 25.0 @ ODR = 1 HzPower Down 0.5

The datasheet of the product does not specify the power modes any further[15]. The device have user-defined pressure threshold interrupts, but is not madeto switch between power modes.


BMP280

The BMP280-pressure sensor has three power modes; sleep mode, normal modeand forcedmode. In sleepmode, nomeasurements are beingmade, in the normalmode, the device continuously cycles between an active measurement period andan inactive standby period, the time periods are user-defined. In forced mode isone single measurement performed and then goes to sleep mode. When the de-vice is in normal mode there are five resolution settings to choose from; ultra lowpower which typically samples in 181.8 Hz, low power which typically samplesin 133.3 Hz, standard resolution with a sample rate of 87.0 Hz, high resolutionwith a sample rate of typically 51.3 Hz and ultra high resolution which typicallysamples in 26.7 Hz [2].

Table 7.14: Current consumption for BMP280.

Power Mode [µA]Sleep 0.1Normal 0.2/720Forced See Table 7.15

Table 7.15 lists the current consumption when the device is set in forcedmode.

Table 7.15: Current consumption for forced mode.

Power Mode [µA]Ultra Low 2.74Low Power 4.17Standard resolution 7.02High Resolution 12.7Ultra High 24.8


7.2.5 Multi sensor solution

For a multi sensor solution, a few options are available on the market. Multi sig-nifies that two or three motion sensors are assembled in a chip to simplify theimplementation. The chips in Table 7.16 consist of three motion sensors, a gy-roscope, an accelerometer and a magnetometer, each with three-axis technologywhich makes it 9-axis chip technology.

Table 7.16: Technical comparison of two 9-axis sensor chips.

Feature MPU-9250 BMX055 UnitVoltage Supply 2.4 - 3.6 2.4 - 3.6 VCurrent Consumptionnormal mode 9-axis

3.7 5.63 mA

Current Consumptionnormal mode 6-axis(A+G)

3.4 5.13 mA

Current Consumptionnormal mode 6-axis(A+M)

730 630 µA

Current Consumptionnormal mode 3-axis (G)

3.2 5.0 mA

Current Consumptionnormal mode 3-axis (A)

450 130 µA

Current Consumptionnormal mode 3-axis(M)

280 500 µA

Gyro Full-Range-Scale ±250/±500/±1k/±2k

±125/±250/±500/±1k/±2k

°/sec

Accele Full-Range-Scale

±2/±4/±8/±16 ±2/±4/±8/±16 g

Mag Full-Range-Scale ±4800 ±1300/±2500 µTNoise 250 150 µg/

√Hz

I2C Yes YesMotion Detection Yes YesMotion interrupts Yes Yes3rd party sensor inter-face

Yes No

Manufacturer InvenSense BoschSensortecCosts per unit @ qty1000

5.37 3.74 USD

For additional features and data, see [17] for the ”MPU-9250” and [3] forthe ”BMX055”. In the sub chapters below, motion detection for the devices isdiscussed.


MPU9250

The MPU9250-device has several power modes which are listed in Table 7.16. Italso provides a motion detection capability called wake-on-motion. A motionsample from any axis that got an absolute value exceeding a user-programmablethreshold. The device possesses a digital motion processor which has access toone of the MPU’s external pins, this can be used for generating interrupts [17].

BMX055

The BMX055-device has several power modes, Table 7.16. The device also has amotion detection for all the sensors which is able to trigger interrupts, this willhappen when a sensor value exceeds a user-defined threshold. The interrupt iscleared when the value falls below the threshold [3].

8Conclusion and Future Work

This chapter is a concluding summary of the project, it also includes discussionabout future work.

8.1 Conclusion

The main focus of this thesis has been to investigate an indoor positioning systemwhich tracks nearby beacons and determines the angle of departure from the in-coming signals. It can be concluded that the M:1 music algorithm can be usedfor this purpose, but further development with real data and implementation isneeded.

Together with the direction-finding information, a localization filter is presentedto demonstrate how this information can be utilized. In a comparison betweenbearing-range and bearing-only estimations, the bearing-range estimations sta-bilize more quickly. But after a few meters, the bearing-only method proves toestimate the position of a target just as well as the bearing-range. Considerableamounts of data processing resources can be saved by using the bearing-onlymethod.

In theory, the presented method is a good complement with the technique basedon the received signal strength. A calibration map is needed to store the actualpositions of the beacons for the receiver to know which signal belongs to whichbeacon.

67

68 8 Conclusion and Future Work

8.2 Future Work

To further analyze the proposed method, an implementation with real data isneeded. This is to test the system with data including real noise in differentenvironments.Another further development is to use the positioning tag research and developa software and a hardware design specific for the intended tag.

Bibliography

[1] BMG160 datasheet. https://ae-bst.resource.bosch.com/media/products/dokumente/bmg160/BST-BMG160-DS000-09.pdf. Ac-cessed: 2015-03-05. Cited on pages 58 and 59.

[2] BMP280 datasheet. https://ae-bst.resource.bosch.com/media/

products/dokumente/bmp280/BST-BMP280-DS001-10.pdf. Ac-cessed: 2015-03-04. Cited on pages 62 and 63.

[3] BMX055 datasheet. http://www.mouser.com/ds/2/621/

BST-BMX055-DS000-01v2-371988.pdf. Accessed: 2015-03-05.Cited on pages 64 and 65.

[4] CC2650 datasheet. http://www.ti.com/lit/ds/symlink/cc2650.

pdf. Accessed: 2015-06-01. Cited on pages 23 and 55.

[5] Estimation of the position of a moving target using the extended kalmanfilter. http://web.cecs.pdx.edu/~ssp/Reports/2006/Quijano.

pdf. Accessed: 2015-06-10. Cited on page 30.

[6] Finding memo. http://complextoreal.com/wp-content/

uploads/2013/01/mimo.pdf. Accessed: 2015-04-05. Cited onpage 8.

[7] Friis equation. http://www.gaussianwaves.com/2013/09/

friss-free-space-propagation-model/. Accessed: 2015-06-10.Cited on page 29.

[8] FXAS21002C datasheet. http://www.mouser.com/ds/2/161/

FXAS21002-520687.pdf. Accessed: 2015-03-05. Cited on pages 58and 59.

[9] The GPS navigation system. http://www.astronomy.ohio-state.

edu/~pogge/Ast162/Unit5/gps.html. Accessed: 2015-03-19. Citedon page 1.

69

70 Bibliography

[10] KX022-1020 datasheet. http://www.kionix.com/sites/default/

files/KX022/20Sell/20Sheet.pdf. Accessed: 2015-02-23. Cited onpages 56 and 57.

[11] KXCJ9-1008 datasheet. http://www.bluetooth.com/Pages/

low-energy-tech-info.aspx. Accessed: 2015-02-13. Cited onpages 56 and 57.

[12] L3G4200D datasheet. http://www.st.com/st-web-ui/static/

active/en/resource/technical/document/datasheet/

CD00265057.pdf. Accessed: 2015-02-18. Cited on page 58.

[13] LIS2DHTR datasheet. http://www.st.com/web/en/resource/

technical/document/datasheet/DM00042751.pdf. Accessed:2015-03-05. Cited on page 56.

[14] LIS3MDL datasheet. http://www.st.com/st-web-ui/static/

active/en/resource/technical/document/datasheet/

DM00075867.pdf. Accessed: 2015-02-18. Cited on page 60.

[15] LPS25HB datasheet. http://www.mouser.com/ds/2/389/

DM00141379-469692.pdf. Accessed: 2015-02-18. Cited on page62.

[16] MAG3110 datasheet. http://cache.freescale.com/files/

sensors/doc/data_sheet/MAG3110.pdf. Accessed: 2015-02-18.Cited on pages 60 and 61.

[17] MPU-9250 datasheet. http://www.invensense.com/mems/gyro/

documents/PS-MPU-9250A-01.pdf. Accessed: 2015-03-05. Cited onpages 64 and 65.

[18] Nyqvist theorem. http://redwood.berkeley.edu/bruno/npb261/

aliasing.pdf. Accessed: 2015-06-16. Cited on page 23.

[19] G. Chen, Y. Zhang, L. Xiao, J. Li, and S. Zhou. Measurement-based RSS-multipath neural network indoor positioning technique. Electrical andComputer Engineering (CCECE), 2014 IEEE 27th Canadian Conference on,2014. Cited on page 1.

[20] J. D. Reed. Approaches to multiple-source localization and signal classifi-cation. MS Thesis Virginia Polytechnic Institute and State University, 2009.Cited on page 21.

[21] E. Erkstam and E. Tjernqvist. Performance enhancement of bearing naviga-tion to known radio beacons. MS Thesis Linköping University, 2012. Citedon page 31.

[22] A. Graham. Communications, Radar and Electronic Warfare. Wiley. Citedon page 7.

Bibliography 71

[23] N. Harter, J. J. Keaveny, S. Ventesh, and B. R. M. Analysis and implementa-tion of a novel single-chanel direction-finding metod. Wireless Communi-cations and Networking Conference, IEEE, 2005. Cited on page 5.

[24] N. M. Harter. Development of a single-channel direction finding algorithm.MS Thesis Virginia Polytechnic Institute and State University, 2007. Citedon pages 9 and 12.

[25] J. Joseph Keaveny. Analysis and implementation of a novel single channel di-rection finding algorithm on a sotfware radio platform. MS Thesis VirginiaPolytechnic Institute and State University, 2005. Cited on page 21.

[26] T. Lavate, A. Sapkal, and V. Kokate. Performance analysis of music and es-prit doa estimation algorithms for adaptive array smart antenna in mobilecomminication. Second International Conference on Computer and Net-work Technology, 2010. Cited on page 11.

[27] R. Muhamed. Direction of arrival estimation using antenna arrays. MSThesis Virginia Polytechnic Institute and State University, 1996. Cited onpages 13, 14, and 21.

[28] R. O. Schmidt. Multiple emitter location and signal parameter estimation.Antennas and Propagation, IEEE Transactions on, 34, 1986. Cited on page16.

[29] H. Tang. DOA estimation based on music algorithm. MS Thesis Linnéuni-versitetet, Kalmar Växsjö, 2014. Cited on pages 12 and 16.

[30] D. Törnqvist. Estimation and detection with applications to navigation.Linköping studies in science and technology, Linköping University, 2008.Cited on page 30.

[31] C. Zhizhang, G. Gokeda, and Y. Yu. Introduction to Direction-of-ArrivalEstimation. Artech House. Cited on page 11.

72 Bibliography

Upphovsrätt

Detta dokument hålls tillgängligt på Internet — eller dess framtida ersättare —under 25 år från publiceringsdatum under förutsättning att inga extraordinäraomständigheter uppstår.

Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner,skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för icke-kommersiell forskning och för undervisning. Överföring av upphovsrätten viden senare tidpunkt kan inte upphäva detta tillstånd. All annan användning avdokumentet kräver upphovsmannens medgivande. För att garantera äktheten,säkerheten och tillgängligheten finns det lösningar av teknisk och administrativart.

Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsmani den omfattning som god sed kräver vid användning av dokumentet på ovanbeskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådanform eller i sådant sammanhang som är kränkande för upphovsmannens litteräraeller konstnärliga anseende eller egenart.

För ytterligare information om Linköping University Electronic Press se förla-gets hemsida http://www.ep.liu.se/

Copyright

The publishers will keep this document online on the Internet — or its possi-ble replacement — for a period of 25 years from the date of publication barringexceptional circumstances.

The online availability of the document implies a permanent permission foranyone to read, to download, to print out single copies for his/her own use andto use it unchanged for any non-commercial research and educational purpose.Subsequent transfers of copyright cannot revoke this permission. All other usesof the document are conditional on the consent of the copyright owner. Thepublisher has taken technical and administrative measures to assure authenticity,security and accessibility.

According to intellectual property law the author has the right to be men-tioned when his/her work is accessed as described above and to be protectedagainst infringement.

For additional information about the Linköping University Electronic Pressand its procedures for publication and for assurance of document integrity, pleaserefer to its www home page: http://www.ep.liu.se/

© Erica Gunhardson

Indoor Positioning Using Angle of Departure Information874882/FULLTEXT01.pdf · 2.1...

Documents

Transcript of Indoor Positioning Using Angle of Departure Information874882/FULLTEXT01.pdf · 2.1...