priv.-doz. dr.-ing. habil. michael meurer german aerospace ... · michael meurer german aerospace...

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DLR und TU-München, Kommunikation und Navigation

Terrestrial Navigation

Priv.-Doz. Dr.-Ing. habil. Michael Meurer German Aerospace Center

Email: [email protected]

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Summary

History of Navigation: Transition from Observation of Natural Phenomena to Radio based Technologies Terrestrial and Satellite Based Positioning Importance of Accurate Time for Precise Positioning Manifold Applications of Localization, E911

Definitions: Self and Remote Positioning Localization Navigation

Quality Measures Accuracy Integrity Continuity Availability

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Terrestrial Navigation

Priv.-Doz. Dr.-Ing. habil. Michael Meurer German Aerospace Center

Email: [email protected]

Chapter 2:Basic Terms and System Model

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Outline and Structure

1. Introduction

1.1 Historic Overview

1.2 Challenges and Applications

1.3 Definitions

2. Basic terms and system model

2.1 Scenario and coordinate system

2.2 Radio propagation

2.3 Characteristic quantity, function and basic idea of radio positioning

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Scenario in Positioning

MS

mx

1x

2x

3( )x

mobile station (MS) observation area

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Scenario in Radio Positioning

AP

AP 1

AP 2

MS

BK

mx

1x

2x

1APx

B

APKx

2APx3( )x

mobile station (MS) observation area

Examples for Anchor Points (AP): Base station, Beacon-Node, Radio Beacons, WLAN access point, GPS satellite, …

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Radio propagation - Overview

multipath propagation usually, direct path (line of sight path, LOS)not always present will arise problems later…

time variance movement of MS and obstacles/objects; Doppler

V

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Radio propagation - Example: Urban Scenario

• multipath propagation! • no Line of Sight (NLOS) !

Source: J. Maurer, W. Wiesbeck et al., Universität Karlsruhe (TH)

MSAP

Building

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Radio propagation – Attenuation

3 components of attenuation:

attenuation with distance, path loss

slow fading

fast fading

Path loss

Slow Fading

Fast Fading

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Radio propagation – Path loss (1)

2

2

isotropic effectiveradiation antennadensity area

4 4t

r t rPP g gd

2

4r

t rt

P cg gP df

Free space propagation:

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Freespace path loss (in logarithmic scale dB):

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Path loss in real world channels without LOS:

Physical explanation:

In case of mobile radio channels without LOS path, Pr decreases with a higher power of d:

Poynting vector at location of scatterer:

Received power:

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slow fading

fast fading

Path loss

Slow Fading

Fast Fading

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Radio propagation – Slow Fading (1)

Vmobile station

base station

Physical Phenomenon:

d

Physical Effect: Shadowing

Received power decreases ifLOS is disturbed by obstacle

For typical mobile radio systems isthe dynamic of slow fading in theorder of seconds

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Statistical properties:

Propagation loss (in dB)

is typically Gaussian distributed

am is the average propagation loss, that depends on the distance d

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Physical Explanation:

1 2 Wa a a a Total attenuation: Total attenuation in dB:

1 2

random variables

dB dB dB dBW

W

a a a a

Central limit theorem:

The PDF of a sum of a large number of independent random variables converges (under some weak side conditions) to a Gaussian PDF!

For a sufficiently large number of W, the total attentuation (in dB) is Gaussian distributed

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For given Pt the PDF of Pr is log-normal,slow fading is termed log-normal fading

2

10

2

10log10 1 expln10 22

t

r

PmP

raa r

ap P

P

Exercise: Derivation of PDF for log-normal distribution,Derivation of average received power Pr

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slow fading

fast fading

Path loss

Slow Fading

Fast Fading

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Radio propagation – Fast Fading (1)

Physical Phenomenon:

Physical Effect: Multipath propagation and constructive / destructivesuperposition of waves

Variations if MS moves in a very small area, distance in the order of half a wavelength

Variation due to fast fading are frequency-dependent

For typical mobile radio systems isthe dynamic of fast fading in theorder of milliseconds

Constructive superposition:

Destructive superposition:

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Statistical properties:Transmitted signal:

Total received signal:

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Derivation of PDF for Rayleigh distribution (1)

Problem:

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Amplitude is typically Rician (A0≠0) or Rayleigh (A0=0) distributed

is the mod. Bessel function

of 1st kind and zero order.

Exercise: Derivation of PDF for Rayleigh / Rice distribution

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Radio propagation – Description as LTI System

Source: H. Rohling, Universität Hamburg-Harburg Karlsruhe

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Radio propagation – Description as LTV System

Source: H. Rohling, Universität Hamburg-Harburg Karlsruhe

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Characteristic Function

PositionCharacteristic

Quantity

Characteristic Function

measured,calculated

mx

m x 1,..., M

M

M

m m

Examples for characteristic quantities: channel impulse responses, signal propagation times, channel attenuation, …

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Positioning:

Determine measurement of the characteristic quantityEvaluate the inverse function

of the characteristic function 1m

ˆˆ x M

MM̂

mx̂

Position Estimator

1 M̂

mx

Basic Principle of Positioning

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Bounds to Positioning Accuracy

Sharpness of the characteristic function (Cramér-Rao bound) 1:1 mapping of the characteristic function ?Accuracy of the knowledge of the characteristic function Accuracy of the measurement of the characteristic quantity

Positioning Accuracy:

MM̂

probabilistic approach to positioning

random errors !

mx

mx

mx

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Probabilistic Positioning

Position Estimator

M̂

-200-100

0100

200-200-100

0100

200

0

1

2

3

4

5

6

x 10-5

mˆp x M

1/mx2 /mx

probabilisticposition

estimator

Maximum-a-posteriori-Estimation (MAP) :

m

m mˆˆ arg max p

xx x M

mx̂glob. maximum at

Alternatives: Minimum-Variance Estimation, ML Estimation, …

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Minimum-Variance Estimation

Objective: Choose estimated position such that themean is minimized

mx̂ 2

m mˆˆE x x M

m

2m m m

ˆˆ ˆarg min E

xx x x M

m mˆˆ Ex x M

Minimum-Variance Estimation (MV) :

Exercise: Derivation of MV estimation

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Special Case: Indirect Positioning

mx̂

Indirect Position Estimator

M̂estimation

of geometricquantities

geometrybased

positionestimator m

ˆp x M

or

Tough direct determination of PDF dueto imperfect knowledge of system and errors

Alternative: model based indirect positioning

mˆp x M

Examples for geometric quantities: distances, distance differences, …

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Summary

Radio Propagation: Scattering, reflection, shadowing, diffraction Multipath propagation, LOS and NLOS scenarios Time variance of radio channel Path loss due to distance Slow fading due to shadowing Fast fading due to multipath propagation, constructive and destructive superposition

of waves

Radio Channel description:

Basics Principle of Radio Positioning: Characterisitc quantity and characteristic function Theoretic bound of positioning accuracy Probabilistic model due to random errors Probabilistic positioning Indirect positioning as special case

Description as linear time-variant system (LTV) in the equivalent lowpass domain

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