School of

Engineering

MSE, Rumc, GPS, 1

References

[1] Jean-Marie Zogg [HTW Chur], „GPS, Essentials of Satellite Navigation, Compendium“,

Document: GPS-X-02007-D, February 2009, http://www.u-blox.com/de/tutorials-links-gps.html.

Chapter 1.1: The principle of measuring signal transit time

Chapter 2.3.4: WGS-84

Chapter 4: GNSS technology: the GPS example

Chapter 7.2: Sources of GPS error

Chapter 8.2: Data interfaces

[2] GPS SPS Signal Specification, 2nd Edition (June 2, 1995),

http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm

[3] beautiful visualisation of the satellites‘ positions by HSR / ICOM

http://icom4u.hsr.ch/giove_a/index.htm

[4] Parkinson, Spilker, „Global Positioning System: Theory and Applications“, Volume I/II,

Progress in Astronautics and Aeronautics, Volume 163/164, 1996.

Terms

NAVSTAR GPS („Navigational Satellite Timing and Ranging - Global Positioning System)

is a GNSS (Global Navigation Satellite System), developed by the US-DoD in 197x and

fully operational since 1993.

Other GNSS under „development“: Glonass (Ru), Galileo (EU), Beidou/Compass (China)

GPS (Introduction)

School of

Engineering GPS-Principle

Assumptions

1. distance A between Tx is known.

2. Tx transmit synchronously,

Rx can only measure TDOA

(time difference of arrival).

Determination of positions via Time-of-Fly measurements

Conclusions

x-position (and time) with 2 Tx and

x,y,z-positions (and time) with 4 Tx

determinable!

Source: [1]

MSE, Rumc, GPS, 2

School of

Engineering

TDOA measurement by code correlation

Tx1 Tx2 Rx

D = (Δt∙c+A)/2

A

Code s1 with N chips

Tx1

Tx2

Rx

t

t

t

DSSS-modulation

(small peak-power

supports CDMA)

after correlation

with code s1

with code s2

∆τ

Tchip

Tchip

∆τ2

∆τ1

N chips

N chips

GPS-Principle MSE, Rumc, GPS, 3

Code s2 with N chips

School of

Engineering

Worldwide Reference Ellipsoid WGS-84

Ellipsoid approximates true (complex) shape of the earth

there are many different reference systems

GPS works with geocentric WGS-84 reference system

Source: [1]

cartesian coordinates

ellipsoidal coordinates (longitude, latitude, altitude) used for further processing

1° Grad = 60’ Bogenminuten.

1’ Bogenminute Breite = 1 Seemeile bzw. 1 nautischen Meile (NM) = 1.852 km.

1’ Bogenminute Länge = 1.852 km mal cos(Breitengrad).

conversion into CH-1903

coordinates required

[1]

GPS-Principle MSE, Rumc, GPS, 4

School of

Engineering

Basic equations

x,y,z,t coordinates and time of user

xi,yi,zi,ti coordinates and time of 4 satellites

(x1-x)2 + (y1-y)2 + (z1-z)2 = [c·(t1-t)]2

(x2-x)2 + (y2-y)2 + (z2-z)2 = [c·(t2-t)]2

(x3-x)2 + (y3-y)2 + (z3-z)2 = [c·(t3-t)]2

(x4-x)2 + (y4-y)2 + (z4-z)2 = [c·(t4-t)]2

4 equations (c: speed of light) and 4 unknowns

GPS-Principle

Source: [1]

MSE, Rumc, GPS, 5

School of

Engineering GPS-Subsystems

(orbital data)

1 Master Control Station (Colorado)

5 Monitor Stations world wide

3 Ground Control Stations

(with Satellite Uplink)

Source: [1]

MSE, Rumc, GPS, 6

School of

Engineering GPS-Space Segment

24 to 32 Satellites

55°

• at a height of 20‘180 km

• 6 different orbital planes

(4-5 satellites per plane)

• time of circulation ≈ 12 h

• always ≥ 4 satellites

visible everywhere on

earth

MSE, Rumc, GPS, 7

School of

Engineering

[1]

coverage area

GPS-Space Segment

Orbit and coverage area

MSE, Rumc, GPS, 8

School of

Engineering GPS-Space Segment

Link budget

25119 km (border of coverage area)

L1 (1575.42 MHz) Coarse/Acquisition (C/A-) Code for civil use

min. sensitivity

specified in [2]

[1]

MSE, Rumc, GPS, 9

School of

Engineering

Spectral power density of received signal and (thermal) noise floor

MSE, Rumc, GPS, 10

Link Budget

<= -130 dBm / MHz

-

source

bandwidth

1 MHz ≈ 1/Tchip

[1]

-174

signal before

despreading

-160

+ 14 dB

signal after

despreading

f – fL1

<= thermal noise + noise figure F

School of

Engineering Satellite-Signal

1575.42 MHz

Tchip ≈ 1 / Bandwidth

Source: [1]

MSE, Rumc, GPS, 11

t / ms 1 2 20

C/A-code C/A-code C/A-code

Tbit

1023 Tchip

School of

Engineering

32 Gold- / PRN-codes with N = 1023 chips

Generation with 2 LFSR, chip rate 1.023 Mchip/s

satellite identified by PRN-number

=> CDMA

GPS-Coarse/Acquisition-Codes MSE, Rumc, GPS, 12

School of

Engineering GPS User Segment

Correlation receiver Source [1]

(Doppler-Shift ± 5000 Hz)

Process-Gain 10·log10(1023) ≈ 30 dB

SNR = -16 dB before despreading => SNR = +14 dB after despreading

correlation time for data demodulation is 20 times longer

Gain

MSE, Rumc, GPS, 13

School of

Engineering GPS Navigation Message

Source: [1]

MSE, Rumc, GPS, 14

School of

Engineering

Navigation message contains 25 frames and lasts 12.5 minutes

a GPS-frame has 5 x 300 = 1500 bits and lasts 30 s

Subframes 1-3 are identical for all the 25 frames

subframe 1 contains clock data of transmitting satellite

subframes 2 and 3 contain ephemeris data of transmitting satellite

ephemeris data are highly accurate orbital data

a receiver has the complete clock values and ephemeris

data from the transmitting satellite every 30 seconds

Time-To-First-Fix (cold start autonomous) at least 18-36 s

=> slow start-up is a system-inherent limitation of GPS

Subframe 4-5 are different for all the 25 frames

subframe 5 contains almanac data of first 24 satellites plus health

almanac data are less accurate than ephemeris data

subframe 4 contains almanac data of satellites 25-32

and difference between GPS and UTC time

GPS Navigation Message MSE, Rumc, GPS, 15

School of

Engineering Accuracy without Selective Availability

Source: [1]

95%- or 2σ-accuracy: 100 m 95%- or 2σ-accuracy: 13 m

Deactivation of SA in the year 2000

68% or σ-accuracy: 6.5 m

MSE, Rumc, GPS, 16

School of

Engineering Improved GPS

Accuracy

90% < 10 m, artifical degradation switched off since 2000

Differential GPS

Main sources of GPS errors

effect of the ionosphere (counter measure: two frequency receiver)

multipath (mainly in urban areas)

effect of the satellite constellation (DOPs [Dilution of Precision])

transmission of

correction factors Source: [1]

MSE, Rumc, GPS, 17

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Engineering

EGNOS (European Geostationary Navigation Overlay System)

34 ground stations calculate correction signals (à la DGPS)

for GPS correction in a radius of about 200 km around the reference station

broadcast of correction signals via 3 geostationary satellites (C/A-Codes >32)

1-3 m accuracy

Improved GPS

Source: [1]

MSE, Rumc, GPS, 18

School of

Engineering Improved GPS

Achievable accuracy with DGPS and SBAS

SBAS: satellite based augmentation systems

[1]

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School of

Engineering Improved GPS

Some Location Based Services are based on satellite navigation

GPS-Rx not always „on“, e.g. because of current consumption

time to first fix (cold start): 18-36 s (missing orbital data)

Assisted GPS (A-GPS)

delivery of missing orbital data via „fast“ channel, e.g. GSM/GPRS

[1]

MSE, Rumc, GPS, 20

School of

Engineering Data Interface to Peripherals

NMEA-0183 data interface

standardized by National Marine Electronics Association (NMEA)

data telegram for serial interface

Example: GGA data set (GPS fix data)

$GPGGA,130305.0,4717.115,N,00833.912,E,1,08,0.94,00499,M,047,M,,*58<CR><LF>

MSE, Rumc, GPS, 21

School of

Engineering Time Pulse

Most GPS-Rx generate 1- 4 time pulses per s

time puls is synchronized to UTC-time

Accuracy 5 - 60 ns

[1]

MSE, Rumc, GPS, 22

GPS-time-pulse is often used to synchronize devices

in a «large» area as e.g. base stations, gliders, …

School of

Engineering Performance Data of a GPS-Rx MSE, Rumc, GPS, 23

NEO-M8 series:

12.2 x 16.0 x 2.4 mm

School of

Engineering Modernization: BOC-Modulation

Advantages higher interference robustness and bandwidth efficiency

[1]

MSE, Rumc, GPS, 24

School of

Engineering Modernization: BOC-Modulation

BOC(1,1) and BPSK(1) have minimal impact on each other

Source: [1]

MSE, Rumc, GPS, 25

School of

Engineering GPS-Modernization

2. and 3. frequency for civil applications

compensation of ionosphere errors!

after 2013

integrity-signals, Search-and-Rescue-Functions

Source: [1]

MSE, Rumc, GPS, 26

School of

Engineering GPS-Simulator: An Example MSE, Rumc, GPS, 27

GPSG-1000 from Aeroflex / Cobham

• validation and test of GPS receivers

as well as navigation and tracking systems

• 3D position may be user entered

or 3D position may be dynamically simulated

• simultaneous GPS/Galileo simulations

antenna coupler

School of

Engineering

GNSS-Update: Frequency Bands see Navipedia http://www.navipedia.net/index.php/Main_Page

and some comments, https://www.zhaw.ch/~rumc/MSEwirecom.html

T. Kouwenhoven, "Gnss navigational frequency bands.png",, Jan 2011, also available at

http://www.navipedia.net/index.php/File:GNSS_navigational_frequency_bands.png

MSE, Rumc, GPS, 28

School of

Engineering Availability of GPS civil signals (Sep 2016) MSE, Rumc, GPS, 29

School of

Engineering Availability of Galileo civil signals (Sep 2016) MSE, Rumc, GPS, 30

School of

Engineering GNSS-Update: Signal-Spectra MSE, Rumc, GPS, 31

Source: Stefan Wallner, http://www.navipedia.net/index.php/GNSS_signal

School of

Engineering GNSS-Update: Signal-Spectra MSE, Rumc, GPS, 32

Source: Stefan Wallner

School of

Engineering Correlation Matrices of GPS-Satellite 9

PRN periode = 20 ms

∆f = 3100 Hz ∆f = 2400 Hz

doppler shift ∆f = 2300 Hz correlations show expected coherence

regarding the doppler shifts (∆f is

proportional to carrier frequency fc)

MSE, Rumc, GPS, 33

School of

Engineering

MSE, Rumc, GPS, 34

Real Time Kinematics (RTK)

• is a differential GNSS technique

• provides cm-level positioning performance in the vicinity of a base station

• carrier-based (rather than code-based) positioning

• see also: http://www.novatel.com/an-introduction-to-gnss/chapter-5-

resolving-errors/real-time-kinematic-rtk/

GNSS-Update: RTK

complicated process

“ambiguity resolution”

is needed to determine

the number of whole cycles.

School of

Engineering

u-blox, „u-blox bringt GNSS-Technologie mit zentimetergenauer Präzision

für den Massenmarkt“, https://www.u-blox.com/de/press-release/u-blox-

brings-centimeter-level-precision-gnss-technology-mass-market

Example: GNSS RTK module from uBlox

RTCM protocol

MSE, Rumc, GPS, 35

NEO-M8P (1-frequency Rx)

faster with multi-frequency GNSS-Rx

some m to 1-10 km