ERRORS IN GNSS

Gabriella Povero
Navigation Technologies

GNSS Training
AIT, Bangkok
14 -18 January 2019©2019 LINKS

1INTRODUCTION
Ideal measured pseudorange

k k  ( xsk  xu ) 2  ( ysk  yu ) 2  ( z sk  zu ) 2  c   tuz

 rk  c   tuxy

Other errors impact on the measurement:k  rk  c  ( tk   tu )  I k  Tk   kCourtesy gAGE
©2019 LINKS

2ERROR SOURCESErrors affecting GNSS performance depend on several factors:➢At system (space-control) level:oSelective availability (off since May 1st, 2000)

o Number of satellites that can be seen from the receiver and theirgeometry (DOP)o➢➢Error in the orbits, ephemerid, clock etc.

During the path from satellite to receiver:oIonosphere effects

oTroposphere effects

At receiver level:o Receiver noiseo Multipaths, interfering signals, etc.

©2019 LINKS4

REMARKS ON ERRORS SOURCES• Navigation solution and error
budgets are valid under thehypothesis of errors:• statistically independent fordifferent SVs• error modeled as random
Gaussian variables with zeromean• Under these hypotheses thestandard deviation of the total
pseudorange error is: UERE 2 j [m]Segment ErrorSource

PPS
1[m]SPS1[m]

SPS(no SA)
1 [m]

Sat. ClockSpaceSV Orbit
S.A.
Other

Control

Ephemeris
Other
Ionosphericdelay
Tropospheri
c delay

Userj

Receiver
NoiseMultipath

OtherUERE©2019 LINKSTOTAL(rss)5

POSITIONING ERRORSThe Gaussian Distribution
LEP©2019 LINKSLEP = Linear Error Probable = length ofline segment containing 50% of fixes (1D)

6POSITIONING ERRORS
Accuracy Indexes

LEP

Circular Error Probable (CEP) = 0.75 drms
Distance root mean square error (drms) =©2019 LINKS

𝝈𝒙 𝟐 + 𝝈𝒚 𝟐
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ACCURACY AND PRECISION• Accuracy: measure of how close a point is to its true position• Precision: measure of how closely the estimated points are inrelation to each otherHighPrecision
Low Accuracy©2019 LINKS

LowPrecision
Low Accuracy

HighPrecision
HighAccuracy
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SYSTEM (SPACE-CONTROL SEGMENT) ERRORS
System errors (clocks,ephemerides, codes, …)

Atmosphericerrors

Doppler
Low SNR

Multipath

Othersystems
Urban canyon
Bluetooth
WLAN

Interferenceand jamming©2019 LINKS

IndoorUWB

9ERROR SOURCES
Errors affecting GNSS performance depend on several factors:➢At system (space-control) level:
oSelective availability (off since May 1st, 2000)

o Number of satellites that can be seen from the receiver and theirgeometry (DOP)o➢➢Error in the orbits, ephemerid, clock etc.

During the path from satellite to receiver:oIonosphere effects

oTroposphere effects

At receiver level:o Receiver noiseo Multipaths, interfering signals, etc.

©2019 LINKS

10Instantaneous Error (meters)

THE EFFECT OF SELECTIVE AVAILABILITY
160140120100806040200-20-40-60-80-100-120-140-160-180-200

Colorado Springs, Colorado

2 May 2000

Horizontal Error (meters)
Vertical Error (meters)

ANALYSIS NOTES▪ Data taken from Overlook PAN Monitor Stationequipped with Trimble SVeeSix Receiver▪ Single Frequency Civil Receiver▪ Four Satellite Position Solution at Surveyed Benchmark▪ Data presented is raw, no smoothing or editing

012345678910Time of Day (Hours UTC)©2019 LINKS

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DILUTION OF PRECISION
The impact of the pseudorange error on the final estimated position depends
on the displacement of the satellites

UEREUncertainty region©2019 LINKS

12DILUTION OF PRECISIONGDOP  g11  g22  g33  g44(x, y, z, and time)

Partial factors can be defined

Position Dilution of Precision (x, y, z)

PDOP  g11  g22  g33

Time Dilution of Precision (time only)

TDOP  g44

Vertical Dilution of Precision (z only)

VDOP  g 33

Horizontal Dilution of Precision (x and y)

HDOP  g11  g22©2019 LINKS

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DOP TYPICAL VALUESDOP Value

RatingDescription<1IdealThis is the highest possible confidence level to be
used for applications demanding the highest
possible precision at all times.

1-2

Excellent

At this confidence level, positional measurements
are considered accurate enough to meet all but themost sensitive applications.

GoodRepresents a level that marks the minimum
appropriate for making business decisions.
Positional measurements could be used to makereliable in-route navigation suggestions to the user.

2-55-10©2019 LINKS

Moderate

Positional measurements could be used forcalculations, but the fix quality could still beimproved. A more open view of the sky isrecommended.

10-20

Fair

Represents a low confidence level. Positional
measurements should be discarded or used only toindicate a very rough estimate of the current
location.

>20

Poor

At this level, measurements are inaccurate by asmuch as 300 meters with a 6 meter accurate device(50 DOP × 6 meters) and should be discarded.

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Error [m]GDOP#Satellites

REAL GDOP BEHAVIOUR

Time [s]©2019 LINKS

15OTHER EXAMPLES©2019 LINKS

16EPHEMERIS AND CLOCK ERRORS➢ Ephemeris data
Transmitted every 30 seconds, but
the information may be up to twohours old➢ Atomic clocks
Noise and clock drift errors
The navigation message contains corrections for ephemeris andclock errors and estimates of the accuracy of the atomic clock.
They are based on observations and may not indicate the clock's
current state.
These problems tend to be very small, but may add up to a few
meters of inaccuracy©2019 LINKS

17REMEDY FOR EPHEMERIS AND CLOCK ERRORSFor very precisepositioning (e.g., ingeodesy), these effects
can be eliminated byDifferential GPS.
Precise Point Positioning (PPP) is an enhanced single point
positioning technique using precise orbits and clocks instead ofbroadcast data.
(Applications: precision farming, hydrography, deformationmonitoring)
These data are freely provided by, e.g., the IGS (International GNSSService). A detailed list of products provided by IGS can be found on
http://igscb.jpl.nasa.gov/.
©2019 LINKS

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RELATIVISTIC EFFECTS➢The satellite clock drift is affected by the relativistic effect. In GPS thesatellite clock frequency is adjusted so that the frequency observed by
the user at sea level has the nominal value.
➢The user has to take into account a relativistic periodic effect due tothe eccentricity of the satellite orbit.

•half of the error is due to the periodic change in the speed of thesatellite relative to the ECI (Earth Centered Inertial) frame•

the other half is caused by the satellite’s periodic change in its
gravitational potential➢ Another relativistic effect is due to the rotation of the Earth during
the signal transmission (Sagnac Effect). During the propagation time, aclock on the Earth’s surface will experience a rotation with respect tothe reference frame©2019 LINKS

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ERROR SOURCES
Errors affecting GNSS performance depend on several factors:• At system (space-control) level:• Selective availability (off since May 1st, 2000)• Number of satellites that can be seen from the receiver and theirgeometry (DOP)• Error in the orbits, ephemerid, clock etc.
• During the path from satellite to receiver:• Ionosphere effects• Troposphere effects• At receiver level:• Receiver noise• Multipaths, interfering signals, etc©2019 LINKS

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ATMOSPHERIC ERRORS
System errors (clocks,ephemerides, codes, …)

Atmosphericerrors

Doppler
Low SNR

Multipath

Othersystems
Urban canyon
Bluetooth
WLAN

Interferenceand jamming©2019 LINKS

IndoorUW
B

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IONOSPHERE AND TROPOSPHERE©2019 LINKS

While radio signals travelwith the velocity of lightin the outer space, theirpropagation in theionosphere andtroposphere is slower.
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IONO-TROPO ERROR COMPENSATION•Single frequency RX:
Ionospheric errors are corrected bycalculations (information in thenavigation message).

• Dual frequency RX:Different frequencies areinfluenced in different ways by theionosphere.
By using two frequencies (e.g, L1and L2) it is possible to eliminate
this inaccuracy by calculation.
The error caused by the troposphericeffect is smaller than the ionosphericerror, but cannot be eliminated bycalculation. It can only beapproximated by a general calculation
model.
©2019 LINKS

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IONOSPHERE➢ Ionosphere is a region of ionized gases (free electrons and ions)➢ Ionization is caused by the sun’s radiation (day/generation –night/recombination)➢ The propagation speed of a radio signal depends on the number of freeelectrons in its path (electron density)➢ Ionosphere is a dispersive medium (refractive index depends on thesignal frequency)
Courtesy gAGE (UPC)

Total electron content (TEC) isdefined as the number of electrons in a
tube of 1m2 cross section from receiver tosatellite

Example of Vertical TEC
Map©2019 LINKS24

IONOSPHERIC ERROR➢ Ionosphere induces a delay on pseudorange measurementI 40.3  TEC
f2➢ The delay in phase measurement has same magnitude but opposite sign
➢ In dual frequency receivers, it can be estimated and compensated for:f 12f 22  2 2 1  2 2  2
f1  f 2
f1  f 2*➢ In single frequency receivers, models are used to partially compensate theerror induced by the ionosphere:©2019 LINKS▪

Klobuchar model in GPS▪

NeQuickG model in Galileo

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TROPOSPHERE• It is extended up to 60 km from theEarth surface• Troposphere is a non dispersive
medium for frequencies up to 15 GHz• Refractivity: N=(n-1)×10-6 where n is therefractive index – it is related to thedelay of signals – n depends ontemperature, pressure, humidity• It can be split in dry and wet refractivity(dry gases and water vapour)©2019 LINKS

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TROPOSPHERE•

Dry (hydrostatic) delay:– Varies with local temperature andpressure– Predictable and slow variation– Error of about 2.3 m for satellites atzenit and 10 m at lower elevation– Can be modeled from surface
temperature and pressure•©2019 LINKS

Wet delay:– Depends on weather conditions(clouds, water vapour)– Varies faster and randomly (difficultto model)– Error of about tens of cm27

TROPOSPHERE MODELS• In general, troposphere delay depends on signal path and can bemodeled as a function of satellite elevation• Several models available in literature• Geodetic-oriented models more accurate, more complex, needsurface data
• Navigation oriented models less accurate but do not needmeteorological data•

Sastamoinen model•

Hopfield model•

TropGrid model (ESA)©2019 LINKS

Courtesy gAGE (UPC)28REMARKS ON ERRORS SOURCES
Segment

Space

Control

User

UERE©2019 LINKS

Error Source

PPS
1s [m]SPS
1s [m]SPS(no SA)
1s [m]

Sat. Clock

3.0

3.0

3.0

SV Orbit

1.0

1.0

1.0

S.A.

-

32.3

-

Other

0.5

0.5

0.5

Ephemeris
prediction

4.2

4.2

4.2

Other

0.9

0.9

0.9

Ionospheric delay

2.3

5.0

5.0

Tropospheric delay

2.0

1.5

1.5

Receiver Noise

1.5

1.5

1.5

Multipath

1.2

2.5

2.5

Other

0.5

0.5

0.5

TOTAL
(rss)

6.6

33.3

8.029

CONTACTGABRIELLA POVEROgabriella.povero@linksfoundation.com
www.navsas.eu
www.ismb.it

LINKS FOUNDATION
Via Pier Carlo Boggio 61 | 10138 Torino+(039) 011 2276 150©2019 LINKS@linksfoundation

linksfoundation@linksfoundation

linksfoundation.com

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