Getting a Handle on GPS Accuracy - Iowa State University in rover position determination are due to: • Satellite position errors UERE –Ephemeris 1-5 –Clock errors 0-1.5 –Selective

Getting a Handle on GPS

Accuracy

3D Pythagorean Theorm

Accuracy Depends On: • Time spent at a location (# of fixes)

• Design of the receiver & antenna

• Relative position of the satellites (DOP)

• Rover configuration settings – Datum blunder (1-100m) -- Elevation mask (DOP)

• User Equivalent Range Error (UERE) – Stand alone GPS (10-15m -- assuming no human error)

• Correction methods – Autonomous uncorrected (5-6m)

– Differential correction (<1 – 5m)

– Phase differential

• Phase processing (10-100cm)

• Wave processing (5 mm)

Errors in rover position

determination are due to:

• Satellite position errors UERE – Ephemeris 1-5

– Clock errors 0-1.5

– Selective Availability (S/A) 0-70

• Atmospheric errors – Ionospheric 0-30

– Tropospheric 0-30

• Receiver errors – Rover Noise & Antenna design 0-10

– Multipath signal 0-1

GPS Error Types System-Wide Errors - DGPS Correctable

S/A: fluctuates of ±50m over course of few minutes

0 20 40 60 80 100

Receiver Noise

Ephemeris

Atmospherics Selective Availability

Meters

Selective Availability

• Discourages hostile forces from using GPS

• S/A - sum of two effects on L1 signal

transmitted by the SVs – Epsilon - ephemeris “fibbing” (lie about where SVs are)

– Dither - clock variations (lie about when C/A was sent)

• S/A is Largest source of Error, but… – As of May 2, 2000 (5:05 am) S/A turned off

– Probably will never be reinstated as our system is no

longer the sole provider.

Selective Availability

The reasons for SA were safety concerns.

For example, terrorists should not be provided with the

possibility of locating important buildings with

homemade remote control weapons.

Paradoxically, during the first gulf war in 1990, S/A had

to be deactivated partially, as not enough military

receivers were available for the American troops.

10,000 civil receivers were acquired (Magellan and

Trimble instruments), making a very precise

orientation possible in a desert with no landmarks.

Non-S/A Time Errors

• Relativistic time delay

• Ionospheric distortion

• Tropospheric distortion

• Multipath

Relativistic Time Delays • Arise in accordance with Einstein’s theories of relativity

– Motion/velocity of the clocks (SV’s) with respect to each other

– Rotation of Earth (receiver) gravitational frequency shifts & time dilation

– ∆ in clock altitude relative to Earth’s surface

– Direction of clock motion (approaching / departing)

• Satellites travel at about 12,000 fps while rover travels only

about 1000 fps ~Earth’s rotation

• If uncorrected would amount to almost 21 miles in 24 hours

Plot of time delay correction between 2 SV’s whose

orbits are inclined 55o from Earth’s equatorial plane &

whose orbits lie 120o opposed to each other.

Horizontal axis is altitude of SV1 above Earth’s

equatorial plane

Different curves correspond to values (diff by 60o) of

the altitude above Earth’s equatorial plane for SV2

A single time transfer: SV1 to SV2

Atmospheric Delay

• GPS PRN Signals are delayed as they

pass through the atmosphere

Ionosphere

(-electrons, + atoms, +molecules)

50-1000 km

Troposphere

17-20 km

Phase advance – of carrier

Group delay – of PRN code (signal

modulating the carrier)

≤ 30 MHz

1200-1500 MHz

Amount delay

• Time delay due to ionosphere is

inversely proportional to the square

of the transmission frequency

• Satellites transmit on two

frequencies

– L1 frequency is 1575.42 MHz

– L2 frequency is 1227.60 MHz

Note: λ = c / f 299,792,458 / 1575,420,000 = 0.19029 m

Course Acquisition Receivers

(C/A Code)

• Receive only the L1 frequency

• Typical of civilian receivers

• Must account for atmospheric delays

by modeling the current behavior of

atmosphere.

• Will reduce ionospheric error by

approximately 50%

Precision Acquisition

Receivers

(P Code)

• Receive both L1 and L2 frequencies

• Typical of military receivers

• Because of the difference in amount

of delay between L1 and L2, can use a

simple mathematical compensation

to remove nearly all ionospheric

delay

Tropospheric Delay

• Delay is larger when satellite is near the horizon

– Signal must pass through much thicker portion of

troposphere

• Delay is larger when rover is near earth’s surface – Compared to aircraft-based less atmosphere above

• Simplest mathematical correction is a function of altitude &

elevation above horizon

– 90% due to dry atmosphere modeled well

– 10% wet atmosphere not modeled well

• Zenith values at MSL (least atmos. path)

– Delay ≈ 2.3 m of error (if not modeled)

• Oblique (near horizon…most atmos. path) at MSL

– Delay ≈ 20-30 m of error (if not modeled)

Multipath Occurs when the GPS signal is reflected

off an object before it reaches your

antenna

Accuracy of GPS Depends on 2 Things:

Accuracy of the Signals Themselves

- Ephemeris data

- SV clock bias

- Atmosphere (iono & tropo)

- Multipath

- Receiver measurements

Geometric Position of the Satellites

- SV Geometry Geometric Dilution of Precision

- Ideal GDOP = 0, but is unrealistic

- Best config 3 SVs low 120o apart & 1 SV over head

Navigational Accuracy depends on

1) Average UERE between SV & Receiver

- Line of sight vector

2) Instantaneous GDOP

- Best 4 SV’s from user’s perspective

The 1 Sigma Navigation Error is approx…

= UERE X GDOP

Overall UERE from different error sources

~ 5.5 to 6.0 meters

Average GDOP ~ 2.3 to 2.4 m

giving an average error of 15.25m

Error Budgets

DOP RATING DESCRIPTION

1 Ideal Highest possible confidence level high precision

2-3 Excellent Positions accurate enough for almost all applications

4-6 Good Allows reliable in-route navigation to user

7-8 Moderate Fix quality could be used…should wait for geometry

9-20 Fair Low confidence Should disregard positions

21-50 Poor Don’t bother….stay home & read a book

Elev. = MSL

Altitude critical