1

GPS processing. Sat05_82.ppt, 2005-12-05.

1. Directly from the observations

2. From differences (especially if vectors between points are to be determined)

(1) Is flexible, no requirements about same satellites or sam epoch

(2) Can only be used for shorter distances

2

GPS Integer-ambguities, Sat05_82.ppt, 2005-12-05.

One more frequency will help (is comming)Methods:• Geometric• Combination of measurements• Search in integer space• Combined

(1) N fixed at beginning, and is kept fixed. Waves are counted. 1.-differences used to eliminate N

(2) Regarded as integer: 2521.08 -> 2521.00Closest integer used

3

Search in integer space. Sat05_82.ppt, 2005-12-05.

.Software will tell how much better chosen solution is compared to next-best.

4

Cycle-slips. Sat05_82.ppt, 2005-12-05.

Due to:

Obstructions

Large ionospheric activity

Multipath

Low height angle

Interference

Sloping antenna

Errors in processing

5

Cycle-slips. Sat05_82.ppt, 2005-12-05.

If station coordinates and orbits well known then one may follow how double differences change.

AtmosphtRtRtRtRttr pi

qi

pj

qj

pqij )()()()(

1)()(

:subtractedposition andorbit from computed Ranges

6

GPS Accuracy, DOP. Sat05_82.ppt, 2005-12-05. Accuracy depends on instrument range error, σr

And on geometric configuration of satellites. Expressed using ”dillution of precision”, DOP.

..

7

DOP. Sat05_82.ppt, 2005-12-05.

..

22

*

PDOPGDOP

time,*

position D-3 ,*

al vertic,*

horizontal ,*

:expression General

TDOP

TDOP

PDOP

VDOP

HDOP

DOP

rT

rP

rV

rH

r

8

DOP computation. Sat05_82.ppt, 2005-12-05.

.

)(

...

..

.C

:obst independen if where

matrix. 4 x 4 ,C

matrix covariance-Variance

22

12XX

11XX

ZZYYXXrP

tt

ZtZZ

YtYZYY

XtXZXYXX

Tr

T

qqq

q

qq

qqq

qqqq

AA

APA

9

H and V DOP. Sat05_82.ppt, 2005-12-05.

Rotation of coordinate system needed:Local East, North, Up

.T

zz

yzyy

xzxyxx

B

q

qq

qqq

B

BXxzyxx

B

..

.C

:matrix covariance- variancedTransforme

),,,( scoordinate Local

sinsincoscoscos

0cossin

cossinsincossin

xx

10

Error measures. Sat05_82.ppt, 2005-12-05.

2-D accuracy: Distance Root Mean Square

Probability of being in a circle with this as radius between 63 % and 68 %.

Sometimes multiplies with 2:

Circular radial error: 95 % - 98 %.

Circular probable error: 50 %

3-D accuracy: Mean radial Spherical error (MRSE):

22DRMS

222MRSE h

11

Earth Rotation. Sat05_82.ppt, 2005-12-05.

We must know Earth rotation:

The Earth moves while the signal is send:

'

sin'cos',sin'cos'

1".about or m 33

iseffect so m/s, 500about rotatesEarth

066.0)/103/(102

on time.transmissi ,87

ZZ

XYYYXX

ssmm

e

12

Relativistic effects on the clocks. Sat05_82.ppt, 2005-12-05. Special theory of relativity: velocity dependent

General theory: Potential difference Earth - Satellite

Main part the same for all GPS satelites (same distance from the Earth):

MHz 9954510.2299999

: tochangedFrequency

s/day.38.3 ChangeHz0045.0

:MHz 10at operatesocillator Basic

107105.1

4.45x10

1-9

10-

f

Hzff

f

f

13

Relativistic effect. Sat05_82.ppt, 2005-12-05.

Potential difference in the Orbit is not constant with respect to the Earth.

Generally corrected in Receivers. What is left disappears in relative obervations.

drift""for ns/s 0.01 and ns 70 : valueMaximal

cos10443.4

derivative-with time

sin10443.4

10

10

dt

dEEAt

EAet

s

s

14

Relativistic correction. Sat05_82.ppt, 2005-12-05.

15

Ionospheric delay. Sat05_82.ppt, 2005-12-05.

…. short too-Carrier

long, too:phase code from Range

:p of negative

,3.40

)1(

3.401,30.41

2

22

s s

egION

eg

ep

dsnf

dsnR

f

nn

f

nn

g

16

First order correction (Code). Sat05_82.ppt, 2005-12-05.

Range on both frequencies must be the same:

See Table 7.15 for magnitudes.

22

21

2221

,1

22

21

22

21

21

22

21

21

,22,11

)(

)(

)11

( then ,*3.40put

ff

fRRR

ff

ffRRK

ffKRRdsnK

RRRRR

ION

s

e

IONION

17

1. Order correction, Phase. Sat05_82.ppt, 2005-12-05.

)2()1()(L

:L2 and L1 Combined

L1.for advance-phase cIonospheri

)))2()2(()1()1((

)1(

22

21

212

22

1

22

0

2

12

12

2

22

Lff

ffL

ff

f

LNLf

fLNL

ff

f

LION

18

1 Frequency receiver correction. Sat05_82.ppt, 2005-12-05. Klobuchar empirical model gives 50% at middle

latitudes:

Or obtain values from GSP-observatories like CODE,Analysis centers: IGS – IAAC. Or predicted values

http://igscb.jpl.nasa.gov/components/dcnav/cddis_products_ionex.html

s.polynomial P,A,

timelocalh 14at sett -of toscorrespond

ns) 5 (night at

dayat )/)(2cos(

(ns)delay Vertical

DCT

PtADCT

T

ION

ION

ION

19

Other effects:. Sat05_82.ppt, 2005-12-05.

• Antenna phase-center variations

• Oscillator instabilities

• Receiver noise

• Troposphere

• Militaty restrictions or noise (SA)

20

GPS Advantages. Sat05_82.ppt, 2005-12-05. • High 3-D precision for both position and velocity

• Independent of weather (- magnetic storms)

• Unlimited number of users

• Precise time-transfer

• Low costs (only receiver) for 1-frequency receivers

• Resistent ot Jamming

But the system does not give physical heights !

Geoid model needed !

Users need coordinates in Local system. Datum-transformation.

21

Datum-shift. Sat05_82.ppt, 2005-12-05. (a) If datum-shift known:

GPS

GPS

GPS

GPSN

GPSN

GPSN

GPS

GPS

GPS

N

N

N

Z

Y

X

C

Z

Y

X

Z

Y

X

Z

Y

X

1

1

1

22

Datum-shift. Sat05_82.ppt, 2005-12-05. (b) Datum-shift un-known:

1. Observed with GPS in a number of points where (XN, YN, ZN ) is known

2. If only one point, Translation vector determined by taking difference

3. If two points also rotation, 3 or more points C (scale-factor)

But often only latitude, longitude and height above mean-sea-level (orthometric height) known. We need ellipsoidal height. (Geoid height needed !)

23

Datum-shift. Sat05_82.ppt, 2005-12-05. In Denmark:

KMS has established points with kown coordinates in ED1950, WGS84

Main-station: Satellite station in Buddinge

Determined in European GPS Campaigns.

7-parameter-shift not satisfactory, and does not agree if more than 2 points. Polynomials are used:

)(),(

)()(

)()(),(

)()(

)()(),(

01000

2002

2020

00101000

2002

2020

00101000

NNN

NN

NNNN

NN

NNNN

cch

bb

bbb

aa

aaa