VieVS User Workshop

9 – 10 September, 2013

Vienna

Vie_LSM and Vie_LSM_scan

(version 2.1)

Kamil Teke and Johannes Böhm

VieVS User Workshop 2013 2

“vie_lsm” is a module of “VieVS”, which

estimates geodetic parameters with least

squares adjustment from VLBI observations.

All the parameters can be estimated as

continuous piece-wise linear offsets

(CPWLO) in sub-daily and daily temporal

resolution.

Introduction

VieVS User Workshop 2013 3

Estimated parameters are:

Clocks (offset (cm), rate (cm/day), quadratic term

(cm/day2), CPWLO (cm)),

Zenith wet delays (cm) as CPWLO,

Troposphere gradients (cm) as CPWLO,

EOP (mas and ms) as CPWLO,

Antenna coordinates in TRF (cm) as one offset per

session or as CPWLO,

Source coordinates in CRF (declinations in mas

and right ascensions in ms) as CPWLO.

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continuous piece-wise linear offsets (CPWLO)

11 2 1

2 1

( )i

t tx x x x

t t

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Partial derivatives of the delay model w.r.t. a sub-daily parameter

1 1

( ) ( ) i

i

xt t

x x x

2 2

( ) ( ) i

i

xt t

x x x

1 1

1ji

j j

t tx

x t t

2 1

ji

j j

t tx

x t t

1j jt t t

VieVS User Workshop 2013 6

bc is a zero

vector

(due to NNT

and NNR

conditions

(1). (15).A A sm A sm

(1). 0

0 (15).

H sm

H

H sm

0

T T T

HA PA H P H CN

C

T T

H

c

A Poc H P ochb

b

design matrix of real observation

equations

design matrix of pseudo-observation

equations (constraints)

x N b 0 ( ) / ( )T T

H H H obs constr unkm v Pv v P v n n n

parameter vector

(estimates)

0xK m N variance-covariance matrix of the

estimates

7

Estimation Settings

The first solution is meant to remove large clock offsets (and rates and

quadratic terms) for numerical reasons. (Clock offsets can be several

kilometers.)

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Parametrization for least squares

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VLBI clock error

2

0 1 0 2 0( ) ( ) ( )poly

clk t t t t t quadratic polynomial for

each clock

11 2 1

2 1

( ) ( )CPWLO

clk

t tt x x x

t t

CPWLO for each clock e.g. at

each UTC integer hour (t1 and

t2)

( ) ( ) ( )poly CPWLO

clk clk clkt t t total clock error at epoch t

10

Parametrization for relative clock errors

This combination adds relative constraints on the clock offsets.

Actually, observation equations are added to the design matrix which

tell that the difference between two adjacent piecewise linear clock

offsets is zero a certain standard deviation . (These constraints are

mainly important to bridge gaps without observations to avoid

singularity of the normal equation system.)

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Troposphere delay

6

0

10 ( ) ( )

tropH

trop h wN s N s ds

( , ) ( ) ( ) ( )cot( ) cos( ) sin( )trop h w w n eZHDm ZWDm m G G

reduced from

observations a

priori to the

adjustment

estimated estimated estimated

12

Parametrization for ZWD and gradients

13

Parametrization for EOP

If you want to estimate one constant value per session, the

recommendation is to set the parameterization as shown

above. Very strong relative constraints of 1e-4 m(a)s/day take

care that the estimates are the same over the session.

Example: The session is from 18 UT to 18 UT. Then, three

piecewise linear offsets are set up for each EOP. (They are set

up a midnight before the session, at midnight during the

session, and at midnight after the session.) The strong

constraints take care that all three estimates per session are

the same.

14

Parametrization for Station Coordinates

15

Parametrization for Source Coordinates

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Session-wise parameterization

17

Session-wise parameterization

18

Session-wise parameterization

19

Session-wise parameterization

20

Session-wise parameterization

Case 1: NNT/NNR (one coordinate offset per session)

21

Session-wise parameterization

Case 2: Fix some station coordinates (one coordinate offset per session)

22

Session-wise parameterization

Case 3: Fix some station coordinates (CPWLO coordinates)

23

Session-wise parameterization

24

Session-wise parameterization

25

Session-wise parameterization

26

vie_lsm scan-wise update

27

Scan-wise update of normal equation system

Claudia Tierno Ros, Third VieVS user workshop, 11-13 September, 2012

28

Scan-wise update of normal equation system

Claudia Tierno Ros, Third VieVS user workshop, 11-13 September, 2012

29

Command window – vie_lsm

30

Command window – vie_lsm

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Conclusions

vie_lsm corrects clock breaks and detects outlier

observations.

vie_lsm provides SINEX input and datum free

normal equations for global solutions (vie_glob).

CPWLO estimates of VieVS are in a good

agreement with those derived from other space

geodetic techniques.

Scan-wise update of normal equation system

ensures a successful process of the future

sessions with lots of observations.

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Thank you so much

for your attention!