VieVS User Workshop

14 – 16 September, 2011

Vienna

VIE_LSM

Kamil Teke and Johannes Böhm

2VieVS User Workshop 2011

Introductionvie_lsm is a module of VieVS, which estimates geodetic parameters with least squares adjustment from VLBI observations.

Estimated parameters are: quadratic polynomial coefficients of clocks (offset in cm, rate in cm/day,

and quadratic term in cm/day2) plus continuous piecewise linear offsets (CPWLO) of clocks in cm,

zenith wet delay (ZWD) CPWLO in cm, troposphere north and east gradients CPWLO in cm, Earth orientation parameters (EOP) CPWLO in mas and ms, TRF coordinates of antennas in cm (CPWLO or one offset per session), CRF coordinates of sources as CPWLO in mas.

Since, the standard deviations of observations are so small, 1 cm added before weights are formed. Weight matrix of observations is diagonal (units are in 1/cm2). Currently, no down weighting is applied due to elevation angles of the observations.

3VieVS User Workshop 2011

Introductionestimates constrained (relative or absolute) to zero with a large or a small standard deviation (loose or tight). This is due to connect the parameters which have no observation in the corresponding estimation interval.

Realistic standard deviations should be assigned to the constraints. If not then outlier observations in small number in an estimation interval will cause unrealtistic estimates.

offset(t+1) - offset(t) = 0 ± mc_rel relative constraintsExample: mc_rel = 30 mas/day Xpol CPWLO relative constraints are loose.mc_rel = 0.001 mas/day Xpol CPWLO relative constraints are tight.

offset(t) = 0 ± mc_abs absolute constraintsExample:mc_abs = 2 mm Troposphere east gradients absolute constraints are loose.mc_abs = 0.01 mm Troposphere east gradients absolute constraints are tight.

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Continuous piece-wise linear offset functions (CPWLO)

11 2 1

2 1

( )i

t tx x x x

t t

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1 1

( ) ( ) i

i

xt t

x x x

2 2

( ) ( ) i

i

xt t

x x x

1 1

1 ji

j j

t tx

x t t

2 1

ji

j j

t tx

x t t

1j jt t t

1,2x are the estimated offsets of a parameter at epochs jt and 1jt e.g. ΔUT1 is the estimated parameter at epochs 15:00 and 16:00 UTC

Partial derivatives of the delay model w.r.t. a sub-daily parameter to be estimated at consecutive epochs

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LS Adjustment

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 THA PA H P H C

NC

T TH

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 TH 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

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VLBI clock error2

0 1 0 2 0( ) ( ) ( )polyclk t t t t t quadratic polynomial for

each clock

11 2 1

2 1

( ) ( )CPWLOclk

t tt x x x

t t

CPWLO for each clock e.g. at each UTC integer hour (t1 and t2)

( ) ( ) ( )poly CPWLOclk clk clkt t t total clock error at epoch t

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Modeling clock breaks

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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 estimatedestimated

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

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VIE_LSM GUIs

Hana will talk

about this GUI

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Thank you so much for your attention!