Centre-of-mass correction issues:Centre-of-mass correction issues:Toward mm-ranging accuracyToward mm-ranging accuracy

Toshimichi OTSUBO otsubo@nict.go.jp

National Institute of Information and Communications Technologyand

Graham M APPLEBYgapp@nerc.ac.uk

NERC Space Geodesy Facility

10 June 2004, 14th International Laser Ranging Workshop (San Fernando)

???

Difficult challenge:We want to achieve mm accuracyusing targets designed for cm accuracy.

+

s a te llite

c entre

(pu ls e trans mittedfrom a ground s ta tion)

(re tro -re flec tedpuls e )

c o rne r c ube

re flec to rs

(imagina rypu ls e re flec ted a t the c entre )

c entre -o f-mas s c o rrec tion x 2

Very Important:High “accuracy” is NOT equivalent to small single-shot rms.

42.0

8.5AJ IS AI

fused silican=1.46

no coatingon back faces

(front)

17.1

LAGEOS

fused silican=1.46

no coatingon back faces

38.1

27.8

27.0

ETALON

fused silican=1.46

alminium coatingon back faces

19.1

(side)

Response functionResponse function

Red: n=1.0Green: n=2.0Blue: best-fit

LAGEOS

AJISAI

ETALON

Centre-of-mass correction

for high energy system … approx. at leading edge

for single photon system … approx. at centroid

System-type-dependent centre-of-mass System-type-dependent centre-of-mass correctioncorrection

LAGEOSFrom Otsubo and Appleby, JGR, 2003.

0.25 0.24 (m)

251 “Standard”257.6r - nL

2453-sigma

242w/o clipping

245Ideal S.P. (<0.1 p.e.)

2491 p.e.

257100 p.e.

25610 p.e.

2561 ps

252100 ps

248300 ps

2441ns

2423ns FWHM

SingleSinglePhotonPhoton

C-SPADC-SPAD

PMTPMT(LEHM)(LEHM)

2502-sigma

2472.5-sigma

247249250252 (n=2.0)

245Hx

System-type-dependent centre-of-mass System-type-dependent centre-of-mass correctioncorrectionAJISAI

SingleSinglePhotonPhoton

C-SPADC-SPAD

1.00 0.95 (m)

1010 “Standard”1028r - nL

9763-sigma

962w/o clip

977Ideal S.P. (<0.1 p.e.)

9901 p.e.

1023100 p.e.

102010 p.e.

10221 ps

1017100 ps

1009300 ps

9931 ns

9763 ns FWHM

9852.5-sigma

9972-sigma

PMTPMT(LEHM)(LEHM)

977 (n=2.0)9879931002

985Hx

From Otsubo and Appleby, JGR, 2003.

System-type-dependent centre-of-mass System-type-dependent centre-of-mass correctioncorrectionETALON

SingleSinglePhotonPhoton

C-SPADC-SPAD

0.60 0.55 (m)

576 “Standard”613r - nL

5563-sigma

552w/o clip

558 Ideal S.P. (<0.1 p.e.)

5731 p.e.

613100 p.e.

60810 p.e.

6121 ps

607100 ps

598300 ps

5781 ns

5623 ns FWHM

5802-sigma

5642.5-sigma

PMTPMT(LEHM)(LEHM)

570575582593 (n=2.0)

565Hx

From Otsubo and Appleby, JGR, 2003.

The most guilty “error”The most guilty “error” … intensity-dependent range bias … intensity-dependent range bias

C-SPAD users:“C-” does NOT mean “compensated” for actual targets!Control the return energy (preferably at single-photon).

MCP-PMT users:Probably not so serious as C-SPAD, but not sure at 1-mm accurate level.

Likely to be elevation-angle-dependent error

We should test at each station! cf: following 2 speakersWilkinson and Appleby (C-SPAD at Herstmonceux)Carman, Noyes and Otsubo (MCP+CFD at Yarragadee)

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Apr 03To

Feb 04

ResidualResidualanalysisanalysis

Residual analysis “bias vs intensity 2003-04”: suResidual analysis “bias vs intensity 2003-04”: summarymmary

The intensity dependency is underestimated in this analysis.Intensity-dependent Elevation-angle-dependent absorbed in parameter estimation

Overall verdictsSingle photon systems (Hx, and Zimm also?) behave very good.MCP systems also good, but a few mm trend seen.C-SPAD systems have “the stronger, the shorter” trend.

… typically p-p 5 cm for AJISAI, p-p < 1 cm for LAGEOSGraz kHz … difficult to tell too many “9999” data.

Very Important:DO NOT be relieved even if your station looked ok.

How guilty of corrupting geodetic resultHow guilty of corrupting geodetic resultis intensity-dependent range bias?is intensity-dependent range bias?

Adding artificial bias to raw LAG1 NP data (50 days: 21 Apr to 9 Jun 03)Station: Yarragadee (7090), Hartebeesthoek (7501) and Graz (7839)Intensity = number of single-shot returns per NP bin

StrongWeak 25% 25%

48 shots/bin 223 shots/binYarragadee

109 shots/bin 322 shots/binHartebeesthoek

65 shots/bin 234 shots/binGraz

+5 mm -5 mm

How guilty of corrupting geodetic How guilty of corrupting geodetic result is intensity-dependent range result is intensity-dependent range bias?bias?

Orbit determination with Pos+RB estimation,with and w/o introducing artificial biasDifference

artificial-original

Height +7.4 mm

Range bias (orig +5.1 mm)

+4.2 mm

Height +8.4 mm

Range bias(orig +8.9 mm)

+4.8 mm

Height +6.0 mm

Range bias(orig +0.1 mm)

+4.9 mm

Yarragadee

Hartebeesthoek

Graz

-5 mm

+5 mm

Conclusions: mm accuracy from cm targets? Conclusions: mm accuracy from cm targets?

LAGEOS is a “large” satellite now!

Eliminate the intensity-dependent bias!

C-SPAD does not fully compensate for satellite returns.MCP systems are more robust, and single-photon systems are the most.

Intensity robustness should be TESTED at EVERY station (cf. following 2 speakers)Strong-Weak test for LAGEOS, AJISAI and any LEO with small CCR array. Please report at the future workshops!

This bias contaminates the geodetic solutions.

Do not go for small single-shot rms.Do not go for many single-shot returns.

For the single photon systems, we can calculate the centre-of-mass corrections.