**Signal Processing Working Group**

Graham Appleby

Charter

The following Charter was created by the ILRS Governing Board at The
Hague ILRS Meeting of 1999 April.

To determine accurate laser range Centre-of-Mass corrections for a
variety of satellites, appropriate to the major observing
configurations.

In particular, to examine the corrections necessary to transform from
raw range measurements to the centre-of-mass of each satellite target,
having regard to:

-   array transfer function

-   pulse-width and signal strength

-   receiver characteristics (single photon, multi-photon, etc.)

To determine optimum processing strategies for each case.

-   location measure in forming normal points (mean, mode, LEHM,
    something else)

-   role of skewness and kurtosis measures

-   filtering and trend-removal procedures

To propose procedures for recording and reporting the data required and
used in determining and applying the corrections.

-   Data base used by Operational, Data and Analysis Centres

-   Station Information data base

-   Explicit data needed in ILRS NP and FR files

-   Format changes as appropriate

**Membership**

The following ILRS members are formally serving on the Working Group,
but other members have contributed to the work being carried out:

Andrew Sinclair, Christopher Moore, Georg Kirchner, John Luck, Leigh
Dahl, Mike Selden, Peter Dunn, Reinhart Neubert, Stefan Riepl, Thomas
Zagwodski, Toshimichi Otsubo, Ulrich Schreiber.

**Introduction**

The ILRS tracking network consists principally of three types of
observing system. Those employing multi-channel plate detectors (MCPs)
and large numbers of return photons, systems employing single photon
detectors (principally SPADs) and working close-to single-photon levels
of return, and systems using SPADs but working at greater than single
photon return levels. Modern SPADs employ a compensation circuit which
can be tuned to the laser pulse-length (Kirchner, *et al*, 1996), and
thus minimise energy-dependent time-walk effects. Most of the systems in
the network continue to produce high-precision laser range measurements,
but this very diversity amongst the systems means that to realise the
full potential accuracy in the measurements they have to be processed in
a way commensurate with the differing observing characteristics. In
particular it has been known for some time that the centre of mass
correction (CoM) to be applied to range measurements varies according to
the type of system making the measurement (Otsubo, *et al*, 1999;
Sinclair, *et al,* 1995). For example, results to date suggest that
measurements to the principal geodetic satellite LAGEOS made by a system
working at single-photon return levels are on average some 10mm *long*
on the same measurements made by an MCP system working at high return
levels. If this effect is not taken into account when the data are
analysed, such a \'range bias\' will be absorbed partly into station
height determination, the quality of which will thus be degraded. For
determination of scale, for which the SLR technique is particularly
suited, such system-dependent differences will necessarily impact on the
accuracy of a solution for GM for example. Advances in understanding
these phenomena have been made over a number of years, most notably
under the guidance of Andrew Sinclair within the EUROLAS network. This
ILRS Working Group will build on that understanding.

During this first year, the strategy has been to understand the
observing practices of some of the major systems in order to model those
processes and derive appropriate CoM corrections. This has been carried
out by involving them in the procedure and by analysing full-rate
satellite and calibration range data and statistical measures of system
stability. At an early stage the Group agreed that the aim is not
necessarily to recommend changes to current processing practices, as
this could potentially create a discontinuity relative to older data
sets from a given system.

**Summary of work carried out to date**

The Group has built on previous work in order to develop and test models
to derive CoM corrections appropriate to various observing systems for a
number of satellite arrays. In particular, the following have been
considered:

-   CoM corrections for LAGEOS and AJISAI for single-photon detector
    systems;

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-   Return energy effects for single-photon detectors;

-   Data clipping effects;

-   Statistics to monitor system stability;

-   Planar array effects (e.g. GLONASS);

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-   TOPEX/POSEIDON array model.

Full details of these studies and results to date are presented by the
originators on a web-site

( <http://nercslr.nmt.ac.uk/sig/signature.html> ) which is also
linked-to in the Working Groups section of the official ILRS web-site.
As an example of some of this work we present here in more detail some
results of determinations of system-dependent centre-of-mass (CoM)
corrections for LAGEOS.

**Principles**

To outline the principles of the ongoing work to derive
tracking-system-dependent CoM corrections for the current constellation
of laser-tracked satellites, we discuss the work being carried out for
the primary geodetic satellite LAGEOS, and specifically for systems
employing single-photon detectors. Our baseline assumption is that the
pre-launch ground tests carried out for NASA on LAGEOS-2 are applicable
only to systems using multi-photon detectors such as MCPs. The CoM
correction determined from these tests was 251mm, the value currently in
use by the analysis community to process range observations from the
entire network.

We can begin to model the laser ranging process by convolving a
(Gaussian) representation of the energy distribution of the laser pulse
with an impulse function for the satellite reflector array (LRA).
Previously both Degnan and Neubert have derived analytical impulse
functions applicable to the spherical laser satellites and which give
relative reflectivity as a function of distance from the surface of
LAGEOS. We use here the impulse function of Neubert (1996). The
resulting distribution represents the probability density function (pdf)
of the returning pulse from the satellite. We can then statistically
sample from this pdf, modelling both the efficiency of the detector and
the return energy (single or multi-photon), and further convolve with a
model of the detector and timing system response. In practice, we use
the range-distribution of measurements to a system\'s calibration target
to represent the whole-system response to a flat target. The mean value
of this response, computed according to the station\'s standard
practice, is the system\'s origin. About this origin we then convolve
the system response with the satellite impulse, obtaining a model of the
expected distribution of range measurements obtained at single-photon
return levels, as a function of distance from the surface of LAGEOS. If
we now process this model to obtain the mean value, using the same
rejection criteria as employed at the station when forming normal
points, we obtain an estimate of the mean value of the CoM correction
appropriate to that system.

This analysis has been carried out for two systems employing compensated
SPADS, namely Herstmonceux, UK, and Koganei, Japan which use similar
observing strategies. Herstmonceux works strictly at a single-photon
level of return for all satellites, while Koganei attempts to keep the
return rate reasonably low. The results of the analysis suggest that for
the Herstmonceux system a CoM correction of 240 mm is appropriate, while
for Koganei a value of 246 mm is indicated. Uncertainties in these
values are estimated to be at a level of about +/- 2 mm.

The distributions of range residuals in histogram form and our empirical
models are shown in Figure 1. The long \'tail\' in the model
distributions is characteristic of the SPAD response. Apparent in the
distributions of range residuals are the different clipping levels
employed by the systems which cause the truncation in the data with
respect to the models.

![](media/image1.png){width="2.9305555555555554in"
height="2.8048611111111112in"}![](media/image2.png){width="3.497916666666667in"
height="2.9in"}

Figure 1. Comparison of data distribution with single-photon empirical
model.

The same analysis has been carried out using calibration and LAGEOS
range data from Graz, Austria. The system employs a compensated SPAD
detector working at a multi-photon level of return, and employs a
tighter clipping level than the other two stations. The result, as shown
in Figure 2, is a more symmetrical distribution of range residuals, and
as expected a poorer agreement of the single-photon model. More work is
required to model properly this scenario, which suggests that a higher
CoM value is appropriate.

![](media/image3.png){width="3.001388888888889in"
height="2.8472222222222223in"}

Figure 2. Comparison of Graz data distribution with single-photon
empirical model.

**Presentation of Results.**

Much of the work carried out by members of the Working Group was
presented during the Colloquium on SLR-System Calibration Issues held in
conjunction with the EOS/SPIE Symposium on Remote Sensing in Florence on
20-24 September 1999. The following presentations were made:

-   Mark Torrence - GM determination from multi-satellite analysis, and
    subsequent CoM deductions;

-   Graham Appleby - Single photon model for LAGEOS;

-   Reinhart Neubert - Data clipping and return energy effects + a model
    for the T/P array;

-   Toshimichi Otsubo - AJISAI and GLONASS array functions and
    systematic effects;

-   Van Husson - Signatures in GLONASS range data;

-   Francois Barlier - Signatures in GLONASS range data;

-   Andrew Sinclair (written report) - Statistics to measure systems\'
    stability;

-   Pippo Bianco - Probable observational evidence of LAGEOS rotation by
    MLRO observations;

-   Stefan Riepl - Turbulence effects in SLR data.

Several of the presentations related to the signature effects of the
large, planar arrays on the GLONASS spacecraft. Both Husson and Barlier
presented observational evidence of systematic \'bias-type\' effects in
range residuals which increase as a function of satellite elevation.
Otsubo presented a novel explanation for the observed effects, pointing
out that SLR systems that work at high return levels will tend to
measure from the edge of the array, whilst those working at low return
levels will obtain reflections from all parts of the visible array. The
systematic difference in the range measurements from these two types of
system can amount to a relative \'bias\' of up to 15cm, this mechanism
possibly explaining the reported radial offset between laser range
measurements and microwave-based orbits for the GLONASS satellites.

The last two presentations related to interesting spin-off applications
from studies of satellite signature effects. The results presented by
Bianco on work carried out with R. Devoti, V. Luceri and M. Seldon were
obtained from analyses of range residuals from LAGEOS-2. The detection
of signature-induced modulation of the residuals was used to infer a
rotation rate of the satellite of about 11 seconds. This technique has
been successfully employed by Otsubo *et al* in the determination of a
time-series of rotation rate values for the Japanese geodetic satellite
AJISAI.

Riepl investigated the presence of range residuals \'ahead\' of the
modelled leading edge, which are evident in Figure 1 and more clearly
seen in the corresponding results from AJISAI investigations. This
slight misfit can be explained by scintillations in the received signal
strength induced by atmospheric turbulence. Due to signal-strength
statistics we cannot exclude the possibility that a SPAD-detector,
operated on average at say 10% return rate, is detecting a few returns
up to the level of 100 photons. Modelling this effect in conjunction
with a time walk model for the SPAD we find that the maximum peak shift
of the resulting signature for AJISAI is about 1cm.

**Recommendations**

From discussions during the colloquium we make the following
recommendations to other ILRS Working Groups:

-   For some current satellites (including GLONASS, ETALON, Starlette),
    this Working Group needs better information on array characteristics
    and configuration (to Missions W/G);

-   For all future missions, this Working Group must have access to
    pre-launch detailed information on composition and 3-D configuration
    of elements of the LRA. (to Missions W/G);

-   That each Site/System Log File include \'standard practice\'
    information (detector, return energy, data clipping) (to Networks
    and Engineering W/G)

**Future Work**.

Detailed information on the location and characteristics of the elements
of the GLONASS and ETALON LRA has been provided by the Russian Space
Agency, thanks to the efforts of H. Kunimori on behalf of the Missions
Working Group. This will enable more precise modelling work for these
two classes of satellites.

Impulse functions for most of the spherical satellites will be computed
by Neubert and Otsubo.

Models will be developed for multi-photon systems (MCP and SPAD).

**References**

Kirchner, G, Koidl, F. Automatic SPAD time walk compensation, proc.
Tenth Int. Workshop on Laser Ranging Instrumentation, pp 293-296. Fumin
Y, Wanzhen, C, eds, Shanghai, 1996.

Neubert, R. An analytical model of satellite signature effects, proc
Ninth Int. Workshop on Laser Ranging Instrumentation, pp 82-91. Luck, J
McK, ed, Canberra, 1996.

Otsubo, T., Amagai, J., Kunimori, H. The centre-of-mass correction of
the geodetic satellite AJISAI for single-photon laser ranging, IEEE
Trans. on Geoscience and Remote Sensing, Vol 37, No. 4, pp 2011-2018,
1999.

Otsubo, T., Amagai, J., Kunimori, H, Elphick, M. Spin motion of AJISAI
satellite derived from spectral analysis of laser ranging data. Accepted
for publication in IEEE Trans. on Geoscience and Remote Sensing.

Sinclair, A.T, Neubert, R., Appleby, G.M. The LAGEOS centre of mass
correction for different detection techniques, proc Annual EUROLAS
meeting, pp 31-36, Sinclair, A.T., ed, Royal Greenwich Observatory,
1995.