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## ILRS SPWG Meeting (Nice 2003)

ILRS ad-hoc Signal
Processing Working Group Meeting

Nice, France

Monday 7th April
2003

Graham Appleby

This report contains notes from the meeting and verbatim comments received afterwards from David Arnold who was not able to attend in person.

**Centre of mass (CoM) values for geodetic satellites**

There now exist CoM corrections for the principal spherical geodetic satellites LAGEOS, ETALON and AJISAI for the three main tracking system types, single-photon, C-SPAD and PMT/MCP (Otsubo & Appleby, 2003). The corrections have been evaluated as functions both of numbers of photoelectrons and of data clipping procedures for the single-photon detectors and as functions of pulse width for the 'leading edge' (PMT/MCP) systems.

Ideally each system would remain strictly in its principal domain; e.g. a single photon system should make careful return-rate calculations in realtime and use attenuating filters in order to maintain the single photon return level; a C-SPAD system should endeavour to work always at a particular return level. But in practice, for the APD systems at least, this is not achieved, since local transparency variations, pointing variations, satellite distance variations, etc., prevent anything other than single photon return levels being maintained. The MCP systems, with discriminating electronics, do have more control since they are usually set to reject returns of fewer than some preset number of photoelectrons, but they do not discriminate with respect to maximum numbers of photoelectrons. Also for these systems there is little dependence of CoM on return level, the appropriate CoM value being determined by system pulse width, which itself is dominated by CfD delay loop settings.

But in order to take best advantage of the detailed CoM information now available, some measure of estimated return level should be available in the ILRS normal point data taken by all the tracking systems. This information would supplement the general information on detector characteristics that is available in each site's log file. The information would probably only need to be fairly 'course' and averaged over each normal point bin. A suggestion was to use a four-point code to indicate whether the normal point was on average observed at single photoelectron (code 1), very high level of return (code 4), or somewhere in between (codes 2 or 3).

**So there are several actions on the SPWG as a result of these
discussions**

- Is there sufficient information in the site logs to assign
each station an 'average' CoM correction for each of the three
geodetic satellites?

- If not, why not, and what further site information do we need?
- From whom can we get the data.

- As a refinement, and principally for the APD systems, can
we get the stations to compute average return levels over
each normal point bin?

- How should that information get into the NP data?

- Will need a recommendation to the DFP WG.

- How should that information get into the NP data?

Can we compute CoM values for STARLETTE (and STELLA) - request
from Frank Lemoine. **Following this request, Reinhart Neubert
has commented that the standard value (75 mm, as computed by David
Arnold) is most likely accurate within 2 mm for all ranging systems**.
This information has been communicated to Frank Lemoine. Toshi
Otsubo has also agreed that it would be interesting to compute
the values using his technique, given that precise characteristics
of the STARLETTE cubes can be obtained.

**Towards getting all available LRA information on the ILRS website**

A start has been made, in collaboration with Mark Torrence. Links to CoM correction tables, taken from Otsubo & Appleby, 2003, are in place for the spherical satellites, and some details are given of satellite-fixed coordinates of LRA phase centres for some other satellites (see http://ilrs.gsfc.nasa.gov/satellite_missions/center_of_mass/ )

Actions on SPWG regarding the information on the website:

- Review the available information
- Where missing details are known (coordinates of LRA, attitude algorithms, etc.), make them available to Mark Torrence.

**Comments received on draft of this report from David Arnold:**

I was very happy to see the recommendation to add signal strength to the information provided with laser ranging data. I have always felt the signal strength in photoelectrons should be measured for each point. I realize this is not going to happen, but I still feel it would be very valuable for all systems, including single pe systems. I do not trust measurements of peak amplitude because of variations in pulse shape and the lack of an absolute system of units.

I feel that ND filter level should also be recorded in order to monitor the cross section of satellites and make comparisons with predicted signal levels. I have just done some comparison of calculated and predicted cross section for some satellites in response to a request from Jan McGarry. The results do not agree for TOPEX. I am led to wonder whether someone neglected to account for neutral density filters in calculating the measured cross section.

It may seem unnecessary to measure signal strength for single pe systems, but I would like to make the following points: In order to avoid multi-pe signals, return rates must be kept very low. This has a number of disadvantages. It reduces the amount of data. It increases the ratio of noise pulses to real data. It makes acquisition more difficult and uncertain (unless larger signals are used to acquire before reducing the signal level).

Simulations that I have done indicate that the largest "time walk" is between 1 and 2 photoelectrons, as one would expect. Even a small number of undetected double returns can bias the average range measurement in single pe systems. There is no good solution to this problem with present systems.

If it were possible to operate closer to a return rate of unity without introducing a bias, it would solve a lot of problems. It seems to me that it might be possible to use double pe returns without creating under certain conditions. If the width of a single photoelectron is small compared to the output pulse width or the pulse spreading by the array, 2 photoelectrons will probably not overlap most of the time. In this case there is no pulse distortion. Even if the photoelectrons do overlap, the average range correction for a double return (with or without occasional overlapping) can be determined by computer simulation. Any error introduced by occasional overlapping of photoelectrons in double returns might be less than the bias introduced by undetected double returns.

As I have said before, it seems to me that some of the signal could be sent to a capacitor to integrate the current vs time which should be quantized. I am sure an electrical engineer could come up with a method for measuring the exact number of photoelectrons using this or some other approach.

Another problem created by having a high ratio of noise pulses
to real data is bias introduced by data clipping. For the spherical
satellite you now have measured return pulse shapes. Since the
distance between the centroid and the tail, and between the centroid
and the leading edge is known, why not use this information instead
of a 1, 2 or 3 sigma screening criterion?

In other words, if (O - C) > 0, the limit would be larger to
allow for the tail. If (O - C) < 0, the limit would be smaller
since a photoelectron cannot be received before the known leading
edge. A 3 sigma criterion might be necessary in the initial iterations
when residuals are large. The final iterations in the orbital
solution could use a fixed criterion for each satellite.

I have theoretically computed CoM data for Starlette (and Stella which is identical). The calculations were published in 1975. It would be interesting to compare theoretical and measured CoM values.

I was happy to see that the single photoelectron CoM value on the website for LAGEOS (242 mm) is in good agreement with the theoretical values I published in 1978. The constant fraction value of 251 mm is also in good agreement. I was concerned about the fact that the measured pre-launch data for LAGEOS stated that the centroid range correction for LAGEOS is 251. Your measurements show that this is not correct for the centroid.

The range corrections for various type of ranging systems and parameters that are now available on the website should give much greater accuracy for the data from these satellites. The range correction is also a function of velocity aberration. At some point I hope it will be possible to include this effect also.

If I understand correctly, the SPAD produced a signal that is largely independent of signal strength. It seems to me that this is a disadvantage in trying to deal with signal strength problems. It is impossible in principle to have an exact measurement of the exact number of photoelectrons.

I see that tests have been done for the SPAD by splitting off some
of the light and measuring its intensity. This is certainly an
improvement and should give good results for strong signals. Perhaps
the range correction could be calibrated vs signal strength rather
than trying to maintain a constant signal level as suggested in
your notes. If the signal strength is low there will be a difference
between the SPAD device and the device that measures the light
intensity due to photon quantization. However, the error can be
reduced by averaging.