# Operating two SLR systems at the Geodetic Observatory Wettzell: from local survey to space ties

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## Abstract

The present paper provides an overview on the design of a new Satellite Laser Ranging (SLR) system, the Satellite Observing System Wettzell (SOS-W). It pays special attention on the local survey, the determination and monitoring of the ties between the established Wettzell Laser Ranging System (WLRS) and the SOS-W. We also introduce an alternative normal point algorithm, which demonstrated fewer systematics in the resulting normal point statistics compared to the standard approach of iterative data editing. Having two highly productive SLR stations on site allows for a rigorous comparison between local survey derived ties and space segment derived ties. One-year observations to the Laser Geodynamic Satellite (LAGEOS) have been processed, and a multitude of different solutions has been calculated. The results show agreement in the sub-millimeter range with respect to the local survey.

## Keywords

Space geodesy Satellite laser ranging Local ties Space ties## 1 Introduction

The Geodetic Observatory Wettzell (GOW) is a fundamental station, where all principal space geodetic techniques, namely Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), the Global Navigation Satellite Systems (GNSS) and Doppler Orbitography and Radio-Positioning Integrated by Satellite (DORIS), are realized. The concept of such a collocation site allows the retrieval intra- and inter-technique systematic error sources.

For more than 30 years, the GOW has supported SLR with several generations of either fixed or mobile stations. Starting its operation in 1990, the Wettzell Laser Ranging System (WLRS) is the workhorse for obtaining SLR observations and the system contributed substantially to the SLR data volume, especially with respect to GNSS satellite observations. As the number of satellite missions equipped with retro-reflectors requiring laser tracking is steadily growing, it was decided to set up a second permanently operated SLR system, the Satellite Observing System Wettzell (SOS-W), to increase the data yield further and to distribute the workload over two systems. The SOS-W completed the ILRS data quality tests in January 2016 and is regarded as a high-performance laser ranging station with respect to both data quality and quantity.

In a classical approach, the local tie vectors between the individual space geodetic systems are determined by terrestrial survey (see, e.g., Klügel et al. 2012) and compared to the coordinate solutions derived from the global space geodetic observation programs. Part of the local survey network is also the external calibration targets for the SLR systems. These external calibration targets provide a sub-millimeter accurate reference distance with respect to the SLR system reference points and thus define the origin for satellite range measurements.

Apart from this classical approach, additional methods have been proposed in recent years (Kodet et al. 2018; Riepl et al. 2011), in order to allow the most fundamental space geodetic techniques to obtain system internal local tie measurements in order to remove systematic errors. To provide one way range measurements for the onsite VLBI telescopes, a microwave beacon has been set up at the Geodetic Observatory Wettzell. This device is spatially referenced to both, a retro-reflector permitting local SLR measurements for multiple SLR systems and a GNSS antenna. It should be emphasized that the microwave beacon emits timing signals derived from a common clock (Schreiber and Kodet 2018), a maser referenced frequency comb attached to a two-way delay compensated time and frequency distribution system with about 1 picosecond long-term delay stability and realized over single mode optical fibers. This concept corresponds to a ”collocation in time” and is set up to synchronize the observing systems for a sub-picosecond common time scale as part of the support infrastructure throughout the observatory. In this context and apart from the local survey, an additional local tie monitoring is implemented at the WLRS and SOS-W, where measurements are taken to local survey targets and other system reference points on a regular basis, in order to keep track of the survey target distances with respect to the SLR system reference points.

## 2 Description of the SOS-W

Minimization of all systematic error sources at or even below the millimeter level.

Optional two-color operation for day and nighttime conditions for the reduction of the atmospheric refraction uncertainty, which, apart from the center of mass correction (Otsubo and Appleby 2003), is the potentially largest systematic error source remaining in the SLR measurements.

Capability of monitoring local ties to support inter-technique combined solutions.

Support of low earth orbiting gravity field missions with an adequate data rate.

Support of navigation satellite missions.

Highly autonomous system operation.

control of the collimation of the laser beam with respect to the azimuth and elevation axis,

control of the laser beam divergence and

internal range calibrations.

For the external range calibration, a special target has been built consisting of two massive steel plates joined at a right angle. On the plate located in front of the transmit telescope, a mirror is placed in the center of the area illuminated by the transmit laser beam, as illustrated in Fig. 2. The laser beam is reflected to the diffuse reflecting second plate. The target vertex length of 120 mm was chosen such that the diffuse reflection can enter the receive telescope. Such a target is also commonly known as an optical square. To include the calibration target in the local survey, a holder for a tachymeter cube corner reflector is located right on the vertex. The difference vector from the SOS-W telescope invariant point to this calibration target provides absolute reference for the satellite range measurements, as shown in Fig. 2. Within several local survey campaigns, the distance of the invariant point to the vertex of the optical square was found to be 2196.4 mm with a parallax of \(\alpha =6.01{^{\circ }}\) arising from the transmit telescope eccentricity of 350 mm and the optical square vertex length of 120 mm.

## 3 Local survey

The determination of the local tie vectors between the geometric reference points of the geodetic space techniques requires a local network of stable reference points. In Wettzell the network consists of 27 deeply founded, double walled concrete pillars and is regularly surveyed at 2–4-year intervals. The 1\(\sigma \) uncertainties of the adjusted coordinates are mostly below 0.2 mm; however, poorly constrained points at the network perimeter may reach 0.6 mm. The repeatability, where pillar motions and different instruments are taken into account, is of the order of 1–2 mm (Klügel et al. 2012).

While non-moving reference points, like GNSS and DORIS antennas, or their reference markers can be surveyed directly, the geometric reference point of the SLR telescopes has to be restituted from numerous measurements of specific markers on the moving telescope structure. By definition, the reference point is the intersection of the azimuth and the elevation axis, also denoted as the invariant point. During the survey, one or more target prisms are attached to the telescope and their coordinates are determined at different telescope positions in azimuth and elevation, while the tachymeter is mounted to different survey pillars in view of the telescope. In this way, a point cloud is generated, where the coordinates of each target prism form a sphere surface with the invariant point in its center. If both axes do not intersect, other techniques aiming for the independent determination of the azimuth and elevation axis have to be applied (Nothnagel et al. 2001; Lösler 2009). In the case of the SOS-W, the eccentricity between both axes is in the order of 0.1 mm (Meuschke et al. 2010) proving that the application of the simple sphere adjustment is justified.

Coordinates in the local system with standard deviations of the invariant point resulting from sphere adjustments of different campaigns. The prism number indicates the use of different retro-reflector types used in the survey

Campaign | Prism # |
| East/m | North/m | Up/m | \(\sigma _E\)/mm | \(\sigma _N\)/mm | \(\sigma _U\)/mm |
---|---|---|---|---|---|---|---|---|

SOS-W 2009 | 1 | 47 | 316.9253 | 180.0425 | 616.5136 | 0.19 | 0.19 | 0.26 |

SOS-W 2012 | 1 | 40 | 316.9256 | 180.0419 | 616.5145 | 0.10 | 0.10 | 0.14 |

SOS-W 2015 | 1 | 83 | 316.9257 | 180.0424 | 616.5142 | 0.05 | 0.05 | 0.07 |

WLRS 2012 | 1 | 39 | 310.4087 | 122.0033 | 618.7181 | 0.12 | 0.11 | 0.19 |

2 | 39 | 310.4088 | 122.0035 | 618.7180 | 0.12 | 0.12 | 0.20 | |

WLRS 2015 | 1 | 39 | 310.4082 | 122.0036 | 618.7179 | 0.10 | 0.09 | 0.17 |

2 | 39 | 310.4082 | 122.0037 | 618.7180 | 0.10 | 0.10 | 0.17 |

Geocentric cartesian coordinates of the invariant points of WLRS and SOS-W, campaign 2012, after transformation into ITRF 2008, epoch 2005, including transformation errors. The last two lines represent tie vectors of the WLRS and the SOS-W calibration target with respect to SOS-W

Vector | X / m | Y / m | Z / m | \(\sigma _X\) / mm | \(\sigma _Y\) / mm | \(\sigma _Z\) / mm |
---|---|---|---|---|---|---|

4075500 + | 931780 + | 4801500 + | ||||

WLRS | 76.7254 | 5.5943 | 83.6525 | 0.33 | 0.26 | 0.36 |

SOS-W | 31.0732 | 1.8415 | 119.9512 | 0.34 | 0.26 | 0.37 |

X / m | Y / m | Z / M | ||||
---|---|---|---|---|---|---|

WLRS-SOS-W | 45.6522 | 3.7528 | \(-\) 36.2987 | |||

Target - SOS-W | 0.2861 | \(-\) 2.1712 | 0.1721 |

## 4 Reprocessing of SOS-W normal points

To overcome the convergence shortcomings an alternative procedure for the normal point calculation was implemented. As there already have been attempts to use convolution techniques in normal point processing (Riepl and Schlüter 2001) and center of mass estimation (Otsubo and Appleby 2003), an optimal (Wiener 1942) or deconvolution filter was set up. The residual data are used to form an unclipped histogram for every normal point interval centered at the mean of the data distribution. Using a strict analytical satellite transfer function provided by Rodriguez (2017), the laser pulse waveform is deconvolved from the histograms representing the measured response function. In ideal cases, the remaining deconvolved pulse would also be centered on the mean of the data distribution, showing the same skewness as the calibration histogram. Thus, the remaining data can be treated just as the calibration data, which are also edited with an iterative 2\(\sigma \) clipping procedure. Figure 5 shows a sample plot of all the wave forms involved for the determination of a normal point. In this example, it yields a mean value of 1.9 mm with respect to the trend function at a reduced rms of 9 mm in contrast to 1.2 cm for the iterative 2\(\sigma \) editing approach. To examine the results obtained from the Wiener normal point procedure, we switch again to the residual statistics shown in Fig. 6, where the normal point residuals with respect to the mean are plotted against the normal point rms in blue. Compared to the standard 2\(\sigma \) algorithm, the data points are much more confined and don’t show any systematics. The normal point data obtained with the deconvolution filter are referred to as the Wiener filter data in the following sections. Figures 7 and 8 display the results from the bias analysis performed on LAGEOS1 data obtained in 2017. For the WLRS, a constant offset of 14 mm is clearly visible in both data sets, which is associated with an incorrect invariant point correction.

Local tie vectors determined from SLR measurements to LAGEOS1 and the offset to the results from the local survey. For the solutions with free velocities the discrepancy in range of the space tie with respect to the local survey tie given in Table 2 amounts to 0.8 mm for the EDC data set and 0.3 mm for the Wiener filtered data

Solution approach | X/m | Y/m | Z/m | \(\varDelta X\)/m | \(\varDelta Y\)/m | \(\varDelta Z\)/m |
---|---|---|---|---|---|---|

Data from EDC for SOS-W | ||||||

pass wise range bias, | ||||||

free velocities | 45.6529 | 3.7535 | \(-\) 36.2991 | 0.0007 | 0.0007 | \(-\) 0.0004 |

weekly range bias, | ||||||

identical velocities | 45.6494 | 3.7530 | \(-\) 36.3033 | \(-\) 0.0028 | 0.0002 | \(-\) 0.0046 |

SOS-W fixed bias, | ||||||

WLRS weekly bias | 45.6465 | 3.7517 | \(-\) 36.3067 | \(-\) 0.0057 | \(-\) 0.0011 | \(-\) 0.0080 |

Wiener filter data for SOS-W | ||||||

pass wise range bias, | ||||||

free velocities | 45.6546 | 3.7530 | \(-\) 36.2961 | 0.0024 | 0.0002 | 0.0026 |

weekly range bias, | ||||||

identical velocities | 45.6497 | 3.7528 | \(-\) 36.3023 | \(-\) 0.0025 | 0.0000 | \(-\) 0.0036 |

SOS-W fixed bias, | ||||||

WLRS weekly bias | 45.6488 | 3.7522 | \(-\) 36.3037 | \(-\) 0.0034 | \(-\) 0.0006 | \(-\) 0.0050 |

## 5 Collocation with LAGEOS Observations

The processing of the collocation campaign between WLRS and SOS-W was performed at DGFI-TUM (Deutsches Geodätisches Forschungsinstitut) with the software package DOGS (DGFI Orbit and Geodetic parameter estimation Software) (Gerstl 1997; Bloßfeld 2015), which is developed and maintained at this institution. In a first step, we processed weekly arcs with the module DOGS-OC (orbit computation) where we fixed the coordinates and velocities of the global network to the ITRF2014 values (Altamimi et al. 2016), applying the station dependent center of mass corrections provided by the ILRS and the rules defined in the ILRS Data Handling File (https://ilrs.dgfi.tum.de/index.php?id=6). We solved for the coordinates and velocities of SOS-W (7827) and WLRS (8834) only and arc-dependent parameter like orbital elements, scaling factors for solar radiation and re-radiation, daily empirical along track acceleration and one once per revolution (sine/cosine term) cross track and along track correction per weekly arc. The earth orientation parameters were fixed to the IERS EOP 14 C04 (IAU2000A) series and applied the sub-daily oceanic tide model of Ray. For the dynamic model of the orbit processing, we followed the IERS 2010 conventions (Petit and Luzum 2010). As gravity model, we used GGM05S (Bettadpur et al. 2015) up to degree and order 30 with time variable coefficients. Non-tidal loading effects were not considered.

We had two data sets available for SOS-W, the official data set from the ILRS archive (Pearlman et al. 2002), obtained through the EUROLAS Data Center (EDC) at DGFI-TUM and the data set created with the Wiener filter, see Sect. 4, generated and maintained by the station. For WLRS, we used the data sets from EDC only. The observations cover a period from January to December 2017. For the center of mass corrections, we used 250 mm for WLRS and for SOS-W we used 245 mm for the data from EDC and 242 mm for the Wiener filtered data. For the bias analysis, we obtained for both stations one range bias value per pass and one range bias value per weekly arc in independent runs. The mean orbital fit rms uncertainty was around 1.6 cm for all versions. The mean error of the station positions is 5.0 mm for WLRS and 8.6 mm for SOS-W. In a second step, we stacked the weekly normal equations with DOGS-CS (computation and solution) and solved for the coordinates, velocities and range biases of the two respective SLR stations. In this step, we applied conditions to force the velocities of the two stations to be equal or we eliminated the range biases for one or two stations. Table 3 shows some results of the various runs we have processed.

## 6 Conclusion

A new method of normal point calculation based on a Wiener filter has been found to effectively reduce systematic errors, which were identified in the conventional 2\(\sigma \) iteratively edited data of the SOS-W. The new normal point algorithm shows also an improvement of the one year average range bias, which is reduced from \(-3.2\) to \(-1.7\) mm.

The collocation results show still discrepancies between the space tie and the terrestrial measured tie depending on the obtained range biases. In general the Wiener filtered data provides a better result for the mean station position error.

Solving for one range bias value per pass and allowing free velocities, the difference in range between the local survey tie and the space based tie is 0.8 mm for EDC data and 0.3 mm for the Wiener filtered data, which demonstrates sub-millimeter agreement. Thus, the performance of the Wiener filter can be considered as superior with respect to the standard 2\(\sigma \) editing approach. The fact that the solutions with free velocities for both stations show the smallest discrepancy with respect to the local tie difference vector suggests that there is some differential movement in station position. To gain further insight, a special collocation campaign putting emphasis on simultaneous observations is mandatory from the authors’ point of view in order to assess the comparison between local survey and space segment invariant point locations.

## Notes

### Acknowledgements

The authors would like to thank J. Rodriguez from the NERC space geodetic facility for providing the LAGEOS transfer function.

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