This is a follow-up to my study about the Galileo broadcast clock parameters oscillations at a frequency of 1/revolution. Be advised that this short post raises more questions than answers.
Category: Space
Spacecraft and space science
Oscillations and relativistic effects in Galileo broadcast clocks
A few days ago, Bert Hubert, the creator of galmon.eu, discovered a sinusoidal oscillation in the clock drift \(a_{f1}\) parameter of the broadcast ephemerides of Galileo satellites. This variation has a frequency that matches the orbital period of 14 hours and 7 minutes. At first, I suggested that it might be caused by relativistic effects, which are given by\[-\frac{\sqrt{\mu}}{c^2}e\sqrt{A}\sin E,\]where \(\mu\) is the Earth’s gravitational parameter, \(c\) is the speed of light, \(e\) is the eccentricity, \(A\) is the semi-major axis, and \(E\) is the eccentric anomaly. In fact, the order of magnitude of the oscillations that Bert was seeing seemed to agree with this formula.
However, then I realised that this relativistic effect is not included in the broadcast clock model. It needs to be included back by the receivers. Therefore, it shouldn’t appear at all in the broadcast clock. Something didn’t seem quite right. This post is an in-depth look at this problem.
QO-100 BPSK beacon frequency measured at Bochum
The experiments about measuring the frequency stability of the local oscillator of the QO-100 NB transponder with a Vectron MD-011 GPSDO I made a few days ago indicated that the Allan deviation of the local oscillator was probably better than \(10^{-11}\) for \(\tau\) between 1 and 100 seconds. The next step in trying to characterize the stability of the local oscillator is to use a reference clock which is more stable than the Vectron.
I contacted Achim Vollhardt DH2VA asking him if it was possible to record the downlink of the BPSK beacon at Bochum, so as to have a recording referenced to the Z3801A GPSDO in Bochum, which is much more stable than the Vectron. He and Mario Lorenz DL5MLO have been very kind and they have taken the effort to make a recording for me. This post is an analysis of this recording made at Bochum.
More frequency measurements of the QO-100 NB transponder
This post is a follow up to my experiments about measuring the stability of the QO-100 NB transponder local oscillator. I am now using the Vectron MD-011 GPSDO that Carlos Cabezas EB4FBZ has lent me to reference all my QO-100 groundstation (see more information about the Vectron GPSDO in this post).
The Vectron MD-011 has an Allan deviation of \(10^{-11}\) at \(\tau = 1\,\mathrm{s}\) and \(2\cdot10^{-11}\) at \(\tau = 10\,\mathrm{s}\) according to the datasheet, so it is an improvement of an order of magnitude compared to my DF9NP TCXO-based GPSDO. I have made more measurements with the Vectron MD-011 as in my previous experiments, measuring the phase of the BPSK beacon transmitted from Bochum and a CW tone transmitted with my station. This post summarizes my results and conclusions.
DSLWP-B crash site found
Back in August, I posted about my calculations of the site where DSLWP-B impacted with the lunar surface on July 31. The goal was to pass the results of these calculations to the Lunar Reconnaissance Orbiter Camera team so that they could image the location and try to find the impact crater.
Yesterday, the LROC team published a post saying that they had been able to find the crash site in an image taken by the LRO NAC camera on October 5. The impact crater is only 328 metres away from the location I had estimated.
This is amazing, as in some way it represents the definitive end of the DSLWP-B mission (besides all the science data we still need to process) and it validates the accuracy of the calculations we did to locate the crash site. I feel that I should give due credit to all the people involved in the location of the impact.
Wei Mingchuan BG2BHC from Harbin Institute of Technology was the first to take the orbital information from the Chinese Deep Space Network, perform orbit propagation and compute the crash location assuming a spherical Moon, thus obtaining an approximate position in Van Gent X crater. Cees Bassa from ASTRON refined Wei’s calculations by including a digital elevation model. Phil Stooke from Western University first suggested to use a digital elevation model, helped us contact the LROC team, and filled in an observation request for the camera. And of course the LROC team and the Chinese DSN, since the quality of their ephemeris for DSLWP-B allowed us to make a rather precise estimate.
The LROC team has posted the images shown below, where in a comparison between an image taken in 2014 and the image taken in October the small crater can be seen.
The image of the crash is M1324916226L, an image taken by the left NAC camera. However, I can’t find this image yet in the LROC archive, so it seems this image hasn’t been made public yet.
The small crater, which the LROC team estimate to be 4×5 metres in diameter, is visible more clearly if we compute the difference between the before and after images (an idea of Phil Stooke). The figures below show this difference both as a signed quantity and as an absolute value.
Though my eye fails to see it, the LROC team says that the long axis of the crater is oriented in a southwest-northeast direction. This is consistent with the direction of the impact, since DSLWP-B was travelling towards the northeast.
For the comparison with the October 5 image, the LROC team has chosen an image taken with a similar illumination angle. In fact, the lunar phase in both images only differs in 10º, so the shadows are very similar, with the sun located towards the southwest. In fact, the newest image of the area was taken on 2018-10-16, but the one from 2014 probably gave the most similar illumination conditions.
In my post in August I included a link to Quickmap showing the estimated area of the impact. Now I have marked in red the location of the crash. For a sense of scale, the large crater northwest of the crash is some 50 metres in diameter. You can see both points in Quickmap here.
It is good to go back to all the simulations I did to have an idea of what the 328m error represents. My final simulation was done with the ephemeris from July 25, so they were 6 days old at the moment of impact. When I used the ephemeris from July 18, the position of the impact changed by 231m, while the ephemeris from June 28 yielded a change of 496m. Therefore, it seems that an error of 300m is well in line with what we could expect of the precision of the Chinese DSN ephemeris.
The impact location computed by Cees Bassa was 2786m away from my estimate. The main problem with Cees’s estimate is that the orbital model he used considered spherical gravity for the Moon, while my studies showed that it was important to consider non-spherical gravity.
I did most of my simulations with a 10×10 spherical harmonic model for the Moon gravity, but to assess whether this was enough, I also made a simulation with a 20×20 spherical harmonic model. This yielded an impact point which was 74m away from the impact computed with the 10×10 model.
According to my Monte Carlo simulations with a 1km ephemeris error, the 1-sigma ellipse semi-axes of the impact position were 876m in the northeast direction and 239m in the southeast direction. With this information, I gave an educated guess of the position error of 600m in the northeast direction and 200m in the southeasth direction. The actual impact point is 328m northwest of my estimate, so somewhat higher than my error estimate but still within the 2-sigma ellipse. This leaves me quite happy with the quality of my estimate.
Can my station measure the QO-100 NB transponder LO stability?
Following a long discussion with Bernd Zoelgert DL2BZ about the frequency stability of the local oscillator of the QO-100 narrowband transponder, I have decided to try to measure the Allan deviation of the transponder. The focus here is on short-term stability, so we are concerned with observation intervals around \(\tau = 1 \mathrm{s}\).
Of course, as with any measurement problem, the performance of the measurement equipment should be better than the “device under test”. In this case, to measure the QO-100 LO it is necessary to compare it against a reference clock which is more stable (ideally an order of magnitude better).
My whole station is locked to a DF9NP GPSDO, which is a 10MHz VCTCXO disciplined by a uBlox LEA-4S GPS receiver. That’s great to measure long-term stability, but for short-term measurements you are essentially relying on the stability of the VCTCXO, which is not so great. Therefore, the whole purpose of this experiment is first to determine whether my station is actually able to measure the QO-100 LO or not. Spoiler: it turns out the answer is “no”, as in most articles whose title is phrased as a question.
Second alpha for gr-satellites 3
Following the first alpha, I have released today v3-alpha1, the second alpha for gr-satellites 3. As I introduced in September, gr-satellites 3 will be a large refactor of gr-satellites, bringing many UI and under-the-hood changes. I am releasing a series of alphas during the development to get feedback from users. Each of the alphas focuses on a different aspect.
The second alpha is focused on input and output formats. New functionality has been implemented to allow the user to choose the input and output in a flexible way. This post describes the main features added.
First alpha for gr-satellites 3
In my last post, I introduced my plans to do a large refactor of gr-satellites, which when ready will originate a version 3.0.0 running on GNU Radio 3.8. During the development of this refactor, I intend to release alpha versions showing important new concepts or functionalities. The main goal of this is both to test if my ideas work well in practice and that interested people can start testing the new software and give feedback.
I have now published the first alpha release, which is called v3-alpha0. In this post I describe the functionality implemented in this alpha and how to use the software.
gr-satellites roadmap
In my talk at GRCon19 last week I presented the roadmap I have planned for gr-satellites for the next months and some longer term developments. The relevant slide can be seen below.
Here I will describe the roadmap in more detail, including how certain things will be done (or how to find your way among the different releases and branches in the Github repository), in order to get feedback from the community.
Ephemeris quality during the Galileo outage
I have spoken about the Galileo incident that occurred in July in several posts already: here I took a look at the navigation message during the outage, here I used MGEX navigation RINEX files to look at the navigation message as the system was recovering, and here I did the same kind of study for the days preceding the outage. Other people, such as the NavSAS group from Politecnico di Torino, and Octavian Andrei from the Finnish Geospatial Research Institute, have made similar studies by looking at the \(\mathrm{IOD}_{\mathrm{nav}}\), data validity and health bits of the navigation message.
However, I haven’t seen any study about the quality of the ephemerides that were broadcast on the days surrounding the outage. The driving force of the studies has been whether the ephemerides were being updated or not, without taking care to check if the ephemerides that were broadcast were any good at all.
The NavSAS group commented seeing position errors of several hundreds of metres during the outage when using the broadcast ephemerides. That is to be expected, as the ephemerides were already many hours old (and indeed many receivers refused to use them, considering them expired). Here I will look at whether the ephemerides were valid (i.e., described the satellite orbit and clock accurately) in their time interval of applicability.
This post is an in-depth look written for a reader with a good GNSS background.