In my previous post I looked at the BGDs and related topics for the Galileo satellites. We saw that satellite E24 has atypically large BGDs, but everything else seems fine and consistent with that satellite. However, Bert Hubert from galmon.eu shows that several RTCM sources broadcast a clock correction of around -5ns for E24. Here we look at the possible causes for that correction, and discuss whether it might be problematic.
Tag: gnss
About Galileo BGDs
A few days ago, Bert Hubert, from galmon.eu noticed that Galileo satellite E24 was somewhat special because it had unusually large BGDs. This raised a number of questions, such as what is the physical interpretation of BGDs, what they have to do with broadcast clock models, and so on.
In this post I will explain a few basic facts about BGDs and related topics, following an approach that is perhaps different to that of the usual GNSS literature, and also study the current values for the Galileo constellation. People who know all the details about the BGDs or who just want to see a few pretty plots can skip all the first section of the post.
Ranging through the QO-100 WB transponder
One of the things I’ve always wanted to do since Es’hail 2 was launched is to perform two-way ranging by transmitting a signal through the Amateur transponder and measuring the round trip time. Stefan Biereigel DK3SB first did this about a year ago. His ranging implementation uses a waveform with a chip rate of only 10kHz, as it is thought for Amateur transponders having bandwidths of a few tens of kHz. With this relatively slow chiprate, he achieved a ranging resolution of approximately 1km.
The QO-100 WB transponder allows much wider signals that can be used to achieve a ranging resolution of one metre or less. This weekend I have been doing my first experiments about ranging through the QO-100 WB transponder.
Earth rotation corrections for range and range-rate in GNSS
In GNSS, when considering the propagation of signals from the satellites to a receiver, it is easier to work in an ECI reference frame, since (ignoring the gravitational potential of Earth), light travels in straight lines in ECI coordinates. However, it is often common to do all the calculations in an ECEF frame, as the final goal is to obtain the receiver’s position in ECEF coordinates, and the ephemerides also use ECEF coordinates to describe the satellite positions. Therefore, a non-relativistic correction needs to be applied to account for the fact that light no longer travels in straight lines when one considers ECEF coordinates. Often, the correction is done as some kind of approximation. These types of corrections are known in the GNSS literature as the Sagnac effect.
The goal of this post is to discuss where the corrections arise from, the typical approximations that can be made, and how these corrections affects the calculation of range and range-rate. I didn’t find a good source in the literature where this is described in detail and in a self-contained way, so I decided to write it myself.
DOP geographical distribution for the Galileo and GPS constellations
I have been wondering about how the DOP for the different GNSS constellation varies geographically, owing to the different number of satellites and constellation geometries. There are many DOP maps, such as this Galileo HDOP map by the Galileo System Simulation facility, but after a quick search in the literature I couldn’t find any survey paper that made a comprehensive comparison. The closest thing I found to what I was looking for was Consellation design optimization with a DOP based criterion, by Dufour etl. This was published in 1995, so it compares the GPS and GLONASS constellations with prototypical constellations such as the Walker delta using different parameters, but it doesn’t mention Galileo, which wasn’t even planned back then.
Therefore, I have decided to do my own simulations and compare the DOP for the Galileo and GPS constellations. Since the actual distribution of the satellites can differ substantially from the slots designated in the constellation, I am considering both the theoretical reference constellations and the real world constellations, as taken from the almanacs at the beginning of 2020. This post is a detailed account of my methodology and results.
More about the Galileo broadcast clocks oscillations
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.
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.
Measuring the Allan deviation of a GPSDO with an SDR
A few days ago I tried to measure the QO-100 NB transponder LO stability using my DF9NP 10MHz GPSDO. It turned out that my GPSDO was less stable than the LO, so my measurements showed nothing about the QO-100 LO. Carlos Cabezas EB4FBZ has been kind enough to lend me a Vectron MD-011 GPSDO, which is much better than my DF9NP GPSDO and should allow me to measure the QO-100 LO.
Before starting the measurements with QO-100, I have taken the time to use the Vectron GPSDO to measure the Allan deviation of my DF9NP GPSDO over several days. This post is an account of the methods and results.
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.
Galileo outage revisited
A few weeks ago, a presentation by Octavian Andrei, of the Finnish Geospatial Research Institute, appeared in YouTube showing technical details about the Galileo constellation outage that happened between July 12 and 16. In the presentation, Octavian studies the navigation data gathered by a geodetic receiver in Metsähovi, showing anomalies in some of the parameters of the navigation message, such as the \(\text{IOD}_{\text{nav}}\), the SISA (signal in space accuracy) and the DVS (data validity status).
Back in July, I looked at the navigation data from the outage in this post, where I used navigation RINEX files collected by the IGS MGEX to study changes and anomalies in the navigation message. In that post I concentrated on July 16 and 17, to show what happened as the system was coming back online. Octavian has discovered some very interesting anomalies that happened before the incident, on July 10 and 11. Indeed, the first anomaly happened at 13:40 GST on July 10, well before July 11 21:50 GST, when the navigation message stopped being updated.
Thus, in view of Octavian’s discoveries, I have revisited my study, including also data from July 10 and 11, and paying special attention to the \(\text{IOD}_{\text{nav}}\) parameter, which can be seen to have the most interesting behaviour in Octavian’s presentation.