Determining the radiant of a meteor using Graves radar (II)

One year ago, I published my experiences about determining the radiant of a meteor using Graves radar. If you read it (I hope you really did it) a question arises immediately: What about three receivers? Fortunately David, amateur astronomer and ham radio operator also known as EA1FAQ joined the team so we could answer this question.

Figure 1: Transmitter and receivers location

We had some doubts. Could the same meteor head echo be received simultaneously by three different stations? some calculations and simulations were made with many interesting results.

Previous simulations

The first question to answer is: When we will be able to receive the same meteor from the three receiving stations? Obviously, the shower radiant must be above the horizon for the four participants: the three observers and Graves transmitter. Also the received doppler must be inside the receiving window: we use common ham radio SSB receivers with a bandwidth about 3 kHz. Because we tune at 143.049 MHz, we are able to detect doppler values between +2000 Hz and -1000 Hz. Dopplers outside this range will not be audible.

Also, the meteor must fall in a point with favorable head echo reflection for the three receivers. At this moment we don't know what geometric properties must have this reflection, but analyzing the recordings is quite clear that head and tail reflections have different reflection geometry.

We don't know (yet) which is this geometry, but we know how to calculate doppler from a falling meteor anywhere in earth coming from any point in the sky, so some simulations can be made.

We started the recording in late August, so there were two major showers ahead of us: Leonids and Geminids. Moving the Leonids radiant through the sky as the day goes, and calculating the doppler from a leonid meteor falling in (almost) every point of the common area between the 3 observers and Graves we could calculate this map:

Figure 2: Leonids common reflection points

The green area is where a falling Leonid produces a head doppler between +2000 and -1000 Hz at the three receiving stations. As you can see, it is a very large moving area, but... Graves don't use a omnidirectional antenna. It uses a sectored directional antenna so the area it illuminates is much much smaller: it has been drawn in red. Only meteors falling at this red area can produce simultaneous head echoes at the three receivers. It was nice, because numbers says it can be possible to receive simultaneous meteors at the three receivers (geometric reflection considerations apart)

What about the Geminids?

Figure 3: Geminids common reflection points, 17:00-19:00 UTC

Figure 4: Geminids common reflection points, 00:00-05:00 UTC

Because of the different radiant declination and lower speed, there are two periods of time when the Geminids radiant can produce detectable echoes at the three receivers, at least in theory.

Different showers, at different declinations and different speeds produce different observing times. So, the larger the area, and the longer it is active, better possibilities to detect that shower. So we calculated the possibilities for every possible radiant between declination -50º up to +90º (north celestial pole)

Figure 5: Shower detection possibilities

The X axis is the meteor velocity in km/s and the Y axis is the radiant declination in degrees. Colour represents the possibility to detect a meteor from that shower at the three receiving sites in arbitrary units. It is clear some showers are much better suited to be detected than others, just look for LEO (Leonids) and GEM (Geminids). The most interesting conclusion for this graph is the best declination for a shower for being detect (for us) is around +44º north. Also the lower the velocity, the better.

Set-up & Measurements

For file capturing and GPS synchronization we used the VLF Receiver Software Toolkit ( http://abelian.org/vlfrx-tools/ ). It works recording audio and the GPS PPS signal, and creating a stream of timestamped audio that can be sent to a remote server. At the remote server the three timestamped streams were combined into a single aligned and timestamped stream that were recorded to disk.

The included (and undocumented) utility vtping were used to automatically detect meteors in the stream, and a homemade software looked for simultaneous meteors in the three streams. In this way, the process was almost automatic. Vtping does a good job finding meteors but miss a small percentage of them, so data was also manually revised for those missing meteors.

Figure 6: Meteor 20150823-130407, example of simultaneous head echo

Once a meteor coincidence is found at the three receivers, a 10 second three channel wav file is extracted and measured. Last year, a doppler-slope measurement were made and meteor was calculated with this. We found this is not very accurate. Measuring slope with precision is very difficult in such small traces, but also don't forget those traces are not straight lines: they are curves. They appear as straight lines because the small observed trace, but in some meteors the curvature is clearly visible, so our approach this year is to match a meteor trajectory to all the observed values. This data is extracted with a FFT of the wav file. To get a higher frequency resolution, FFT bins where barycentered. This simple operation worked very well. For example, the wav from the previous image is reduced to these time-doppler values for each receiver:


Meteor 20150823-130407

     EB3FRN            EA4EOZ            EA1FAQ
  T     Doppler      T    Doppler      T    Doppler
=====  ========    =====  =======    =====  =======
5.104  1526.041    5.120  674.600    5.120  736.955
5.120  1473.333    5.136  636.982    5.152  638.205
5.136  1444.976    5.152  602.272    5.184  565.625
5.168  1345.941    5.168  548.251    5.200  520.591
5.200  1245.666    5.184  498.407    5.216  476.420
5.216  1199.000    5.200  459.280    5.232  433.713
5.232  1161.530    5.216  415.045    5.248  387.071
5.248  1104.168    5.232  367.402    5.264  332.252
5.296   962.215    5.248  324.155    5.280  290.406
5.312   910.198    5.264  280.729    5.296  254.441
5.328   867.804    5.280  242.606    5.312  212.206
5.344   814.470    5.296  201.676    5.328  177.529
5.424   556.487    5.312  162.611    5.344  125.237
5.440   500.097    5.328  106.431    5.360   83.436
5.456   447.075    5.344   62.148    5.376   35.756
                   5.360   25.835    5.392   -3.577

With these set of time-doppler values, transmitters and receiver positions, and the well know doppler formula in vectorial form:

the goal is to fit a meteor trajectory to the observed data. That trajectory must meet these requirements:

• Visible (over the horizon) from Graves and the three receivers
• Inside the area illuminated by Graves
• Height above sea level between 80 and 120 km (approx.)
• Velocity between 12 and 72 km/s
• Moving in a straight line with no appreciable (de)acceleration
• Falling from the sky (this is moving up-down)

To look for those trajectories several bounded and unbounded minimizers and solvers were tested. The best results were obtained with those based in least squares data fitting. The meteor solver works simulating a meteor at a random starting point (Mx, My, Mz) with a random velocity (Vx, Vy, Vz). The next step is to calculate the produced doppler from this simulated meteor at every receiver. Then, the least square fitting algorithm moves the meteor and varies its velocity trying to match the observed values.

Each starting point gives a different result, so we calculated every meteor using 100 different random starting points with random velocities. Many of these 100 results provide real good match to the observed doppler traces. Others don't. A real good match has a very small residuals, with RMS errors around 5 Hz, A poor match can have RMS error over 1000 Hz, so the results are sort and the one with the smaller RMS error is taken as the result for that meteor.

Because doppler was measured with bin sizes about 15 Hz wide, any RMS error under 15 Hz can be taken as an excellent result. Most meteors gave us RMS errors well under 10 Hz, and only a few had errors around 15-20 Hz. Why? Well... I suspect the lack of frequency disciplined receivers is the cause: for sure there was some hertzs between the receivers and this value was not constant over the receiving periods.

Results

We were recording during three weeks, on later August, November (Leonids) and December (Geminids). Yes, we missed the Orionids in October. Tons of individual meteors were recorded, but only a small fraction of them were simultaneous receptions. From this small fraction, an even smaller fraction produced usable / measurable doppler traces.

It's very easy to hear meteor head echoes using Graves, but when you try to listen them from three different places at the same time, soon you find the reflection is good in only one or two receivers, and almost marginal on the remaining ones. Of course there are some exceptions to this, but very few. Actually these exceptions are the meteors we could measure.

In this video you can see and hear the 43 detected meteors. Sound is mapped in this way: EB3FRN at left, EA4EOZ at center, and EA1FAQ at right channel. Use headphones for proper listening.

Video with all detected meteors. Best viewed at https://www.youtube.com/watch?v=L6TBfrrbXEI in cinema or full screen mode.

August

During August 2015 we were recording from day 20 to 23, not for catch any shower but for testing the VLF RX Toolkit, its performance and the server requirements. Even while in testing, 12 simultaneous meteors were detected:

Figure 7: Meteors received from 20 to 23 august, 2015

     Meteor        Ra    Dec    Vel    Notes
===============  =====  =====  ====  ========
20150821-015234  353.4   11.8  32.5
20150821-023050  344.6   26.8  31.6
20150822-025755  343.4   13.0  33.6
20150822-030628  343.1    2.9  38.9
20150823-035554  359.8    6.1  40.3
20150822-042554    0.7   12.9  36.3
20150822-064444   55.1   -9.9  67.8
20150823-021411  344.0   12.4  32.3
20150823-041014    0.2    8.7  37.1
20150823-043010  355.0  -10.3  35.7
20150823-130407  141.9   24.3  36.8
20150823-130555  136.7   13.2  27.8

During those days only two main radiants were active Perseids (PER) and Kappa Cygnids (KCG). None of the detected meteors came from them, they all seem to be sporadic meteors. But two of them from different days came from the same radiant at Pegasus' neck with the same velocity around 33 km/s. Probably they are related.

November

On November 2015 we were recording from November 16 to 22.

Figure 8: Meteors received from 16 to 22 November, 2015

     Meteor        Ra    Dec    Vel    Notes
===============  =====  =====  ====  ========
20151117-014527   68.5   22.4  32.9  NTA?
20151118-030654   73.5   29.7  34.0  
20151118-034114   88.3   25.4  50.7  
20151119-021356   65.5   13.1  26.4  STA
20151119-051432  118.5   15.5  64.2  
20151119-072111  139.2    6.2  65.9  
20151119-075415  154.8   19.0  69.6  LEO
20151120-021917   73.8   15.2  30.8  
20151120-050516  101.9   16.9  53.1  
20151120-055431  126.5   11.9  67.6  

Four main radiants were active those days: Leonids (LEO), Alpha Monocerotids (AMO), North Taurids (NTA) and South Taurids (STA). 10 meteors were received those days. The most interesting was this one, the 20151119-075415, a really strong head echo only meteor we suspected it was a Leonid. Later the calculations showed it was really a Leonid.

Figure 9: 20151119-075415 meteor, a confirmed Leonid meteor (click to enlarge)

Another meteor, the 20151119-021356 was a South Taurid: According to the 2015 IMO Calendar, on November 19 the STA radiant is around, Ra  = 64º, Dec = +16º with a velocity of 28 km/s. Just compare these values with the ones we obtained.

Figure 10: 20151119-021356 meteor, a confirmed South Taurid (click to enlarge)

The 20151117-014527 meteor could be a North Taurid, but it is somewhat away from the radiant position and the calculated velocity is about 5 km higher.

Figure 11: 20151117-014527 meteor, probably a North Taurid (click to enlarge)

December

On December 2015 we were recording from December 14 to 20.

Figure 12: Meteors received from 14 to 20 December, 2015

     Meteor        Ra    Dec    Vel    Notes
===============  =====  =====  ====  ========
20151214-020323   95.7   30.1  30.4
20151214-021341   99.8   33.9  36.1
20151214-030902  123.0    5.8  32.0
20151214-030948  111.1   28.9  33.1  GEM
20151214-032851  112.8   30.4  34.2  GEM
20151214-033457  112.4   29.6  33.4  GEM
20151214-033501  117.2   35.3  37.4  GEM?
20151214-044840  110.8   -7.3  42.7
20151215-083922  194.2   34.1  69.4
20151215-124645  249.2  -17.5  32.7
20151216-072325  180.6   -5.1  68.7
20151217-012634   90.4   23.1  29.8
20151218-064500  173.2   13.1  68.5  COM?
20151218-113344  238.1   16.7  40.2
20151219-055047  143.2    4.7  55.4
20151219-061611  159.2   21.6  61.5
20151219-085001  199.9   21.3  63.3
20151219-101315  208.6    3.7  61.4
20151219-123447  261.6   -3.5  32.8
20151220-015017  104.5    2.3  38.3  MON?
20151220-081955  176.6  -12.1  72.0

Some radiants were active those days, being the principal the Geminids (GEM). Three of the received meteors were Geminids, who had the radiant around Ra = 113º, Dec = +33º with an entry velocity of 34 km/s. There is a fourth possible member, the 20151214-033501, but it comes a little north-east, and a little faster to be for sure a Geminid.

Figure 13: From left to right, 20151214-030948, 20151214-032851 and 20151214-033457, three confirmed geminid meteors

The meteor 20151218-064500 is about 6º from the December Comae Berenicids (COM) radiant, and it has also a large velocity of 68 km/s (64 km/s for COM) so it is probably related to that radiant.

Similar case for 20151220-081955, who is also about 6º from the December Monocerotids (MON) radiant, with a velocity of 38 km/s (42 km/s for MON).

Conclusions

This experiment have been quite interesting for many reasons. Comparing simulations with observational data have aroused many questions we are not able to answer (yet) and some facts.

For example: we were recording simultaneously 24 hours a day during 18 days. In that period 43 simultaneous meteors were detected and measured. This means about 2 meteors per day. It is a very low rate. Some days the meteor count was just zero. Yes, zero. Keep in mind the Leonids and Gemininds were active, and peaked while observing. They are strong showers. Why the rate count is so low? The leonid meteor was detected one day after the peak, and the geminid ones were detected in a 30 minutes interval almost at the peak of the shower. No other meteors were detected from these radiants in the remaining days, even while their respective showers were still quite active.

With this information it is somewhat incredible that 90% of the detected meteors were sporadic ones. Maybe this discrepancy is related to the operating frequency. Despite Graves enormous output power, 143 MHz is a very high frequency for meteor detection, and ever higher for the weak head echoes. Probably the head echoes received with Graves are not meteors, but fireballs or at least very large meteors.

The reflection mechanism for the tail is very well known. But the head reflection seems to have its own reflection mechanism or geometry: It is very common to receive really strong head echoes with no traces of tail echoes, for example, the 20151119-075415 leonid. But other meteors present head echoes and tail echoes, for example the three received geminids. And many meteors present only strong tail echoes with no signs of head echoes. We can't figure out what is the geometric conditions needed to receive a head echo.

There is one interesting thing we have noticed. There is a strong correlation between the time of a detected meteor and its radiant right ascension as you can see in this image:

Figure 14: Meteor radiant vs UTC detection time.

This means the detected meteors have their radiants roughly at the same area of the sky when they are detected. Plotting all those radiants in azimuthal coordinates as seen from Graves at their respective detection times give us this image:

Figure 15: Detected radiants as seen from Graves at their respective detection time.

This graph is quite interesting. All detected meteors came from azimuth from 200 to 250 degrees. This 50º span is a perfect match with the azimuth of the receivers as seen from Graves: 209º for EB3FRN, 227º for EA4EOZ and 235º for EA1FAQ. Also, the detected meteors came from elevations from 20 to 70 degrees: another 50 degrees span. Probably these two similar spans are related to the head echo reflection mechanism. It seems the relative positions of Graves and the three observers become some kind of high directional meteor sensing device able to detect only meteors moving approximately along the TX-RX direction.

Although it is very tempting to dream with an amateur network of meteor radiant determination using Graves, the truth is this is not a very effective method and it is strongly biased. From a total of 43 meteors detected, 5 came from a known shower, another 4 probably too, and the remaining 34 meteors were sporadic ones. Don't forget those showers were active and peaked during the observations. We have no explanation for this low detection rate.

There is no doubt restricting meteors to those received simultaneously by the three receivers reduces the chance to detect any given meteor, so a question arises immediately: What about trajectory fitting with two receivers? Or even one receiver?

Well... it is possible to fit a meteor trajectory to the doppler trace observed by just one receiver. But you only need to rotate that trajectory along the axis determined by the line connecting TX and RX sites to get infinite trajectories producing the very same doppler trace. Also there are many symmetries who do not help at all. ( maybe some useful information could still be extracted, but not immediately: further study will be needed to confirm this)

At first sight, two receivers should be enough for trajectory determination. But tests are not conclusive about this. Every one of the 43 detected meteors were calculated three more times using only two receivers: EB3FRN-EA4EOZ, EA4EOZ-EA1FAQ and EA1FAQ-EB3FRN. Some times the meteor resolved with two receivers had the same radiant as resolved with three receivers, but some times it doesn't. Why?

Maybe three receivers are really needed to determine unequivocally a meteor trajectory. Or maybe just two receivers does not provide enough data to fit a trajectory with confidence. We don't know which one of these two possibilities is the correct one.

Finally, we must conclude that it is possible for amateurs to calculate meteor radiants using doppler only measurements using signals from Graves radar, but it is a strongly biased and incredible ineffective process, nowhere close to any professional meteor detection radar, like for example CMOR.

In this post you will find more details about the process with the utilities needed to solve a meteor by yourself.

Acknowledgments

I wish to thank to:

• David Cardeñosa, EA1FAQ, for joining the group and allow us to do this experiment.

• Iban Cardona, EB3FRN, for his interest and their selfless disposition of resources

• Iban's computer, the one we affectionately call "The Cray" (a computer with more cores, CPUs and RAM that I could remember) for running our complex simulations and calculations in just an evening.

• Julio Castellano, for his infinite patience and for being the mathematical brain in this experiment.

without any of them, this experiment couldn't have be done at all.

Miguel A. Vallejo, EA4EOZ