[DSP-10] More EME-2 tests

[Bob Larkin]

Hi Courtney,

I've been away for the last week or so. Thanks to W7CQ for catching the 
fact I missed this e-mail!

The accuracy of the EME-Doppler corrections in the DSP-10 was felt to be 
important, as most of the special modes were quite frequency 
sensitive.  The goal was to make the Doppler error smaller than the 
spreading due to libration.  More on the accuracy in a moment.

The common way of calculating Doppler in amateur radio programs is a 
"partial derivative" method that starts by identifying the components of 
Doppler, such as the Earth's rotation and the elliptical orbit of the Moon, 
and determining these individually.  I started out this way, and kept 
adding more components, such as the changing declination of the Moon's 
orbit relative to the Earth's axis. This kept getting better, but by no 
means good enough. There are many subtle components.

I soon gave this approach up as inadequate, and went to a conceptually very 
simple method.  The distance from each of the two QTHs to the Moon center 
is calculated for two times, separated by about a second. Then the change 
in distance during this time makes the Doppler easily calculated.  This 
transfers the problem to accurate calculation of the Earth-Moon distance 
for a point on the Earth's surface.  A trigonometric series for this 
distance has been worked on by a number of people going back many years. 
Jean Meeus gathered together a very useful summary (Astronomical 
Algorithms, Willmann-Bell 1998) and that is the basis for the C program 
I  wrote for the DSP-10 (moonsun.c, and moonsun.h).  Taking differences of 
two very similar, large numbers can be problematic.  The calculations are 
all done in double precision, and experimentally have been found to be 
equally accurate for 0.1 second as for 1 second. (I did not go back to 
check the period currently being used, but it is in the 1 sec 
order-of-magnitude).  These methods should degrade very slowly, but one 
always wonders!

We have had various opportunities to check the accuracy. Most of these were 
several years ago. One example is an accuracy of 29 Hz, observed by W7LHL 
at 10 GHz ( http://www.proaxis.com/~boblark/wksig1.htm )  Some of that 
error may be caused by a few seconds of clock error.  The Doppler changes 
quite rapidly and an accurate setting of UTC is important.  In any event, 
the 2-meter error must be less than one Hz.

If anyone does EME-2, please report back the Doppler error observed. More 
measurements are always good!!

BTW, the angular accuracies end up being exceedingly good as a by-product 
of getting good Doppler. The az-el errors should be in the range of no more 
than a few thousandths of a degree.

Be sure to keep the clock on UTC.

Again any confirmations or other data on this question would be most useful.

73, Bob  W7PUA

Also, keep after that integration of the data. It is an amazing process, 
and lots of fun.


At 12:03 AM 5/16/2006 -0700, you wrote:
>I'm conducting more moon-rise and moon-set EME-2 tests at 30 watts to a 12 
>element yagi.  I've decided not to invest in an amplifier or elevation 
>rotator just yet (and struck out trying to borrow one, at least so 
>far).  I've decided, rather, to attempt a post-processing program.
>
>This will lead to more questions.  I'll try to figure it all out from the 
>source code, documentation, comments, and inspection, but if I get really 
>stuck I'll post questions here.
>
>This program will allow some editing of the data, deciding to throw away 
>more points for more reasons (good ones or arbitrary ones).  The "noise 
>blank" feature already does this sort of thing.  In post processing, I'll 
>be able to "try things" on the same set of data.
>
>I expect to need maybe a dozen of the hour-long passes I currently get 
>(quiet ones at that).  I have two in the can so far.  :-)
>
>So here's the first question.  As I sit here watching EME-2 slowly make 
>integrations (watching a pot boil....) I sometimes see features develop 
>that seem like they might be something.  Like, five adjacent bins will 
>make a nice little hill, but not necessarily centered at Cntr Sig.
>
>At first I was worried that there might be a Doppler error of a few 
>bins.  Before I continue, let me say that I've decided (after watching 
>several of these pots boil) that I'm just seeing coincidences and they 
>don't represent the signal that I'm looking for beginning to 
>emerge.  However, it did get me to wondering how accurate the Doppler 
>calculation is.
>
>I compared to a 90s vintage satellite tracking program (from AMSAT) 
>Instantrack 1.50.  IT's az/el for the moon was exactly the same to 0.01 
>degree display resolution, as far as I could tell by eyeball synchronizing 
>the clocks.  This means that the two codes agree in moon/station position 
>to a few tens of km.  The Dopplers, however, were different by several Hz, 
>varying from time to time in the month. Right now, for instance, they are 
>13 Hz different.
>
>I corresponded with one of the maintainers of IT (KB5MU) and learned that 
>IT uses what they call the "truncated Meeus model", that is, the 
>polynomials are truncated to the A + BT or first order terms.  This is for 
>computational speed where amateur-grade pointing accuracy is the only 
>competing requirement.  Your average OSCAR user would think 10-20 Hz 
>Doppler accuracy and 0.05 degrees in az/el was great.
>
>So the question is, how accurate is the DSP-10 moon Doppler 
>calculation?  I saw in the documentation that (five years ago) there were 
>errors on the order of 15 parts per billion.  That is about the same size 
>as a bin at 2 meters the way I'm set up right now (323 Hz center) so I 
>would expect to not quite be able to see that.  Is there something about 
>the formulation that might degrade over several years?  (If there's a 
>place in the code that discusses this, just point me to it.)
>
>The reason I ask is that I could put a per pass (or per point for that 
>matter) frequency offset in my program if it would help.
>
>2.3 Hz at 2 meters is 4.6 meters per second.  Not a bad precision for the 
>three-body problem!
>
>Courtney