Eric and I have mostly been working on multiplet scoring: estimating the likelihood that a set of signals is something other than noise. This is work in progress and I'll report on it later.

I had some new ideas about finding non-barycentric multiplets. Recall that these are things we'd expect to hear from transmitter that sends a constant frequency and is in an accelerated reference frame: e.g. on the surface of a planet that's orbiting a star, or in orbit around such a planet, or in orbit around a star.

The signal from such a transmitter would reach us with a time-varying Doppler-shift, reflecting the change in the transmitter's radial velocity in our direction. The amount of this shift, and its rate of change, would depend on various physical parameters: the size and period of the orbit, the rotational period, and so on. Eric has established plausible ranges for these parameters, based on what's known about actual stars and extrasolar planets. Given these ranges, the frequency range of a non-barycentric signal could be as much as 200 KHz.

In terms of finding non-barycentric multiplets, the general situation is that we're processing a particular pixel (sky location). This pixel was observed some number of times, on the order of 10. Each observation is on the order of 10 seconds. We're considering a particular 200 KHz frequency band. Within each observation there may be signals sprinkled across the entire band. This is shown here:


Gray bands are observation periods. The wiggly line is the kind of transmission we're looking for; the fast wiggles are rotation, the slow wiggles are orbit.

Out of all these signals, we're trying to find a subset (a "multiplet") that

• Have frequencies and chirp rates that are consistent with their originating from a transmitter of the form described above;
  
• Has the highest "score", subject to being consistent. More signals, and higher-power signals, means higher score.
  

"Consistent" means, roughly speaking, that frequency and chirp rate don't change too fast. In a short period of time (like an observation) the frequencies of our signal should be in a fairly narrow window (like 250 Hz), and the chirp rates should similarly close.

Our previous way to finding non-barycentric multiplets enforced this consistency within observations, but not between observations. There might, for example, be two observations a minute apart, and we could select groups of signals from each one that are internally consistent, but the groups are so far apart in frequency or chirp rate that they couldn't possibly come from the same physical source. Thus, our list of top-scoring non-bary multiplets could be full of multiplets that can't actually be ET. We don't want this.

I pondered this and came up with what I think is a good approach. It's based on a "consistency function" C(S1, S2) where each S is a combination of (time, frequency, chirp rate). C returns either true or false according to whether S1 and S2 could originate from the same source, given our assumptions. Eric found this function empirically, by looking at the signals we generate for birdies.

The idea of the new algorithm is: as we form a multiplet, we discard signals as necessary to maintain consistency; and in deciding what to discard, we try to keep the higher-power signals.

The details: given a set of signals as described above, we process them in time order, one observation at a time. For each observation we've processed, we keep track of

• the set of signals we selected from that observation (this set is always consistent);
  
• the median frequency and chirp rate of that set;
  
• the total power of signals from that set.
  

To process a given observation, we first find a consistent subset S of its signals; we do this in the same ways as before. We compute the median frequency, chirp rate, and time of signals in S, and their total power X.

Then we go through previous observations, and see which of them are consistent (based on the function C) with S. We compute the total power Y of the observations that are inconsistent with S. If X < Y, we need to discard S; keeping it would require discarding more valuable signals. So we discard S, then try to find a consistent subset of the remaining signals. If there are none, we move on to the next observation. Otherwise we repeat the above.

If X > Y, we keep S, and remove the signals from the previous observations that conflict with S (if there are any).

I implemented this and tested it; it seems to work. For the pixels I looked at, it found occasional inconsistencies, and it removed the right things when these occurred.

I hasten to say: this is a crude, heuristic algorithm. It rules out extreme cases of inconsistency with our physical assumptions, but it doesn't actually guarantee that the resulting multiplets are consistent. A better algorithm - which maybe I or someone else will devise someday - would do some kind of data-fitting over the range of orbital/rotational parameters, and would find multiplets that are consistent with a specific set of these parameters.

By the way: as far as we know, this is the first-ever attempt to find persistent non-barycentric signals.

I remembered Einstein@home search for pulsars. They try to fit the data with a set of potential orbital parameters. This is very similar to SETI@home's search, except that SETI@home data is not continuous, more like Asteroid@home. It might lead to increased sensitivity as well as ability to making a statement about "no SETI signal with power greater than X", something like Einstein@home publications about continuous GW.