[time-nuts] exponential+linear fit

[Magnus Danielson]

Hi Jim,

On 10/05/2013 05:47 PM, Jim Lux wrote:
>> Ah. Then after the initial transient, all you want to do is estimate the
>> drift term and remove it from your data. That's not too hard to do with
>> a simple least square algorithm.
>
> yes..
OK. Then we are on the same page.
>
>  I've also made variants of ADEV
>> processing that accumulates values such that the linear drift can be
>> taken out of the ADEV without re-iterating, but in that case the
>> Hadamard does it too. When doing a least square you get frequency and
>> drift parameters and can then get a reduced sample-set for ADEV and
>> friends to chew on.
>>
>> You only need to estimate the exponential decay if your samples are
>> precious and you need to get those early samples.
>>
>
> Exactly...
>
> It's a fairly simple model.
>
> I'll have to look at a bunch of data sets and decide if the
> exponential part is something I can just chop off.  In the previous
> system, the time in the exponential part was a significant fraction of
> the total data set, but in this one it seems to be a lot faster.
> Cursory estimation by eye makes it look like out of the 2000 samples
> in the plot, the transient has died out by 200 samples.  Since the
> typical data epoch is 10s of thousands of samples, losing the first
> 200 is no big deal.
>
> That's why I was loathe to leap in and turn the full power of Matlab
> nonlinear fits into it.
Indeed. I'll have some code that probably can do exactly what you want
in plain C. Just need a few lines for the prepping of the model to suit
the needs.

Toss me a few datasets if you can.

Cheers,
Magnus