> 1) what methods of time estimation can we think of? (eg. the current 
> one-point 

> method, averaging over X amount of time...)

Without being able to add sensors into the battery itself, what we are left 
with is a machine learning problem: predict, on the basis of what can be 
measured, the remaining battery life.  The two biggest influences on this are 
the remaining capacity, obviously, and the power draw - if we draw exactly 
double the current, the battery won't last exactly half as long.  Temperature 
is another influence, but I'll leave that for now.  With these measurements, we 
then need some sort of model on which to base our predictions.  This is where 
the learning comes in: battery models depend on what battery it is, how old it 
is, how it's been used etc. etc. We cannot possibly hope to guess what a 
reasonable battery model is, but we can approximate one over time.

One way to do this is to record an average figure of how long each % of battery 
life lasts, normalising for power draw.  We'd have a figure d for how long the 
% from 96 to 95 lasts, obtained over n discharge cycles, and every time we get 
a new figure c for this (on the current discharge cycle):

d' = (n*d + c) / n + 1

Then, to find remaining time - given the current power draw - sum these figures 
from the current charge to 0%, and adjust for power usage.

(Wrapped up in that is the assumption that we can 'normalise for power draw'.  
That necessitates a separate model, using similar techniques: learn the 
relationship between the load and the discharge rate.)

So, doing this 'right' is non-trivial, which is probably part of the reason why 
it hasn't been done before.  It comes back to what Aaron was saying: there's so 
much going on, it's hard to be precise.  We could do a bit better than the 
current situation, providing estimated time remaining for current conditions, 
so at least reported time left adjusts for a USB toaster being plugged in.  We 
could also report how much time is left if the user cuts back on power usage.

It's still an open area of research, if you want to do a literature survey - 
without being able to put sensors into the battery, we're basically left with 
software models.  It's not something I have time to do myself, but I can put my 
Dr Coles hat on to field questions on the learning/prediction/AI side of things 
if someone else wants to work on this topic.

Andrew



      
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