A useful technique in this kind of application is that of the first order lag,
or an exponentially-mapped moving average. I'll repeat a previous posting, for
equally-spaced samples:
MAVGT(i) = (MAVGT(i-1) * T + x(i)) / (T + 1)
where T is a selected number of samples. The moving average is simple to
compute, and does two things for you. First, it smooths the data. Second, it
tends to represent the data T units ago, if the change is linear or close to it
over T samples. Selection of thje proper T is important, of course. Several
moving averages with different Ts can be maintained for different puposes.
What we do, of course, is to compare the current data, or the current data
smoothed with a very small T, to a value which represent the smoothed values
some time back. If a big enough change is detected, we have a candidate for a
new label, and note the time. We can then check how many times in the next
(short) period of time we meet the this criterion for a new value; if we meet
the criterion say 3 times out of four, then our new label can be considered
valid, and we have recorded the time at which the new label was valid enough to
be considered. We can also reinitialize our long-term moving average now to the
new situation.
There are all kinds of variations on this theme, of course, but the above is
one approach which works for us in a hospital intensive care unit.
Hope this helps - William Siler
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