Hi, I have data of the form:

t            x           y          trip

t1        x1+e     y1+e        A
t2        x2+e     y2+e        A
t3        x3+e     y3+e        B
t4        x4+e     y4+e        B
t5        x5+e     y5+e        B
...         ...         ...           ...

where t is time and x/y are positions in space and e is a random error
term. Trips A/B/C/etc are entirely independent from each other. I'd like to
estimate the total distance traveled for each series (trip) of points
(there are actually a few thousand points in each trip, and thousands of
trips). A loess curve fits the data nicely, essentially eliminating the
error term (I realize not exactly but it is close enough for my purposes).
However I don't see an easy way to find arc length of a loess fit (without
using an inefficient loop of distance between t1,t2 + distance t2,t3, etc.)

Thanks for any advice.

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