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I have a sequence of points from GPS and OBD for some vehicles.

Each point has the instantaneous power of the engine $(P)$, the time elapsed from the last points $(T)$ and the distance traveled from the last points $(M)$. For each sequence, I'd like to calculate the efficiency in $\mathrm{kWh/km}$ of the period.

I basically have 3 ideas:

  1. $P_{\mathrm{avg}} \times \frac{\Delta T}{\Delta M}$

  2. $\left(P\times \frac{T}{M}\right)_{\mathrm{avg}}$

  3. $\left(\frac{\Delta P}{2} \times \frac{\Delta T}{\Delta M}\right)_{\mathrm{avg}}$

Idea (1) considers the sequence as a whole. Idea (2) takes the average for each point. Idea (3) does an interpolation between two consecutive points and takes the average at the end.

My question is, which one seems to be better?

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  • $\begingroup$ How far apart are these points in distance & time generally? For highway driving, one point per few seconds up to maybe a minute could yield good results, but for city driving the points would need to be once per second or more. $\endgroup$
    – Señor O
    Commented Apr 14, 2022 at 2:58
  • $\begingroup$ The GPS samples at 1 Hz regardless. Sometimes it fails, like inside tunnels, so the time difference is longer, but does not happen often. $\endgroup$
    – Rodrigo Sasse
    Commented Apr 14, 2022 at 6:19
  • $\begingroup$ The calculations seem pretty trivial, have you compared the three with the data you have? $\endgroup$
    – Kyle Kanos
    Commented Apr 15, 2022 at 15:54
  • $\begingroup$ Yes, they are very similar among them. In some cases, there's a fail in the GPS device and the difference between one point is much longer than 1 second, then I have a problem. I'd actually like to find the best model to deal with it. $\endgroup$
    – Rodrigo Sasse
    Commented Apr 15, 2022 at 16:46

1 Answer 1

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I would recommend doing the third one: $ \frac{P_1 + P_2}{2} \times \frac{T}{M} $

for each point, then taking the average of all of them, but throwing out any where:

  1. T is greater than 2-3 seconds
  2. $P_1$ isn't within 10% of $P_2$, because then the car was likely slowing down or speeding up.
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  • $\begingroup$ I personally like the third one better myself. Can you elaborate on why would you discard those? I actually want to deal with scenario 1 better (T greater), but scenario 2 is not a problem to me, it's quite common, actually. $\endgroup$
    – Rodrigo Sasse
    Commented Apr 19, 2022 at 21:28

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