Correction Factors and Scaling with permanent counters

[VeloCityPlanner]

Greetings everyone,

This may be a silly question, but when dealing with applying correction factors to permanent counters, does best practice recommend applying the correction factor to the grand total or to each individual hour and then adding all the hours? Do the fractions add up and create discrepancies?

[Frank Proulx]

Hello,

If you're just using a multiplicative correction factor (i.e. best
estimate = A*counter observation), it doesn't matter. Volume estimate =
sum over i (A*C_i) = A* sum over i (C_i), where C_i is the counter's
observation in period i. In other words, if it's just being multiplied
you can factor out (in an algebraic sense) the correction factor.

However, if you're using some sort of non-linear correction like
volume_i = A*C_i + B*(C_i)^2, this wouldn't work. This might be the case
if you find your counter performs substantially worse in high
volume-intensity periods, for example.

Cheers,
Frank Proulx
UC Berkeley