I have emulated 60 km long near 1 h lasting real travelling by a car from my home to a village house of my parents.

There is listed summary of speed profiles of particular route segments and related Excel graph.

There are listied graphs for time constants of the exponential filters 100 s ( alfa 0.99 ), 200 s ( 0.995 ) and 500 s ( 0.998 )

Right axis is for current avgspeed provided by the filter ( solid lines )

Left axis is predicted ETA in form of number of seconds since departure.( dashed lines )

Horizontal axis is time since departure in seconds.

It seems longer constants - comparable with trip length have general advantage for ETA estimation,

while shorter constants ( much shorter than trip length ) may take advantage if last miles are very different then average..

An idea hit me about an adaptive time constant of the filter,

when the filter response would get faster with approaching the destination.

Like e.g.

timeconstant = (RemaindingDistance/avgspeed) / 5 = Remainingtime / 5

( initially 12 min for 1 h trip, 2 min for last 10 min )

alfa = 1 - 1 / timeconstant