How do i increase gps speed refresh rate with “interpolated” speed?

Let's assume you get your speed at 1Hz

By comparing the speed at tn-1 and tn, you can see if you are running faster or slower or if you kept the same speed.

Assuming you have your Speedtn at instant tn in m/s, if there is a difference during the previous second, the acceleration is simply:

Atn = (Speedtn - Speedtn-1) / 1

The denominator 1 being 1 second, since this is your refresh rate (1Hz)

now that you know the current acceleration, you can infer speed before getting the new sample from the GPS :

at tn + 0.1s your speed is

Speedtn+0.1s = Speedtn + 0.1*Atn

and then similarly

Speedtn+0.2s = Speedtn+0.1s + 0.1*Atn

etc

(you could also decide that the acceleration is not constant and do the same thing by taking into account the acceleration of the acceleration...)

this is probably worth it only if the acceleration is significant enough to have an impact during 0.1s intervals