How to calculate the tangential velocity?

I can't access freely to the PDF document you cite in your question, so I cannot give a complete answer to your question. However, here are some preliminary remarks:

1. The relationships you mention in your question are limited to a uniform circular motion (on a straight line, you have $a$ finite and $w = 0$).

2. In theory, you don't need $omega $, you can integrate (numerically) $ a $ over time

$a = dv / dt$,

so

$v = v_{0} + int^{t1}_{to} a dt$

But that implies monitoring the acceleration from the beginning of the trip to the finish, without interruption... (in which case $v_{0} = 0$).

3. An easier way to get an estimate of a vehicle's speed is to check the change of GPS coordinates at regular intervals and calculating an average speed based on the distance traveled during time intervals.

Here is a paper which proposes combining both approaches: https://www.researchgate.net/publication/260725857_Vehicle_speed_estimation_using_GPSRISS_Reduced_Inertial_Sensor_System

Notice that in equation 2, as the angular velocity goes to zero, the centripetal acceleration also goes to zero (as does the tangential velocity). Also in circular motion, the linear speed is the magnitude of the tangential velocity (unless the radius is also changing). The components, $v_x$ and $v_y$, both change as a function of time (unless you are letting the, xy, coordinate system rotate).

It doesn't make sense that you have a value for the centripetal acceleration $a$ while $omega$ tends to zero. Those two follow each other.

Physically, if you have a centripetal acceleration $a$ causing you to move around a curve, then you also must have a nonzero angular speed $omega$ around that curve. Otherwise you wouldn't be moving around the curve and then there wouldn't be a centripetal acceleration in the first place.

Mathematically, if you do have an $omega$ tending to zero, then $a$ will as well tend to zero. You can see that from your equation $(2)$.

$$quadomegato 0 quadRightarrow quad a=Romega^2to 0$$

And then you can't conclude that the tangential speed grows to infinity anymore since not only the denominator in your equation $(3)$, but also the numerator simultaneously tend towards zero.

$$omegato 0 quadland quad ato 0 quad Rightarrow quad v=frac a omegato,?$$