I'm following [a research paper](http://dx.doi.org/10.1109/PLANS.2010.5507251) ([PDF via RG](http://www.researchgate.net/publication/224154935_Accelerometer_Assisted_Robust_Wireless_Signal_Positioning_Based_on_a_Hidden_Markov_Model)), part of which is about using the accelerometer of a smartphone to assist the user's positioning via WLAN.

Accelerometer is used to determine if the user is static, slow walking or fast walking.

Here is the algorithm:

[![Pedestrian Status Determination via Accelerometer](https://i.stack.imgur.com/wFYes.png)](https://i.stack.imgur.com/wFYes.png)

For the implementation I'm using Swift on iOS. I've calculated the Euclidian Norm of the accelerometer data which I receive every second.

The problem is that I'm having difficulty obtaining $v\_a$ in the algorithm. How should I pass from acceleration to $v\_a$ in this particular situation?