I understand that there were some programs that used Alphabet's (Google's parent company) API for speech recognition in Ubuntu. But, it seems that you needed to be connected to Alphabet's servers in order to use that. Presently, Alphabet cut off the use of their database.
I did come across one write up that mentioned a couple of programs for Ubuntu. But, they seemed to perform pretty poorly (low accuracy).
I want to know what the outlook is like for speech recognition in Ubuntu. My sense is that it's a tough (expensive, time consuming, and/or academic/ mentally rigorous) technology to develop and so Ubuntu is kind of at the mercy of the existing giants-- Apple, Alphabet, and Nuance (Dragon Dictate's owner).
There is a program called Simon and Amith KK from this forum posted these instructions on how to install it when using Ubuntu 18.04.
Here is also a link to that thread: I would like to install Simon Voice recognition software on Ubunu 18.04
Install the build dependencies
And then build it