I'm not hearing a lot of filter movement, so I think an envelope filter might not hit the spot with this.
Definitive answer - you're looking for a dedicated bass synth pedal. Some that would nail this are: Akai Deep Impact (expensive, discontinued), Markbass Super Synth (needs computer to tweak some settings), Korg G5 (discontinued), Boss SYB5 (doesn't track as well as the previous ones), Behringer BSY600 (clone of the Boss) plus others. If you need something new and reliable, get the Super Synth, but connect it to your computer and spend some time with the control panel software.
Suggestion - if you've not got any pedals at the moment, buy a Zoom B3. It has some synth effects in it which can be tweaked nicely, and you'll get loads of other useful effects in an easy to use package.