Sometimes, especially as controllers age, you may get some sort of
"drifting" going on, such as the player moving forward without you
touching anything. The PlayStation 3 console itself does not include any
controller calibrartion tools. HOWEVER, the PS3 controller is designed
to self-calibrate every time it is connected or when the console is
turned on. But, maybe a hard-reset on the controller will do the trick.

First, turn off the console and unplug the contoller if connected via
USB. Next, perform a hard-reset on the controller itself via a tiny hole
underneath the controller near the L2 button. Insert a paperclip or
similar into this hole until a button is pressed down and held down for
three to five seconds. You will not hear a click or see any lights but
feel a slight depression on the button. When sure of reset, you can now
connect the controller back to the PS3 via the USB cable and press the
PS button to turn on the console so as to pair it.

You may not have realized it, but PS3 controllers have their own
internal software. Holding this hard-reset button down discharges
residual power and resets the firmware. It is sort of like when you
remove a CMOS battery to reset a BIOS on an old computer or when a game
cartridge battery is replaced and you loose your game saves, except
you are holding down a button to temporarily sever power rather than
removing anything.


STILL NOT FIXED
---------------
HOWEVER, be aware that this still may not fix the issue. These official
controllers are getting old; you may need to replace with an after-
market or refurbished controller. You could also get one still in the
original Sony PS3 box, but those can get expensive.

Also, there are other projects out there to help with adding more
controller support:

https://github.com/aldostools/PS3xPAD
https://consolemods.org/wiki/PS3:PS3XPAD