Joystick Yaw axis jittering wildly when at rest

The yaw axis of my Saitek X52 Pro works fine in both directions whenever an input is applied, but when it is at rest it will "jitter" all over the place, giving commands to the computer without any input on the stick. I tried adjusting the deadzone so that it just wouldn't affect my gameplay, but the phantom inputs are seemingly random and will fluctuate all the way to 100% input and back rapidly from side to side, so unless I disable the Yaw axis, it is constantly causing my game's ship to shake wildly side to side.

How can I get my Yaw axis to operate properly again, perhaps a dirty sensor? If it is, which sensor would it be, and what method would be best for its repair?