Does your employer know about your project? They don't have to know. In fact, when I was in your position, I was advised to keep my side project as secret as possible to avoid warranting a lawsuit. Like DenisM says, they have nothing to gain by OK'ing your project, so no need to even tell them about it.
There is a VERY good reason to tell them, and document the fact. If you commit a violation and they know about it they must act within 3 years or lose their case. However if they don't know about the violation they can go after you 15 years later. Don't do it in secret. If you afraid they'll kick you out line up another job just in case.
