Whenever that happens (not often), my approach is perhaps a bit reductive, but goes something like the following:
• I feel like an imposter at the moment. Cool. It's merely a feeling. It's not true or false. It's just a feeling. And then that feeling goes away briefly. Basically, like a stoic sort of mindset, recognizing the actual feeling, and then move on.
• Other times I'll just tell myself to not fight it, and just play along with it. "I don't have Imposter Syndrome! I just simply am an Imposter!" This way, so be it. Just be an imposter, instead of being in denial!
I'm sure there are other ways that are perhaps more productive than mine. But my thought process serves me well in terms of finding peace with myself. I kind of don't care if people think I am a great musician. I know myself, and I "know" I'm not great. I'll let them think whatever they think.
On another note, I recently won an artist competition for playing some patriotic music on the piano by ear (it wasn't some huge competition, but still cool). I was the closing act for their artistic (mostly singing and instrumentals etc) event. The guy before me was nervous, and he asked me if I was nervous. I said, "nope - I can either be nervous and mess up, or I can NOT be nervous and mess up. Either way, I'm going to mess up! Might as well just be not nervous about that!" And I ended up playing my piece quite well. Lol.
Anyway. Yes, I am an Imposter. No, I am not an Imposter. Whatever. I basically don't care what I am. I'll just focus on playing! : )