Converter causes radio static: will a filter help?

I have always had poor radio reception in my trailer -- I chalked it up to a poor radio (which might be true). But yesterday, my trailer was plugged into shore power in my driveway, and I was listening to the ballgame on a radio inside my garage. The reception was unusually poor. I happened to go into the trailer and turned on a light -- I could hear the static increase on my garage radio. I turned off the light -- static was reduced. Thinking it might be the LED lights, I plugged in a power strip inside the trailer and plugged in a rechargable lantern (without the LED lights). Same thing -- more static.

So this sounds like a problem in the converter. Short of replacing the converter, is there any other solution -- some kind of an in-line filter, maybe?

Thanks in advance for your advice!