Noise/ground loop problem with car 220v inverter and subwoofer

[jorgen_re]

I've got an 220v inverter in my car which is driving a 220v home theatre subwoofer. The output of the inverter is floating. I use a audio splitter cable to feed both my car stereo and the subwoofer with audio from my phone. When I power up the sub I can immediately hear ~100Hz humming in the sub, but it disappears when I connect the audio cable to the sub and effectively ground the sub's output to the car's chassis. However when I connect the audio cable to the sub, the humming noise manifests to the car's speakers. It is possible to drown out the hum with uncomfortably high volume.

I could solve this problem easily with a dedicated car subwoofer but I don't want to spend money on one at the moment. Another thing to note is that I am feeding the whole signal to the sub with no low pass filtering. It works fine without, but an active LP-filter could both be beneficial in terms of audio quality and maybe stop the hum going the "reverse direction" back to the original car audio system?

Help and suggestions is appreciated!

[Psi]

car audio isolation transformer