There's no specific filter. The main effect is blending the previous frame with the current frame. When blending, I modify the coordinates and add some noise. This makes the graphics look less basic and it creates this noisy trail when things move.

The source code is here: https://github.com/laurentlb/shmup8/blob/main/src/shaders/sc...

Blending is on lines 241, 242.

I didn't try to get a specific 80s look, I just played with formulas.