The linear independence of knots under satellite operation has been frequently studied in the field of knot theory. Most of the prior works focused on the independence of knots under a fixed satellite operation. In this talk, I will talk about my recent result which goes the other way: using the instanton filtration invariant r_s developed by Nozaki-Sato-Taniguchi, we show for a certain family of satellite patterns and fixed companion knot, such family of satellite knots are linear independent. We subsequently will show our criterion depends only on some classical and computable invariant for some specific cases.