Chances are that your main speaker will show an acoustic high pass response.
Set the sub crossover at the dropoff frequency for starters. Then do the following-
Place the sub at the manufacturers recommended position. It is not necessary and often sub optimal to put the sub "in the middle".
Set the sub to polarity inverted.
Get a sub with continuous phase angle adjustment- e.g. JL Audio D110, Some REL, etc. This is a critical adjustment.
Also critical is high level (speaker level) inputs. Run the cables in parallel with your main speaker cables. Integration is more successful when the sub input sees the same signal and signal timing at the amplifier- not the preamp.
Play the sub at a louder level than the mains and measure again. Is the sub showing it’s dropoff frequency that correlates to your preciously measured main speaker? If not, adjust the crossover.
Now look for peaks and valleys through the useable bass range- e.g. 20 to 125 Hz.
Adjust the phase angle in steps (e.g. 1/4 turns) until you measure the smoothest response with no peaks and valleys.
Adjust the sub level to match the mains.
Do the ear test- and only adjust the sub level to taste.
I have successfully integrated a single sub into many systems this way including recently JL Audio D110 with KEF LS50s and Harbeth C7s. In each case my response at the listening position was flat from 20Hz through the entire bass region and it sounds phenomenal. You simply cannot hear the sub- all the bass is perfeclty centered with the main speakers.
Done right there is no need for additional processing or filters.