Prone is not cover or concealment, so it is unaffected by IPS.
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RAW regarding prone characters says nothing about it granting cover or concealment. It merely says that it is easier to hit with melee attacks, and harder to hit with ranged attacks (on the ground the character has less mobility, making a melee attack easier to hit on that PC; from a ranger standpoint, the character has less surface area for the ranged attack to affect, making it harder to get a solid hit), hence the +4/-4 simulation in math.
RAI, the PC is on the ground. Using a realistic example, World War soldiers would go prone to give the enemies less surface area (and thusly make it harder) for them to be seen or hit. Regardless of where they go prone, the surface area is less and thusly harder to hit with, meaning they don't get any sort of cover or concealment.
Reviewing the RAW:
Your ranged attacks ignore the AC bonus granted to targets by anything less than total cover, and the miss chance granted to targets by anything less than total concealment. Total cover and total concealment provide their normal benefits against your ranged attacks.
Emphasis mine.
Bolding the relevant sentence, the first italicized part says what IPS bypasses, and says what quantifies the bypass. RAW, it ignores the "AC" bonus" granted from "anything less than total cover;" this can easily be extrapolated to mean it even bypasses all other forms of AC other than that granted by total cover. But that is not the case.
The feat is supposed to eliminate all but the highest levels of Cover and Concealment. Since going prone does not grant Cover or Concealment, the IPS feat does not affect the penalty incurred from going prone.
It's one of those weird inconsistency's. By RAW, with IPS if someone is lying on the ground in plain sight they're harder to hit than someone standing behind a solid rock wall with nothing but his big toe sticking out. Hopefully your GM will use common sense.