...then a self calibration hardly makes sense!

Why? Because sensors showing such a huge tolerance very often show hysteresis of same extent. Hysteresis is an error which cannot be taken into account by any calibration. Hysteresis is part of "repeatability error", which no calibration on earth can ever wipe out.

So, don't make the mistake to use a cheap pressure sensor and to believe you can make it precise by a smart calibration scheme.

If you want highest precision, then look for a pressure sensor which offers lowest repeatability error. Manufacturers selling them often provide a special calibration service by producing an "error matrix" (which is a two dimensionable error table [pressure & temperature]) and "error poylnomial" for each individual pressure sensor. This data is also delivered to the customer, to allow him to perform a "digital compensation".

Everything to calibrate then is the electronics, unless you have an electronics that is as (or even more) precise as the pressure sensor itself. In earlier days you had analog switches, which first, during a power on for instance, electronically removed the sensor from input, then connected one or several calibrated reference signals to it and finally adjusted the computing section. But, today, we try to omit it, because the analog switches introduce lots of noise and interference to the signal chain.

Kai