Fluxgate current sensor without equal saturation of core in both directions?

[Faringdon]

Hi,
What if the schem on fig3, page 3  (of the below) is done without the compensation error amplifier , U2?

Fluxgate current sensor:
http://www.cpdee.ufmg.br/~troliveira/docs/papers/Induscon_2018.pdf

This article was sent to us by our Chinese associates, who are offering us ferrite nanocrystalline cores so we can do this.
The article , and its predecessor, has been known to me, and mutiple of my previous companies, for the past  15 years, and the article , and its predecessor, has been freely available on the web for >15 years.

[David Hess]

What if the schem on fig3, page 3  (of the below) is done without the compensation error amplifier , U2?

The compensation balances the flux in the core to zero where linearity is maximum because the core is acting as a null detector.  Operating this way, the gain and linearity of the core is removed as an error term.