Originally it was supposed to be filmed in Canada like discovery but in the Missisauga location. Patrick didn't want to leave L.A. though and pushed that it be filmed there instead. This is actually a bad thing for fans though as the reason the Discovery sets are so impressive is the following reasons:
1) The studio space at Pinewood is MUCH larger
2) The US dollar goes farther in Canada
3) The taxes are cheaper in Canada
4) The talent from set design to construction is cheaper. Extra's too.
I'm sure the tax incentive Picard show got from California alleviated at least some of those financial worries. $15.6 million supposedly.