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What happens if you try to do an LPV approach in the UK?

Yes; I discovered this, after going down a rabbit hole in some GPS software I was writing, and here are my comments in the code

The table carries on…

In practice, a modern GPS receiver will be picking up 10+ satellites at any time, often 20 or more. But the ones in avionics are not modern designs and tend to have a tracking limit – probably around 10. Probably why none of them use Galileo – even if it actually worked.

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Shoreham EGKA, United Kingdom
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