> Naturally, large range uncertainty increases the ambiguity of position, but the relative position of the satellites also matters. If they aren’t well spread, the exactness of calculated location also suffers. (see the excellent example in OP) Fun tidbit, the resulting error is known for the system in closed form as Geometric Dilution of Precision, and is a 3x3 (edit: or 4+x4+ if you are estimating bias or quantitie…
Interferometry isn't convex, even the kernel trick won't save you. I don't think...
This person deserves to get filthy rich off of their patreon.
Not just filthy rich i guess. Bartosz is a one of a kind explainer of things - no matter what topic he touches, he always manages to outright nail the communication of the core concepts in a manner almost anyone can understand. Let alone the interactive visualizations. There should be some sort of Nobel Prize for people that contribute to humanity’s education - and methods therof. Kudos!
I like this idea much also I would say that Ben Eater also deserve such a prize if one will exists
Considering GPS was originally created for military purposes, I find it fascinating that the largest holes are over the north and south poles. The northern polar region is where the US-launched missiles and bombers would travel. Does the lesser orbital coverage in that area not negatively affect GPS precision?
I don't believe ICBM's are using GPS. They're programmed like they always have been and follow a very predictable path and don't change course (unlike hypersonic missiles). It's the "smart weapons" that are usually plane/ship dropped/launched that are gps guided as they are smaller munitions that have a much smaller blast radius and need to be more precise to be effective (as opposed to just carpet bombing the whole area). Those are "close" range weapons. You don't need to be very precise with an ICBM to obliterate the target, as it's usually city-sized. A mile off here or there will still destroy the target. Planes can and do still fly without GPS. There also haven't been too many wars involving the poles as basically no one lives there except science teams and no one wants the "land" as you can't do anything economically practical with it. Most of our ICBM's are still ancient Minuteman III's which were manufactured in the 1960's (my dad launched one in 68 out of Minot AFB, ND) and recently updated in 2015 to extend their useful life.
Very nice primer. I worked on the GPS program (first at Boeing, then at a small subcontractor when Lockheed won the GPS III work) - though I worked on the software simulator for the satellites (focused on the operational side of the constellation) so didn't get much into the weeds of how the PNT actually works for clients on the ground :)
If you want to explore deeper, there's some fun (and well commented) open source GPS processing codes in Octave/Matlab [1], coming from the excellent book [2]. Those are compatible with cheap RTL-SDRs. [3] also looks nice, but as I recall is Linux only.
> Naturally, large range uncertainty increases the ambiguity of position, but the relative position of the satellites also matters. If they aren’t well spread, the exactness of calculated location also suffers. (see the excellent example in OP) Fun tidbit, the resulting error is known for the system in closed form as Geometric Dilution of Precision, and is a 3x3 (edit: or 4+x4+ if you are estimating bias or quantitie…
Interferometry isn't convex, even the kernel trick won't save you. I don't think...
Look there in equation 6: That's the FIM being left multiplied when solving these types of problems. (under standard gauss-newton step, which is also common)
GPS is fascinating, especially the development period. Due to the complexity of the signal processing (relativity means that the clocks onboard run faster than on earth) there was much scepticism. The story I heard was that they only let them launch 1 Block 1 satellite to prove that could work, and then the first block of 10 satellites was used to validate the system before spending enough to get the full 24 satellit…
And the story about why the GPS satellites carry a NUDET payload (NDS) is a fun one too.
Considering GPS was originally created for military purposes, I find it fascinating that the largest holes are over the north and south poles. The northern polar region is where the US-launched missiles and bombers would travel. Does the lesser orbital coverage in that area not negatively affect GPS precision?
ICBMs don't use GPS. The almost universally use a inertial guidance system. For example: https://en.wikipedia.org/wiki/Advanced_Inertial_Reference_Sp... . Bombers use a similar inertial guidance system, but with updates from GPS and star trackers as applicable. The reduced precision from GPS doesn't matter too much, as the inertial guidance systems are pretty good now.
The assumption is that in a nuclear conflagration, expect GPS to become... unavailable.