4 ms·
I said it downthread, but GPS is even more absurd. And we take it for granted. But it's based on the same idea, only getting position as a derivative of veloci
by beerandt 2y ago
I said it downthread, but GPS is even more absurd. And we take it for granted.
But it's based on the same idea, only getting position as a derivative of velocity. (And some borderline-magic statistics applied.)
And that's before taking into account the absurdity of how low power the broadcast signal is.
- CamperBob2 2y agoGPS doesn't work that way. It uses instantaneous time-of-flight computation.
- beerandt 2y agoHow do you think the 'instantaneous time-of-flight' computation is done? There's a lot of math that phrase is hiding. It's not a magic black box. It just often seems that way.
- CamperBob2 2y agoAt no point is velocity differentiated when computing a GPS fix. (Or integrated, which may be what you meant.) Your point stands, though... the way it does work is pretty much indistinguishable from magic, from a 1970s perspective. Those guys were wizards.
- rx_tx 2y agoIf you want to understand GPS more, https://ciechanow.ski/gps/ https://ciechanow.ski/gps/ is always an amazing read, witchcraft confirmed.
- deleted 2y ago[deleted]
- HPsquared 2y agoIsn't it about finding the time difference between pseudorandom coded signals. Granted the satellite positions and paths need to be known, which is another part of the puzzle. That involves some calculus, I'm sure.
- beerandt 2y agoYes but measuring diffs in either the pseudocode itself or the underlying carrier wave is basically measuring relative velocities wrt each sat and the observer. It's all summing dx/dt + dy/dt + dz/dt, for i paths between satellites and ground stations (or more receivers for differential or rtk or vrs style). [2] Which reduces most of the time to summing DELTA-Xi + DELTA-Yi + DELTA-Zi + delta-t(timeerrors). For i paths between each sat and ground receiver. Which you should recognize the transformation if you've ever taken calculus. Even if you don't integrate every time you get a fix. Part of what I describe as math 'magic' is that you can cancel out most of the unknowns and most of the unsolved calculus if you add a second fixed receiver. Google and Apple location services 'cheat' and do this via subbing a nearby wifi MAC with known coordinates, which for them is good-enough. But augmented gps from FAA or DOT or coastguard etc work the same way, but with real gps receivers on the ground in realtime. Obviously without having to substitute anything. Either way- the extra known variable greatly simplifies the math via canceling-out terms. Plus there are both closed and open form solutions developed since initial GPS deployment that allow solving without direct integration. Chapter 12 of [0] Surveying gets into the math, including transformations, if you want to see the math details. Or [1] GPS by van Sickle for a good overview of the various methods/ technologies. (Also survey-centric). [0]https://books.google.com/books/about/Surveying_theory_and_practice.html?id=4-lRAAAAMAAJ https://books.google.com/books/about/Surveying_theory_and_pr... [1]https://books.google.com/books?id=J0fLBQAAQBAJ&pg=PA63&source=gbs_toc_r&cad=2#v=onepage&q&f=false https://books.google.com/books?id=J0fLBQAAQBAJ&pg=PA63&sourc... [2] despite wgs84 and lat/lon being associated as default 'GPS coordinates', the 'raw' gps system data is xyz Cartesian in feet, then transformed to lat lon or whatever else.
- HPsquared 2y agoMy assumption was that GPS doesn't use dead reckoning to get a fix (other than the satellite paths). Do receivers use the Doppler effect to directly measure velocity? Edit: this article seems to support my view that they don't start with velocities: https://insidegnss.com/wp-content/uploads/2018/01/marapr15-SOLUTIONS.pdf https://insidegnss.com/wp-content/uploads/2018/01/marapr15-S... "How does a GNSS receiver estimate velocity?"