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This is very nice. Very clear, and the 3D interactives are excellent at guiding the explanation. One thing that I thought was a little confusing was right at t

by SamBam 5y ago

This is very nice. Very clear, and the 3D interactives are excellent at guiding the explanation. One thing that I thought was a little confusing was right at the beginning, when we were estimating the position of the figurine and there was an area of uncertainty shown by the yellow circle. It isn't clear how you're estimating position, and why we have an area of uncertainty. At first I figured it was going to explain it using triangulation (measurement of angles) but there's no reason triangulation wouldn't be exactly as accurate as the tape measure method on a 2D surface, so wouldn't explain the area of uncertainty. The description merely says: > Just by using these three reference points we can relate the figurine’s position in the environment to an approximate placement on the map as show with the yellow shape on the right. I worry that having this ambiguity so early on might put some people off from reading the rest, because they figure they don't understand that and so won't understand the rest of it.

thehappypm 5y ago
Literally left the article to come here to see if anyone addressed this yet. I can’t figure out what it means.
- tazjin 5y ago
  It's about literally looking at it (in 3D) and guessing the exact position on the 2D map, which is easier closer to the landmarks. At least that's my interpretation.
  - thehappypm 5y ago
    Yeah, I suppose it’s like “you are a human standing on a flat plain looking at these 3 landmark towers. Where on the map are you? Intuitively you would be able to eyeball the angles between the landmarks, and eyeball the relative distances. I don’t think I’d draw a circle though. I’d probably have way less confidence for the landmark farther away and balloon out my estimate.
    - randomifcpfan 5y ago
      I think the confusing example is assuming just distance estimation, not angles. If angles were used the estimate would be much more precise.
justusthane 5y ago
I think it's as though you were the yellow figure standing in the landscape, and you were trying to position yourself on the map by going "Okay, the red landmark is quite close to me to the east, the blue landmark is a bit farther away to the north-west, and the green landmark is way over to the south-west. Now, where am I on the map?"
jessriedel 5y ago
Yes, that section is poorly written. More generally, the assumptions about what things were uncertain and what could be taken as exact were poorly motivated. The author should wither justify them with real-world constraints ("satellites can host atomic clocks but destroyers can't" -- not obvious!) or explicitly announce the assumptions as unjustified, but he shouldn't make it seem like the assumptions could have been reasoned to by the reader. I also was disappointed the author used circles/spheres and guesses for the timing offset rather than the much more edifying choice of hyperbolas. Just as you can think of a sphere as points reachable by the end of a rope of fixed length tied to a post, you can think about a hyperbola as the points reachable by tying separate ropes to two posts and spooling out equal amounts of rope.
kenjackson 5y ago
I had the same question. I moved on in the article, and its great, but this still puzzled me. If the author cleared this up, this article would be an absolute masterclass.
throwaway64643 5y ago
Was taught in college that if we get stuck, just move on forwards, things ahead can clear that up. And it works in this case for me. That part really doesn't matter much. At the end of the day, our brain is not a linear programming interpreter.
- marcellus23 5y ago
  I stopped reading there because frankly, if there’s such a flaw in the article that early, I was worried about the accuracy of the rest of it. The concept is just not explained at all. I spent too long making sure I didn’t miss some sentence somewhere explaining what was happening in that diagram. It felt like the article was wasting my time, and that maybe the author himself didn’t really understand what was happening.
  - YXNjaGVyZWdlbgo 5y ago
    You are assuming instead of knowing because you are talking about something you didn't read. LOL
    - marcellus23 5y ago
      No. I definitely did read that part of the article. I also went back and read the rest of the article this morning before I posted that comment, and he never goes on to explain that part. He just brushes past it and never clears it up.
      - jameshart 5y ago
        It’s not really relevant to how GPS works? It’s just scene setting an intuition for, crudely, how you might estimate your position relative to landmarks. If your take is then ‘well, he didn’t rigorously define how he derived the error bounds on crude position estimation, therefore all this stuff building into the level of precision GPS is capable of rests on a flimsy foundation of lies’, perhaps you are not the target audience for this kind of didactic presentation.
thrdbndndn 5y ago
After reading all the replies, I still have no idea what that part means.
butwhywhyoh 5y ago
I actually stopped reading the guide when I got to this point, and I have a lot of experience working with GPS. My thought was, "If the simple parts are this unclear, I don't want to spend time getting to the more complex portions".
- SeanA208 5y ago
  You should consider reading the rest of it, it's excellent after this.
Bedon292 5y ago
Think about it as if you are standing somewhere in relation to the monuments and are trying to figure out where you are on the map. You don't have precise measurements of distances or angles, you only have the estimated distance / angle you are from each of them that you get by looking at them. And without precise measurements there is uncertainty in where you are located. You probably know exactly where you are on the map if you are within a meter of a monument. As you move farther away from the monuments your estimation of the distance from each one becomes less precise. At least when I am estimating a distance things end up rough really quickly. At 10m I might be off by 1m. By 50m I am off by 10m, and so on. Now translate that into an exact position on the map. It not possible, there is always some level of uncertainty. I didn't realize it at first, but all of the examples are interactive. You can move the figure around, I found that pretty helpful and fun as well. In the very first example: place the figure somewhere, and then try and point to where it is on the map. I found myself circling areas naturally, even though the scale is relatively small. Especially when viewing it from an angle. The second example is quite exaggerated as far as the circles go but it is representative of the idea.

by SamBam 5y ago

thehappypm 5y ago

Literally left the article to come here to see if anyone addressed this yet. I can’t figure out what it means.

tazjin 5y ago
It's about literally looking at it (in 3D) and guessing the exact position on the 2D map, which is easier closer to the landmarks. At least that's my interpretation.
- thehappypm 5y ago
  Yeah, I suppose it’s like “you are a human standing on a flat plain looking at these 3 landmark towers. Where on the map are you? Intuitively you would be able to eyeball the angles between the landmarks, and eyeball the relative distances. I don’t think I’d draw a circle though. I’d probably have way less confidence for the landmark farther away and balloon out my estimate.
  - randomifcpfan 5y ago
    I think the confusing example is assuming just distance estimation, not angles. If angles were used the estimate would be much more precise.

justusthane 5y ago

I think it's as though you were the yellow figure standing in the landscape, and you were trying to position yourself on the map by going "Okay, the red landmark is quite close to me to the east, the blue landmark is a bit farther away to the north-west, and the green landmark is way over to the south-west. Now, where am I on the map?"

jessriedel 5y ago

Yes, that section is poorly written. More generally, the assumptions about what things were uncertain and what could be taken as exact were poorly motivated. The author should wither justify them with real-world constraints ("satellites can host atomic clocks but destroyers can't" -- not obvious!) or explicitly announce the assumptions as unjustified, but he shouldn't make it seem like the assumptions could have been reasoned to by the reader. I also was disappointed the author used circles/spheres and guesses for the timing offset rather than the much more edifying choice of hyperbolas. Just as you can think of a sphere as points reachable by the end of a rope of fixed length tied to a post, you can think about a hyperbola as the points reachable by tying separate ropes to two posts and spooling out equal amounts of rope.

kenjackson 5y ago

I had the same question. I moved on in the article, and its great, but this still puzzled me. If the author cleared this up, this article would be an absolute masterclass.

throwaway64643 5y ago

Was taught in college that if we get stuck, just move on forwards, things ahead can clear that up. And it works in this case for me. That part really doesn't matter much. At the end of the day, our brain is not a linear programming interpreter.

marcellus23 5y ago
I stopped reading there because frankly, if there’s such a flaw in the article that early, I was worried about the accuracy of the rest of it. The concept is just not explained at all. I spent too long making sure I didn’t miss some sentence somewhere explaining what was happening in that diagram. It felt like the article was wasting my time, and that maybe the author himself didn’t really understand what was happening.
- YXNjaGVyZWdlbgo 5y ago
  You are assuming instead of knowing because you are talking about something you didn't read. LOL
  - marcellus23 5y ago
    No. I definitely did read that part of the article. I also went back and read the rest of the article this morning before I posted that comment, and he never goes on to explain that part. He just brushes past it and never clears it up.
    - jameshart 5y ago
      It’s not really relevant to how GPS works? It’s just scene setting an intuition for, crudely, how you might estimate your position relative to landmarks. If your take is then ‘well, he didn’t rigorously define how he derived the error bounds on crude position estimation, therefore all this stuff building into the level of precision GPS is capable of rests on a flimsy foundation of lies’, perhaps you are not the target audience for this kind of didactic presentation.

thrdbndndn 5y ago

After reading all the replies, I still have no idea what that part means.

butwhywhyoh 5y ago

I actually stopped reading the guide when I got to this point, and I have a lot of experience working with GPS. My thought was, "If the simple parts are this unclear, I don't want to spend time getting to the more complex portions".

SeanA208 5y ago
You should consider reading the rest of it, it's excellent after this.

Bedon292 5y ago

Think about it as if you are standing somewhere in relation to the monuments and are trying to figure out where you are on the map. You don't have precise measurements of distances or angles, you only have the estimated distance / angle you are from each of them that you get by looking at them. And without precise measurements there is uncertainty in where you are located. You probably know exactly where you are on the map if you are within a meter of a monument. As you move farther away from the monuments your estimation of the distance from each one becomes less precise. At least when I am estimating a distance things end up rough really quickly. At 10m I might be off by 1m. By 50m I am off by 10m, and so on. Now translate that into an exact position on the map. It not possible, there is always some level of uncertainty. I didn't realize it at first, but all of the examples are interactive. You can move the figure around, I found that pretty helpful and fun as well. In the very first example: place the figure somewhere, and then try and point to where it is on the map. I found myself circling areas naturally, even though the scale is relatively small. Especially when viewing it from an angle. The second example is quite exaggerated as far as the circles go but it is representative of the idea.