6 ms·

I don't know what your exact definitions is of "cheap", "millimeter-level", and "every few hours", but your comment does sound a bit misinformed. What you are

I don't know what your exact definitions is of "cheap", "millimeter-level", and "every few hours", but your comment does sound a bit misinformed. What you are possibly referring to is called dimensional control in geomatics and civil engineering, and there are various measurement techniques that can be applied, including GNSS-based. In a way, the hardest part of it is the planning phase, where you have to decide which technique is most appropriate to meet precision, accuracy, timeliness, and cost constraints. All those factors kind of fight against each other. Finding the sweet spot is non-trivial.

Dylan16807 10y ago
Okay, tell me where I'm wrong: AFAIK you can buy a few hundred to few thousand dollar receiver that tracks the carrier phase, let it sit around for a few hours, and then with aggressive post-processing you should be able to figure out the right phase and know your location within a few mm. Edit: And worst-case, you should be able to do an exact survey once, and then you can remember that and know which phase to use in the future. (Barring sudden multi-cm shifts, but in that case you have bigger problems.) You still have atmospheric fluctuations to deal with, but that's why you're measuring all day.
- 7952 10y ago
  Vertical accuracy is usually lower than horiztonal accuracy. It is more difficult to calculate elevation than lat/long.
  - Dylan16807 10y ago
    Not by a huge amount. Should be less than 2x, at least at some point during the day.
    - jofer 10y ago
      Much worse that 2x. Closer to an order of magnitude worse.
      - mturmon 10y ago
        Indeed. Just to anchor this with current state-of-the-art numbers, I took a look at the CSV data file linked to by the page referenced in my above comment: https://news.ycombinator.com/item?id=13040765 https://news.ycombinator.com/item?id=13040765 The quoted horizontal standard errors of the daily position measurements are ~1.5mm. The vertical standard errors are ~5-7mm. (Not as bad as a factor of 10, but certainly worse than 2x.) The vertical position measurement responds well to averaging of daily errors to beat down the RF propagation effects that cause them.
    - deleted 10y ago
      [deleted]
  - tgb 10y ago
    Huh, why's that?
    - cperciva 10y ago
      It has to do with the geometry: GPS is measuring the differences between the distances to satellites which are mostly "overhead". In a sense it's similar to how our stereoscopic vision can resolve movement from side to side more accurately than movement towards or away from us. If you're at the top of a skyscraper you can mitigate this somewhat by looking at satellites closer to the horizon as well -- this solves the geometry problem -- but then you run into increased noise from the larger amount of atmosphere you're looking through.
      - tgb 10y ago
        Hmm, I still don't see it. The comparison to stereoscopic vision seems misplaced: we judge side-to-side motion by an entirely different (and non-stereoscopic) mechanism than depth, and neither mechanism is mathematically very similar to that of GPS. And my understanding is that GPS receivers compute their distance to various satellites, which means if all the satellites were all nearly overhead, I would expect the vertical component to be the best understood. I Googled and found some vague and unsatisfying explanations, but, luckily, wikipedia tells us how to do the math: https://en.wikipedia.org/wiki/Dilution_of_precision_(navigation) https://en.wikipedia.org/wiki/Dilution_of_precision_(navigat...
        cperciva 10y ago
        You judge depth not from a single image but from the difference between two images. Similarly, GPS works not by measuring signal arrival times, but by measuring the differences between arrival times.
        tgb 10y ago
        Good point, but I'm afraid the analogy still isn't spelled out enough for me to actually make sense of it. Like why does that make a horizontal/vertical discrepancy?

Dylan16807 10y ago

Okay, tell me where I'm wrong: AFAIK you can buy a few hundred to few thousand dollar receiver that tracks the carrier phase, let it sit around for a few hours, and then with aggressive post-processing you should be able to figure out the right phase and know your location within a few mm. Edit: And worst-case, you should be able to do an exact survey once, and then you can remember that and know which phase to use in the future. (Barring sudden multi-cm shifts, but in that case you have bigger problems.) You still have atmospheric fluctuations to deal with, but that's why you're measuring all day.

7952 10y ago
Vertical accuracy is usually lower than horiztonal accuracy. It is more difficult to calculate elevation than lat/long.
- Dylan16807 10y ago
  Not by a huge amount. Should be less than 2x, at least at some point during the day.
  - jofer 10y ago
    Much worse that 2x. Closer to an order of magnitude worse.
    - mturmon 10y ago
      Indeed. Just to anchor this with current state-of-the-art numbers, I took a look at the CSV data file linked to by the page referenced in my above comment: https://news.ycombinator.com/item?id=13040765 https://news.ycombinator.com/item?id=13040765 The quoted horizontal standard errors of the daily position measurements are ~1.5mm. The vertical standard errors are ~5-7mm. (Not as bad as a factor of 10, but certainly worse than 2x.) The vertical position measurement responds well to averaging of daily errors to beat down the RF propagation effects that cause them.
  - deleted 10y ago
    [deleted]
- tgb 10y ago
  Huh, why's that?
  - cperciva 10y ago
    It has to do with the geometry: GPS is measuring the differences between the distances to satellites which are mostly "overhead". In a sense it's similar to how our stereoscopic vision can resolve movement from side to side more accurately than movement towards or away from us. If you're at the top of a skyscraper you can mitigate this somewhat by looking at satellites closer to the horizon as well -- this solves the geometry problem -- but then you run into increased noise from the larger amount of atmosphere you're looking through.
    - tgb 10y ago
      Hmm, I still don't see it. The comparison to stereoscopic vision seems misplaced: we judge side-to-side motion by an entirely different (and non-stereoscopic) mechanism than depth, and neither mechanism is mathematically very similar to that of GPS. And my understanding is that GPS receivers compute their distance to various satellites, which means if all the satellites were all nearly overhead, I would expect the vertical component to be the best understood. I Googled and found some vague and unsatisfying explanations, but, luckily, wikipedia tells us how to do the math: https://en.wikipedia.org/wiki/Dilution_of_precision_(navigation) https://en.wikipedia.org/wiki/Dilution_of_precision_(navigat...
      - cperciva 10y ago
        You judge depth not from a single image but from the difference between two images. Similarly, GPS works not by measuring signal arrival times, but by measuring the differences between arrival times.
        tgb 10y ago
        Good point, but I'm afraid the analogy still isn't spelled out enough for me to actually make sense of it. Like why does that make a horizontal/vertical discrepancy?