6 ms·

Math Invented for Moon Landing Helps Your Flight Arrive on Time

117 points by wglb 7y ago

pgnas 7y ago
Wow. Clearly worth the trillions spent, good investment.
- melling 7y ago
  These days we have yearly budget deficits of a trillion dollars. At some point, we’ll be paying more on interest for the national debt than the Apollo program: https://www.nytimes.com/2018/09/25/business/economy/us-government-debt-interest.html https://www.nytimes.com/2018/09/25/business/economy/us-gover... I imagine as a percentage the government spends a lot less on research. R&D pays future dividends. Most of what we waste our money on now has little future value.
- jhayward 7y ago
  The comment is unworthy of the achievement. Kalman filters are used in many, many things today, including your smartphone's location and motion sensor processing. They are very important and have added a whole lot of economic value since being first used for Apollo.
  - deleted 7y ago
    [deleted]
- mochomocha 7y ago
  How would have you invested the money differently? Double the budget of the US military for one year? One thing that struck me when I visited the CERN in Switzerland is actually how much of the money spent on fundamental research spilled over into the "real economy" through the byproduct of all the interesting technologies invented.
  - bdamm 7y ago
    Such as the World Wide Web. Good example!
    - cameronbrown 7y ago
      Easily a couple dollars return to the global economy!
- merpnderp 7y ago
  We waste more in medicaid/medicare fraud than NASA's budget. If you're worried about bad investments, I'd go after the money going to dirtbag criminals who literally steal resources from the sick and needy before I'd go after NASA which has a long history of paying massive quality in life dividends from their relatively tiny budget.
- dugluak 7y ago
  comments like these appear all the time when a country like India achieves something significant in Space. People question "why put money in space if millions are starving".
  - Karunamon 7y ago
    To go full devil's advocate, that's because they're not doing much that's new. The space race of decades past and everything surrounding it was pushing human frontiers in science, technology, and exploration. Lots of that technology found its way into everyday use. As far as I can tell, the launch technology here (the GLSV) is bog standard, the mission is unmanned, and it's using a rover that's less sophisticated than Curiosity. The ground being covered here is well-trodden. Lest anyone think I'm pooh-poohing the achievement here, I'm not. Human spaceflight is still in its infancy, and being the 5th country to make a soft landing on the moon is a big deal, and a practical demonstration of a lot of technical prowess. The problem is.. it appears to be mostly a demonstration at the end of the day. Is mapping the surface of the moon and detailing its composition more or less important than lifting 90 million people out of poverty? I know what my opinion is here, but I think it's something that reasonable people can disagree on.
    - fastball 7y ago
      Arguably the future of humanity is more important than 90 million present day humans.
      - cameronbrown 7y ago
        An incredibly cold and privileged view. How is feeding/clothing a hundred million people any less valuable than what India's space programme is doing? You say that the "future of humanity" is what's being progressed - well for all you know the next Einstein/Feynman/Tesla could be in that group and his/her potential is going to be wasted.
        fastball 7y ago
- _verandaguy 7y ago
  Considering how many cost reductions it's achieved in multi-billion dollar industries, yeah, it was probably a good investment, without even getting into the Apollo program letting us do things we straight up couldn't do before.
  - dsfyu404ed 7y ago
    Few people appreciate what a small cost increase or decrease does when you apply it to large chunks of the economy.
- king_magic 7y ago
  I mean, you do realize that it didn't cost trillions just for the Kalman filter piece of the moon landing, right?
- T-A 7y ago
  "Project Apollo cost $25.4 billion (or approximately $153 billion in 2018 dollars when adjusted for inflation via the GDP deflator index)." https://en.wikipedia.org/wiki/Apollo_program#Costs https://en.wikipedia.org/wiki/Apollo_program#Costs
  - melling 7y ago
    Perhaps he’s confused? The $168 billion “investment” in the Vietnam War (a trillion today) definitely could have been better spent. https://www.thebalance.com/vietnam-war-facts-definition-costs-and-timeline-4154921 https://www.thebalance.com/vietnam-war-facts-definition-cost... If we’d put all that money into another moonshot, say the war on cancer instead, can you imagine the knowledge gained?
Isamu 7y ago
About the significance of the Schmidt-Kalman filter (from a related abstract): >In most target tracking formulations, the tracking sensor location is typically assumed perfectly known. Without accounting for navigation errors of the sensor platform, regular Kalman filters tend to be optimistic (i.e., the covariance matrix far below the actual mean squared errors) ... The Schmidt-Kalman filter (SKF) does not estimate the navigation errors explicitly but rather takes into account the navigation error covariance provided by an on-board navigation unit in the tracking filter formulation. By exploring the structural navigation errors, the SKF is not only more consistent but also produces smaller mean squared errors than regular Kalman filters.
romwell 7y ago
Kalman filters are useful for much more than that :) I'm barely acquainted with them, but this[1] seems to be a good introduction that doesn't shove math under the rug. Schmidt's modification of Kalman filter allowed for a practical implementation of it on the Apollo computer. The history and the motivation for the changes are excellently described in a survey paper co-authored by Schmidt himself in 1985[2]: >Dr. Kalman's original formulation would have required an on-board crew to make a continuous sequence of optical measurements equally spaced in time throughout the lunar mission, an impractical scenario. Therefore, to implement our measurement and course-correction schedule, the original formulation had to be revised. This paper, [2], offers amazing historical tidibtis (especially relevant on HN): computational challenges, project running 6 months behind schedule, why it was better than least-squares methods (computation time!), numerical stability, implementation details that allowed for use of floats (single precision) vs. double precision, FORTRAN implementation vs. specialized hardware, etc. I find it amazing that nearly 60 years later, we are still dealing with the same issues in machine learning and high-performance computing: from single vs. double precision and numerical stability down to, well, using Kalman filters - and yes, FORTRAN and specialized hardware. And projects running behind schedule. (Last time I had to touch FORTRAN code was.. a month ago. Also guess what powers all your shiny NumPy/SciPy computations: a lot of FORTRAN.) [1]https://towardsdatascience.com/kalman-filter-an-algorithm-for-making-sense-from-the-insights-of-various-sensors-fused-together-ddf67597f35e https://towardsdatascience.com/kalman-filter-an-algorithm-fo... [2]https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860003843.pdf https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/198600...
- ska 7y ago
  > I find it amazing that nearly 60 years later, we are still dealing with the same issues in machine learning and high-performance computing: from single vs. double precision and numerical stability down to, well, using Kalman filters - and yes, FORTRAN and specialized hardware. And projects running behind schedule. On the other hand, I don't find this amazing at all. Numerics are fundamentally difficult, the people who worked on them at the beginning were very smart. Projects have always been behind schedule. It doesn't surprise me at all that we've been stuck on at least a local maxima on many of these things....
acqq 7y ago
The paper by McGee and Schmidt (1985): https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860003843.pdf https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/198600... "Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry -- Leonard A. McGee and Stanley F. Schmidt"
salty_biscuits 7y ago
Are they just talking about the extended kalman filter? If so it is funny that there was such a big conceptual gap between the linear and linearized versions (i.e. a few years gap). Hindsight is a wonderful thing.
- 6gvONxR4sf7o 7y ago
  Nope, as far as I can tell, the schmidt-kalman filter is a way of reducing dimensionality in a KF. You split the states between those you are interested in and those you aren't. Sometimes those states you don't care about (e.g. sensor biases) are still important for estimating those you do care about (e.g. position). Adding a state to a typical KF for each of these dimensions is one solution, but it's expensive (covariance calcs scale quadratically with dimension). The Schmidt-Kalman filter is another solution.

117 points by wglb 7y ago

pgnas 7y ago

Wow. Clearly worth the trillions spent, good investment.

melling 7y ago
These days we have yearly budget deficits of a trillion dollars. At some point, we’ll be paying more on interest for the national debt than the Apollo program: https://www.nytimes.com/2018/09/25/business/economy/us-government-debt-interest.html https://www.nytimes.com/2018/09/25/business/economy/us-gover... I imagine as a percentage the government spends a lot less on research. R&D pays future dividends. Most of what we waste our money on now has little future value.
jhayward 7y ago
The comment is unworthy of the achievement. Kalman filters are used in many, many things today, including your smartphone's location and motion sensor processing. They are very important and have added a whole lot of economic value since being first used for Apollo.
- deleted 7y ago
  [deleted]
mochomocha 7y ago
How would have you invested the money differently? Double the budget of the US military for one year? One thing that struck me when I visited the CERN in Switzerland is actually how much of the money spent on fundamental research spilled over into the "real economy" through the byproduct of all the interesting technologies invented.
- bdamm 7y ago
  Such as the World Wide Web. Good example!
  - cameronbrown 7y ago
    Easily a couple dollars return to the global economy!
merpnderp 7y ago
We waste more in medicaid/medicare fraud than NASA's budget. If you're worried about bad investments, I'd go after the money going to dirtbag criminals who literally steal resources from the sick and needy before I'd go after NASA which has a long history of paying massive quality in life dividends from their relatively tiny budget.
dugluak 7y ago
comments like these appear all the time when a country like India achieves something significant in Space. People question "why put money in space if millions are starving".
- Karunamon 7y ago
  To go full devil's advocate, that's because they're not doing much that's new. The space race of decades past and everything surrounding it was pushing human frontiers in science, technology, and exploration. Lots of that technology found its way into everyday use. As far as I can tell, the launch technology here (the GLSV) is bog standard, the mission is unmanned, and it's using a rover that's less sophisticated than Curiosity. The ground being covered here is well-trodden. Lest anyone think I'm pooh-poohing the achievement here, I'm not. Human spaceflight is still in its infancy, and being the 5th country to make a soft landing on the moon is a big deal, and a practical demonstration of a lot of technical prowess. The problem is.. it appears to be mostly a demonstration at the end of the day. Is mapping the surface of the moon and detailing its composition more or less important than lifting 90 million people out of poverty? I know what my opinion is here, but I think it's something that reasonable people can disagree on.
  - fastball 7y ago
    Arguably the future of humanity is more important than 90 million present day humans.
    - cameronbrown 7y ago
      An incredibly cold and privileged view. How is feeding/clothing a hundred million people any less valuable than what India's space programme is doing? You say that the "future of humanity" is what's being progressed - well for all you know the next Einstein/Feynman/Tesla could be in that group and his/her potential is going to be wasted.
      - fastball 7y ago
_verandaguy 7y ago
Considering how many cost reductions it's achieved in multi-billion dollar industries, yeah, it was probably a good investment, without even getting into the Apollo program letting us do things we straight up couldn't do before.
- dsfyu404ed 7y ago
  Few people appreciate what a small cost increase or decrease does when you apply it to large chunks of the economy.
king_magic 7y ago
I mean, you do realize that it didn't cost trillions just for the Kalman filter piece of the moon landing, right?
T-A 7y ago
"Project Apollo cost $25.4 billion (or approximately $153 billion in 2018 dollars when adjusted for inflation via the GDP deflator index)." https://en.wikipedia.org/wiki/Apollo_program#Costs https://en.wikipedia.org/wiki/Apollo_program#Costs
- melling 7y ago
  Perhaps he’s confused? The $168 billion “investment” in the Vietnam War (a trillion today) definitely could have been better spent. https://www.thebalance.com/vietnam-war-facts-definition-costs-and-timeline-4154921 https://www.thebalance.com/vietnam-war-facts-definition-cost... If we’d put all that money into another moonshot, say the war on cancer instead, can you imagine the knowledge gained?

Isamu 7y ago

About the significance of the Schmidt-Kalman filter (from a related abstract): >In most target tracking formulations, the tracking sensor location is typically assumed perfectly known. Without accounting for navigation errors of the sensor platform, regular Kalman filters tend to be optimistic (i.e., the covariance matrix far below the actual mean squared errors) ... The Schmidt-Kalman filter (SKF) does not estimate the navigation errors explicitly but rather takes into account the navigation error covariance provided by an on-board navigation unit in the tracking filter formulation. By exploring the structural navigation errors, the SKF is not only more consistent but also produces smaller mean squared errors than regular Kalman filters.

romwell 7y ago

Kalman filters are useful for much more than that :) I'm barely acquainted with them, but this[1] seems to be a good introduction that doesn't shove math under the rug. Schmidt's modification of Kalman filter allowed for a practical implementation of it on the Apollo computer. The history and the motivation for the changes are excellently described in a survey paper co-authored by Schmidt himself in 1985[2]: >Dr. Kalman's original formulation would have required an on-board crew to make a continuous sequence of optical measurements equally spaced in time throughout the lunar mission, an impractical scenario. Therefore, to implement our measurement and course-correction schedule, the original formulation had to be revised. This paper, [2], offers amazing historical tidibtis (especially relevant on HN): computational challenges, project running 6 months behind schedule, why it was better than least-squares methods (computation time!), numerical stability, implementation details that allowed for use of floats (single precision) vs. double precision, FORTRAN implementation vs. specialized hardware, etc. I find it amazing that nearly 60 years later, we are still dealing with the same issues in machine learning and high-performance computing: from single vs. double precision and numerical stability down to, well, using Kalman filters - and yes, FORTRAN and specialized hardware. And projects running behind schedule. (Last time I had to touch FORTRAN code was.. a month ago. Also guess what powers all your shiny NumPy/SciPy computations: a lot of FORTRAN.) [1]https://towardsdatascience.com/kalman-filter-an-algorithm-for-making-sense-from-the-insights-of-various-sensors-fused-together-ddf67597f35e https://towardsdatascience.com/kalman-filter-an-algorithm-fo... [2]https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860003843.pdf https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/198600...

ska 7y ago
> I find it amazing that nearly 60 years later, we are still dealing with the same issues in machine learning and high-performance computing: from single vs. double precision and numerical stability down to, well, using Kalman filters - and yes, FORTRAN and specialized hardware. And projects running behind schedule. On the other hand, I don't find this amazing at all. Numerics are fundamentally difficult, the people who worked on them at the beginning were very smart. Projects have always been behind schedule. It doesn't surprise me at all that we've been stuck on at least a local maxima on many of these things....

acqq 7y ago

The paper by McGee and Schmidt (1985): https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860003843.pdf https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/198600... "Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry -- Leonard A. McGee and Stanley F. Schmidt"

salty_biscuits 7y ago

Are they just talking about the extended kalman filter? If so it is funny that there was such a big conceptual gap between the linear and linearized versions (i.e. a few years gap). Hindsight is a wonderful thing.

6gvONxR4sf7o 7y ago
Nope, as far as I can tell, the schmidt-kalman filter is a way of reducing dimensionality in a KF. You split the states between those you are interested in and those you aren't. Sometimes those states you don't care about (e.g. sensor biases) are still important for estimating those you do care about (e.g. position). Adding a state to a typical KF for each of these dimensions is one solution, but it's expensive (covariance calcs scale quadratically with dimension). The Schmidt-Kalman filter is another solution.