7 ms·

The idea behind inertial navigation is to keep track of the missile's position by constantly measuring its acceleration. By integrating the acceleration, you ge

The idea behind inertial navigation is to keep track of the missile's position by constantly measuring its acceleration. By integrating the acceleration, you get the velocity. And by integrating the velocity, you get the position. This sounds like it couldn't possibly work (surely all the little errors compound?) but apparently it's how Apollo navigated https://wehackthemoon.com/tech/inertial-measurement-unit-mechanical-engineering-wizardry https://wehackthemoon.com/tech/inertial-measurement-unit-mec...

Zircom 2y ago
I mean it's a nuclear missile, millimeter accuracy isn't really necessary. Somewhere in the general vicinity is good enough for it's purpose of going boom.
- mannyv 2y ago
  In general, the USSR had bigger bombs because they weren't as accurate as US bombs. So yes.
- nox101 2y ago
  shooting something 12000 miles away, 0.1% off is 12 miles. That's missing the target and will not destroy whatever you were trying to destroy
  - lazide 2y ago
    In the early days, that’s why nukes went into the megaton range. Because then 12 miles will still destroy your target. Then they got a lot more accurate than .1%
- deleted 2y ago
  [deleted]
- kens 2y ago
  Well, accuracy makes a big difference if you're trying to hit a hardened target like a missile silo. Missile guidance has been a constant effort to squeeze out more and more accuracy. Minuteman I started with an accuracy of 2 km, but now Minuteman III is said to have an accuracy of 120 meters. The Peacekeeper (MX) missile, no longer in service, is said to have an accuracy of 40 meters. You can use a much, much smaller warhead if you're 40 meters away compared to 2 kilometers.
  - wkat4242 2y ago
    One thing I never understood is why they phased out the peacemaker and not the much older minuteman.
    - _djo_ 2y ago
      The START II treaty limited Russia and the US's ICBMs to a single warhead each, and the Peacekeepers were optimised as a platform to host multiple independently targetable re-entry vehicles (MIRVs) and when the US agreed to revert to a single warhead per missile the Minuteman III was much cheaper to maintain than the Peacekeeper. So even though Russia withdrew from START II almost immediately, the US continued to unilaterally remove the MIRV capability from its ICBM fleet and stick to single warhead Minuteman IIIs.
  - chickenbig 2y ago
    The following was an interesting read on the super-fuze. https://thebulletin.org/2017/03/how-us-nuclear-force-modernization-is-undermining-strategic-stability-the-burst-height-compensating-super-fuze/ https://thebulletin.org/2017/03/how-us-nuclear-force-moderni...
jonathanyc 2y ago
I also could not believe inertial navigation systems worked as well as they do when I first learned about them. At some point in time the most sophisticated IMUs were actually export-controlled! Maybe this has changed or is ineffective now that smartphone/quadcopter IMUs have caught up.
- jandrewrogers 2y ago
  Advanced IMUs are still export controlled and the state-of-the-art is classified. The US military considers this a cornerstone technology and has invested heavily in R&D over the years. The IMUs that are widely available commercially have improved significantly over the years but so have the military versions.
- krisoft 2y ago
  > Maybe this has changed or is ineffective now that smartphone/quadcopter IMUs have caught up. They did not caught up. There are two kind of IMUs: one where you have to account for the rotation of the Earth during signal processing and one where there is no point because it will be lost in the noise anyway. The smartphone/quadcoptee IMUs are the second kind. The first kind is still export controlled.
- rcxdude 2y ago
  consumer-grade IMUs are still well below the performance of even much older military-grade IMUs (which tend to be impressive feats of precision engineering with pricetags to match, but also physically much larger). You'll still find anything that's useful for working out position over any time period is export-controlled (dual-use or stricter).
  - jonathanyc 2y ago
    That's super interesting to learn, thanks for letting me know! I'm a software guy but I love learning about sensors, it's always amazing.
benjam47 2y ago
It is how Apollo navigated, although both the ground (via ground tracking) as well as the crew (via locating stars through a extant, and the Apollo computer having a database of the position of several dozen bright stars) could update their current position throughout the flight.
- embedded_hiker 2y ago
  Apollo used star sightings to check the accuracy of the gyros that measured which way the spacecraft was pointed. The stars could not be used to determine position like a ship at sea could do. Besides inertial navigation, they had a transponder that would echo back a continuous pseudorandom bit stream, and the delay gave a precise measurement of distance.
  - benjam47 2y ago
    Thank you for the correction, but are you sure that is accurate? I was definitely under the impression that although their position was normally updated by the ground (to the AGC, via their uplink capability), and the sextant was normally used to determine their orientation, the astronauts could use their optical equipment and calculations to determine their position as well as their orientation, albeit it with less precision. This NASA website (https://www.nasa.gov/history/afj/compessay.html#:~:text=Optical%20navigation%20subsystem%20sightings%20of,alignment%20of%20the%20stable%20platform https://www.nasa.gov/history/afj/compessay.html#:~:text=Opti...) seems to say as much: "Optical navigation subsystem sightings of celestial bodies and landmarks on the Moon and Earth are used by the computer subsystem to determine the spacecraft's position and velocity and to establish proper alignment of the stable platform." And Wikipedia (https://en.m.wikipedia.org/wiki/Apollo_PGNCS https://en.m.wikipedia.org/wiki/Apollo_PGNCS): "The CM optical unit had a precision sextant (SXT) fixed to the IMU frame that could measure angles between stars and Earth or Moon landmarks or the horizon. It had two lines of sight, 28× magnification and a 1.8° field of view. The optical unit also included a low-magnification wide field of view (60°) scanning telescope (SCT) for star sightings. The optical unit could be used to determine CM position and orientation in space."
- bigiain 2y ago
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 ago
  GPS doesn't work that way. It uses instantaneous time-of-flight computation.
  - beerandt 2y ago
    How 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 ago
      At 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 ago
        If 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 ago
      Isn'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.
KK7NIL 2y ago
> surely all the little errors compound? Random errors (i.e. noise) cancel out in the long run thanks to integration. You're then only left with systematic offset errors which can presumably be calibrated out to a large extent.
- petermcneeley 2y ago
  Really depends on what you mean by random. If it is truly random then you will end up with a random walk. https://en.wikipedia.org/wiki/Random_walk https://en.wikipedia.org/wiki/Random_walk
  - KK7NIL 2y ago
    We can assume the error will have a random (whether it's actually truly random or merely pseudo-random doesn't matter here, just assume it's indistinguishable from truly random for this discussion) and a non-random component. The random component I assume to be gaussian (thermal noise, for example) and therefore symmetrical around the real value. It's obvious we can remove this type of noise through averaging (of which the core operation is integration). The non-random component I assume to be a skew that can be calibrated out. With these two assumptions in mind you can see that yes, it's indeed a random walk, but a very well behaved one.
    - kens 2y ago
      No, you can't remove the random walk error by integrating. The point is that after integrating, what you're left with the random walk error. To make this concrete, if you buy a commercial-grade gyroscope for $10, it will have a random walk error of several º/√h. So after summing the errors for an hour, you're left with several degrees of random error, which is bad. If you spend $100,000 on a navigation-grade gyroscope, you'll get a random walk error < 0.002º/√h, which is much better. As far as calibrating out the skew, of course you can do that to some extent, but it's not a magic bullet. The Minuteman periodically measures skew and even applies equations for the change in skew with acceleration. The problem is that skew is not constant; it changes with time, changes with temperature, changes with position, and changes randomly, so you can't just calibrate it out. That's one reason why missiles use strategic-grade IMUs for a million dollars rather than a commercial-grade gyro for $10: you're getting drift of .0001º/hour instead of .1º/second.
jfoutz 2y ago
When the MacBook got the acceleration sensor, I hacked up a little program to estimate velocity, and a button to reset at stoplights. Some friends drove me around, it worked poorly. it did pretty ok on the highway, but awful in the city. I think if I kept messing with it, it'd get a lot better, but I sorta lost interest. This was more of a fun weekend toy. I think all phones have them, and they might be reachable through chrome/safari. And it is kinda fun to play with, but you'll probably hit sampling rate errors pretty quick. you gotta guess the shape of the curve between datapoints.
ghaff 2y ago
At least modern ICBMs do a star sight to calibrate at the top of their trajectory but, yes, that’s what inertial guidance is. Draper Labs basically pioneered.
- jojobas 2y ago
  It's far from the top of their trajectory (by then the warheads are long separated), and only submarine-launched missiles need it.
  - ghaff 2y ago
    Ah. I'm only somewhat familiar with Trident.
    - jojobas 2y ago
      Ground-based launch sites can supply both position and orientation very accurately (few seconds of angle), more accurately than stellar correction can, and their gyro platform can keep it within a few seconds of angle as well. Submarines can determine their position accurately enough, but their orientation data can be improved upon using stars. The MIRV bus takes in the angular fix just before it starts giving the warheads their individual nudges.
      - ghaff 2y ago
        You obviously know more than I do. I just have some second-hand non-classified info related to submarine-launched.
kevin_thibedeau 2y ago
That is how all self-guided weapons systems worked before GPS was viable. Many still retain that capability as a fallback. Notably, the Tomahawks fired during Desert Storm had to transit over Iranian airspace because they needed the mountainous terrain to correct for their inertial drift before turning toward their targets over the flat Iraqi plains. https://en.wikipedia.org/wiki/TERCOM https://en.wikipedia.org/wiki/TERCOM
- lupusreal 2y ago
  Almost all. Walleye television-guided glide bombs used edge detection on a television signal to aim themselves in. A human would designate a target at the start but then the bomb would autonomously track the target. An optical fire-and-forget system developed in the 1960s. Sidewinders are another example. Both developed at China Lake.
- flavius29663 2y ago
  > before GPS was viable GPS can be jammed (see Russia-UKraine war), so inertial systems are still very important for rockets, for example some HIMARS rockets start with GPS and then rely only on inertial while getting close to target.
  - missedthecue 2y ago
    Himars relies on inertial navigation the entire flight and uses GPS updates to course correct. If the GPS is blocked for a sufficient amount of flightime, even with the intertial navigation, the accuracy can become unusably low. This is how the Russians have been throwing double digit percentages of launches off course.
    - ethbr1 2y ago
      Terminal guidance since ~1995 on higher-end weapons has switched to hybrid inertial + scene matching (various sensor types). F.ex. the 90s Tomahawk used terrain contour matching to orient itself For more details see https://apps.dtic.mil/sti/tr/pdf/ADA315439.pdf https://apps.dtic.mil/sti/tr/pdf/ADA315439.pdf (US translation of a mid-90s Chinese survey of the guidance space, but it covers the material and is publicly available) Afaik, most modern systems use infrared target matching for final course correction. (Initially developed to allow anti-shipping missiles to autonomously prioritize targets, but now advanced enough to use in land scenarios as well)
dingaling 2y ago
The little errors do compound, but the errors have been made progressively littler; a modern ring-laser gyro INS has a drift of one millidegree per hour or less. Or you can add an external correcting factor, such the Trident's astronav system that takes star-shots to recalibrate the INS.
ddalex 2y ago
When Nintendo Wii motes first appeared, they were some of the few devices at the time with cheap MESM accelerometers and gyroscopes that were programmer-friendly. I remember taping two together back to back and integrating acceleration across them. That's when I learned Kalman filters. It was accurate enough so I could throw it across my desk and measure the desk length :)
- djmips 2y ago
  Kalman filters were also used in the AGC - useful for landing on the moon. I suspect they were not used by the Minuteman - does anyone know? https://en.wikipedia.org/wiki/Kalman_filter#History https://en.wikipedia.org/wiki/Kalman_filter#History https://github.com/chrislgarry/Apollo-11/blob/master/Luminary099/KALMAN_FILTER.agc https://github.com/chrislgarry/Apollo-11/blob/master/Luminar...
JR1427 2y ago
See https://news.ycombinator.com/item?id=40692333 https://news.ycombinator.com/item?id=40692333
rjsw 2y ago
Operation Black Buck [1] used inertial navigation. [1] https://en.wikipedia.org/wiki/Operation_Black_Buck https://en.wikipedia.org/wiki/Operation_Black_Buck

Zircom 2y ago

I mean it's a nuclear missile, millimeter accuracy isn't really necessary. Somewhere in the general vicinity is good enough for it's purpose of going boom.

mannyv 2y ago
In general, the USSR had bigger bombs because they weren't as accurate as US bombs. So yes.
nox101 2y ago
shooting something 12000 miles away, 0.1% off is 12 miles. That's missing the target and will not destroy whatever you were trying to destroy
- lazide 2y ago
  In the early days, that’s why nukes went into the megaton range. Because then 12 miles will still destroy your target. Then they got a lot more accurate than .1%
deleted 2y ago
[deleted]
kens 2y ago
Well, accuracy makes a big difference if you're trying to hit a hardened target like a missile silo. Missile guidance has been a constant effort to squeeze out more and more accuracy. Minuteman I started with an accuracy of 2 km, but now Minuteman III is said to have an accuracy of 120 meters. The Peacekeeper (MX) missile, no longer in service, is said to have an accuracy of 40 meters. You can use a much, much smaller warhead if you're 40 meters away compared to 2 kilometers.
- wkat4242 2y ago
  One thing I never understood is why they phased out the peacemaker and not the much older minuteman.
  - _djo_ 2y ago
    The START II treaty limited Russia and the US's ICBMs to a single warhead each, and the Peacekeepers were optimised as a platform to host multiple independently targetable re-entry vehicles (MIRVs) and when the US agreed to revert to a single warhead per missile the Minuteman III was much cheaper to maintain than the Peacekeeper. So even though Russia withdrew from START II almost immediately, the US continued to unilaterally remove the MIRV capability from its ICBM fleet and stick to single warhead Minuteman IIIs.
- chickenbig 2y ago
  The following was an interesting read on the super-fuze. https://thebulletin.org/2017/03/how-us-nuclear-force-modernization-is-undermining-strategic-stability-the-burst-height-compensating-super-fuze/ https://thebulletin.org/2017/03/how-us-nuclear-force-moderni...

jonathanyc 2y ago

I also could not believe inertial navigation systems worked as well as they do when I first learned about them. At some point in time the most sophisticated IMUs were actually export-controlled! Maybe this has changed or is ineffective now that smartphone/quadcopter IMUs have caught up.

jandrewrogers 2y ago
Advanced IMUs are still export controlled and the state-of-the-art is classified. The US military considers this a cornerstone technology and has invested heavily in R&D over the years. The IMUs that are widely available commercially have improved significantly over the years but so have the military versions.
krisoft 2y ago
> Maybe this has changed or is ineffective now that smartphone/quadcopter IMUs have caught up. They did not caught up. There are two kind of IMUs: one where you have to account for the rotation of the Earth during signal processing and one where there is no point because it will be lost in the noise anyway. The smartphone/quadcoptee IMUs are the second kind. The first kind is still export controlled.
rcxdude 2y ago
consumer-grade IMUs are still well below the performance of even much older military-grade IMUs (which tend to be impressive feats of precision engineering with pricetags to match, but also physically much larger). You'll still find anything that's useful for working out position over any time period is export-controlled (dual-use or stricter).
- jonathanyc 2y ago
  That's super interesting to learn, thanks for letting me know! I'm a software guy but I love learning about sensors, it's always amazing.

benjam47 2y ago

It is how Apollo navigated, although both the ground (via ground tracking) as well as the crew (via locating stars through a extant, and the Apollo computer having a database of the position of several dozen bright stars) could update their current position throughout the flight.

embedded_hiker 2y ago
Apollo used star sightings to check the accuracy of the gyros that measured which way the spacecraft was pointed. The stars could not be used to determine position like a ship at sea could do. Besides inertial navigation, they had a transponder that would echo back a continuous pseudorandom bit stream, and the delay gave a precise measurement of distance.
- benjam47 2y ago
  Thank you for the correction, but are you sure that is accurate? I was definitely under the impression that although their position was normally updated by the ground (to the AGC, via their uplink capability), and the sextant was normally used to determine their orientation, the astronauts could use their optical equipment and calculations to determine their position as well as their orientation, albeit it with less precision. This NASA website (https://www.nasa.gov/history/afj/compessay.html#:~:text=Optical%20navigation%20subsystem%20sightings%20of,alignment%20of%20the%20stable%20platform https://www.nasa.gov/history/afj/compessay.html#:~:text=Opti...) seems to say as much: "Optical navigation subsystem sightings of celestial bodies and landmarks on the Moon and Earth are used by the computer subsystem to determine the spacecraft's position and velocity and to establish proper alignment of the stable platform." And Wikipedia (https://en.m.wikipedia.org/wiki/Apollo_PGNCS https://en.m.wikipedia.org/wiki/Apollo_PGNCS): "The CM optical unit had a precision sextant (SXT) fixed to the IMU frame that could measure angles between stars and Earth or Moon landmarks or the horizon. It had two lines of sight, 28× magnification and a 1.8° field of view. The optical unit also included a low-magnification wide field of view (60°) scanning telescope (SCT) for star sightings. The optical unit could be used to determine CM position and orientation in space."
bigiain 2y ago

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 ago
GPS doesn't work that way. It uses instantaneous time-of-flight computation.
- beerandt 2y ago
  How 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 ago
    At 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 ago
      If 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 ago
    Isn'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.

KK7NIL 2y ago

> surely all the little errors compound? Random errors (i.e. noise) cancel out in the long run thanks to integration. You're then only left with systematic offset errors which can presumably be calibrated out to a large extent.

petermcneeley 2y ago
Really depends on what you mean by random. If it is truly random then you will end up with a random walk. https://en.wikipedia.org/wiki/Random_walk https://en.wikipedia.org/wiki/Random_walk
- KK7NIL 2y ago
  We can assume the error will have a random (whether it's actually truly random or merely pseudo-random doesn't matter here, just assume it's indistinguishable from truly random for this discussion) and a non-random component. The random component I assume to be gaussian (thermal noise, for example) and therefore symmetrical around the real value. It's obvious we can remove this type of noise through averaging (of which the core operation is integration). The non-random component I assume to be a skew that can be calibrated out. With these two assumptions in mind you can see that yes, it's indeed a random walk, but a very well behaved one.
  - kens 2y ago
    No, you can't remove the random walk error by integrating. The point is that after integrating, what you're left with the random walk error. To make this concrete, if you buy a commercial-grade gyroscope for $10, it will have a random walk error of several º/√h. So after summing the errors for an hour, you're left with several degrees of random error, which is bad. If you spend $100,000 on a navigation-grade gyroscope, you'll get a random walk error < 0.002º/√h, which is much better. As far as calibrating out the skew, of course you can do that to some extent, but it's not a magic bullet. The Minuteman periodically measures skew and even applies equations for the change in skew with acceleration. The problem is that skew is not constant; it changes with time, changes with temperature, changes with position, and changes randomly, so you can't just calibrate it out. That's one reason why missiles use strategic-grade IMUs for a million dollars rather than a commercial-grade gyro for $10: you're getting drift of .0001º/hour instead of .1º/second.

jfoutz 2y ago

When the MacBook got the acceleration sensor, I hacked up a little program to estimate velocity, and a button to reset at stoplights. Some friends drove me around, it worked poorly. it did pretty ok on the highway, but awful in the city. I think if I kept messing with it, it'd get a lot better, but I sorta lost interest. This was more of a fun weekend toy. I think all phones have them, and they might be reachable through chrome/safari. And it is kinda fun to play with, but you'll probably hit sampling rate errors pretty quick. you gotta guess the shape of the curve between datapoints.

ghaff 2y ago

At least modern ICBMs do a star sight to calibrate at the top of their trajectory but, yes, that’s what inertial guidance is. Draper Labs basically pioneered.

jojobas 2y ago
It's far from the top of their trajectory (by then the warheads are long separated), and only submarine-launched missiles need it.
- ghaff 2y ago
  Ah. I'm only somewhat familiar with Trident.
  - jojobas 2y ago
    Ground-based launch sites can supply both position and orientation very accurately (few seconds of angle), more accurately than stellar correction can, and their gyro platform can keep it within a few seconds of angle as well. Submarines can determine their position accurately enough, but their orientation data can be improved upon using stars. The MIRV bus takes in the angular fix just before it starts giving the warheads their individual nudges.
    - ghaff 2y ago
      You obviously know more than I do. I just have some second-hand non-classified info related to submarine-launched.

kevin_thibedeau 2y ago

That is how all self-guided weapons systems worked before GPS was viable. Many still retain that capability as a fallback. Notably, the Tomahawks fired during Desert Storm had to transit over Iranian airspace because they needed the mountainous terrain to correct for their inertial drift before turning toward their targets over the flat Iraqi plains. https://en.wikipedia.org/wiki/TERCOM https://en.wikipedia.org/wiki/TERCOM

lupusreal 2y ago
Almost all. Walleye television-guided glide bombs used edge detection on a television signal to aim themselves in. A human would designate a target at the start but then the bomb would autonomously track the target. An optical fire-and-forget system developed in the 1960s. Sidewinders are another example. Both developed at China Lake.
flavius29663 2y ago
> before GPS was viable GPS can be jammed (see Russia-UKraine war), so inertial systems are still very important for rockets, for example some HIMARS rockets start with GPS and then rely only on inertial while getting close to target.
- missedthecue 2y ago
  Himars relies on inertial navigation the entire flight and uses GPS updates to course correct. If the GPS is blocked for a sufficient amount of flightime, even with the intertial navigation, the accuracy can become unusably low. This is how the Russians have been throwing double digit percentages of launches off course.
  - ethbr1 2y ago
    Terminal guidance since ~1995 on higher-end weapons has switched to hybrid inertial + scene matching (various sensor types). F.ex. the 90s Tomahawk used terrain contour matching to orient itself For more details see https://apps.dtic.mil/sti/tr/pdf/ADA315439.pdf https://apps.dtic.mil/sti/tr/pdf/ADA315439.pdf (US translation of a mid-90s Chinese survey of the guidance space, but it covers the material and is publicly available) Afaik, most modern systems use infrared target matching for final course correction. (Initially developed to allow anti-shipping missiles to autonomously prioritize targets, but now advanced enough to use in land scenarios as well)

dingaling 2y ago

The little errors do compound, but the errors have been made progressively littler; a modern ring-laser gyro INS has a drift of one millidegree per hour or less. Or you can add an external correcting factor, such the Trident's astronav system that takes star-shots to recalibrate the INS.

ddalex 2y ago

When Nintendo Wii motes first appeared, they were some of the few devices at the time with cheap MESM accelerometers and gyroscopes that were programmer-friendly. I remember taping two together back to back and integrating acceleration across them. That's when I learned Kalman filters. It was accurate enough so I could throw it across my desk and measure the desk length :)

djmips 2y ago
Kalman filters were also used in the AGC - useful for landing on the moon. I suspect they were not used by the Minuteman - does anyone know? https://en.wikipedia.org/wiki/Kalman_filter#History https://en.wikipedia.org/wiki/Kalman_filter#History https://github.com/chrislgarry/Apollo-11/blob/master/Luminary099/KALMAN_FILTER.agc https://github.com/chrislgarry/Apollo-11/blob/master/Luminar...

JR1427 2y ago

See https://news.ycombinator.com/item?id=40692333 https://news.ycombinator.com/item?id=40692333

rjsw 2y ago

Operation Black Buck [1] used inertial navigation. [1] https://en.wikipedia.org/wiki/Operation_Black_Buck https://en.wikipedia.org/wiki/Operation_Black_Buck