
How to build an Anti Aircraft Missile: Bayes’ Theorem and the Kalman Filter - pizza
http://georgemdallas.wordpress.com/2013/07/13/how-to-build-an-anti-aircraft-missile-probability-bayes-theorem-and-the-kalman-filter/
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jandrewrogers
Interestingly, terminal guidance has been the simple part for decades. Back
when people thought "hitting a bullet with a bullet" type of kinetic intercept
was hard, what they did not realize is that the software is relatively
straightforward and even primitive computers are fast enough to do hypersonic
intercept. Newtonian physics is slow compared to a computer.

The hard part, outside of having an adequate sensor to begin with (a problem
of many early designs), is designing a high-performance steerable rocket motor
that can consistently deliver the precision that the software is capable of
demanding under the performance envelopes required. This turns out to be an
exotic materials science and precision fabrication problem so comfortably in
the domain of conventional hardware engineering. As cool as it is to design a
terminal guidance system, that is the easy part of building a practical anti-
aircraft system.

Also, most vaguely modern systems do not track objects per se, they extract
the features of the designated target with broad spectrum imaging and only
chase that. In other words, the missile does not chase _a_ plane, it chases
_the_ plane. This means that the Hollywood trope of being hit by your own
missile generally won't work in reality.

~~~
gaius
The sensor in the original Sidewinder is fascinating - a spinning disk with a
reflective strip on it. When the reflector is pointing towards the target, the
reflection off the strip into one of a ring of sensors tells you in which
direction to steer. This meant that the missile couldn't see straight ahead,
only at an angle that would bounce from the disk into the sensors, hence it
would sort of edge sideways into the target, and that's why it's called the
sidewinder.

~~~
wazoox
Interesting, I always thought the name alluding to the typical wingtip mount
of these missiles.

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gpcz
If anyone is interested in learning these types of probabilistic perception
algorithms, especially pertaining to robotics, Prof. Edwin Olson's Mobile
Robotics video lectures at the University of Michigan are excellent. They are
located here:
[http://april.eecs.umich.edu/courses/eecs568_f12/wiki/index.p...](http://april.eecs.umich.edu/courses/eecs568_f12/wiki/index.php/Calendar)
. He even jokes near the end of the course that you could build a cruise
missile with the math he teaches in the course, and kindly asks the students
not to do so (I believe it was the Sensor Zoo video).

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michaelstewart
The variance of the combined Gaussian will not always shrink with more data.
Consider the case that you have one sensor that predicts 100m at a high
accuracy and then you get another sensor predicting 10,000m with the same
accuracy. At first you thought you had a very good idea of the location then
with more information you realize that you actually have no idea and you get a
Gaussian with mean of 5,050m and a very high variance.

~~~
Symmetry
The post left out the some important parts of the Kalman Filter, where you
adjust your certainty in how well you're able to predict where the target will
go and how accurate your sensors are in response to how they perform over
time. So even if you're Gaussians are 10 klicks apart the variance for this
prediction still shrinks, but your future Gaussians would be much wider. I
think what was described in the post was more an alpha-beta filter.

[http://en.wikipedia.org/wiki/Kalman_filter](http://en.wikipedia.org/wiki/Kalman_filter)

[http://en.wikipedia.org/wiki/Alpha_beta_filter](http://en.wikipedia.org/wiki/Alpha_beta_filter)

~~~
abstrakraft
Adjusting the measurement covariance to fit the residuals is not part of the
Kalman filter algorithm. One could make the argument that any real-world
implementation needs to address this problem, but as far as the algorithm is
concerned, the measurement covariance is externally computed.

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taspeotis
> It’s easy to write a program that will do this automatically without any
> human input. What if the plane is changing altitude? The problem becomes
> slightly harder, but not too hard. It’s just a matter of figuring out how
> far to plan in advance.

This reminds me to some extent of Basic Mechanisms in Fire Control Computers
[1]. The whole thing is worth watching, but the link will take you to the
point that I was reminded of.

[1]
[http://www.youtube.com/watch?v=s1i-dnAH9Y4#t=612](http://www.youtube.com/watch?v=s1i-dnAH9Y4#t=612)

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streetnigga
It is far easier to buy a FN-6 from China or seize a Soviet/Russian variant
from a failing state's coffers, yielding a better chance to take down an
airplane than a DIY model. I've been following events in Syria since protests
started to get shot up, to the security void created under aerial attacks
allowing foreign fighters to swarm in.

For the aspiring MANPAD or Anti-Air battalion a better ROI would probably be
what I mentioned above. Evidenced by this is a group having four MANPAD
variants in hand enabling me to make a lovely group panorama of the set[1].
For some analysis on the weapons shown in the image you can read a write-up by
N.R. Jenzen-Jones including the group shot here[2] or here[3].

This is a lovely exercise for the mind but obviously like most weaponized
missile/rocket systems it is best to leave it for the pros. :)

[1] [http://imgur.com/gallery/KFH6b04](http://imgur.com/gallery/KFH6b04)

[2] [http://rogueadventurer.com/2013/05/31/9k338-igla-s-and-
other...](http://rogueadventurer.com/2013/05/31/9k338-igla-s-and-other-
manpads-in-syria/)

[3] [http://www.armsresearch.org/post/51809092891/9k338-igla-s-
sa...](http://www.armsresearch.org/post/51809092891/9k338-igla-s-sa-24-and-
other-manpads-in-syria)

~~~
shn
Pictures remind me of 2nd rate action movies. Probably because those movies
are closer to real life than the 1st rate Hollywood action movies.

~~~
VladRussian2
or may be because both - the pictures and the 2nd rates movies - try to
imitate the 1st rate movies.

Whenever i find Youtube videos from real recent conflicts - it looks nothing
like movies, 1st or 2nd rate.

