Missile defense is NP-complete

dboreham

It's been known since the 1960s that effective anti ballistic missile defense is impossible.

zabzonk

Oh, I thought this was going to be about the old trackball arcade game. Or perhaps it is? Same sort of rules? The maths is going so far over my head I can't hear the whoosh.

delichon

Add multiple decoys and the missile math tends to become an argument for the importance of preemption. Han shot first for a good reason.

heyitsmedotjayb

Would be interesting to know how the probabilities change once all your X band radars are destroyed. And then again how they change when all your L band radars are destroyed...

jsw97

The author explains that this problem is actually adversarial, in the sense that the attacker gets to observe defenses and allocate warheads and decoys accordingly. Thinking of our current circumstances, this suggests another cost of war: our offensive capabilities, as well as our defensive capabilities become more observable. Our adversaries are studying our strengths and weaknesses in Iran, and they will have a much improved game plan for countering us in future conflicts.

u_sama

Great nerd title, the maths made me nostalgic as I haven't seen a Sigma/Pi in a few years

owenmarshall

Two more sobering axes to introduce: cost and manufacturing capability. Numbers are hard to find for obvious security reasons, but using the numbers most optimistic to the defender[0] suggests an adversary using a Fatah type hypersonic is spending 1/3rd the cost of an Arrow interceptor, and is launching missiles that are produced at a much faster rate. Interception is deeply asymmetric in favor of the attacker. [0] https://www.jpost.com/israel-news/defense-news/article-82314...

srean

Game theory would be useful for these kinds of modeling. Perhaps the government should have and advisory body that employs the smartest mathematicians for running these scenarios. Of course a lot of randomness needs to be modeled too. Wonder what would be a good name for such a body :) Paradoxically, if anyone leaks unpalatable information from the inside that would be a problem for the government. https://en.wikipedia.org/wiki/Daniel_Ellsberg https://en.wikipedia.org/wiki/Ellsberg_paradox https://en.wikipedia.org/wiki/RAND_Corporation

quotemstr

The sole mention of directed energy: > Directed energy has been proposed as a cost-effective alternative, but introduces its own scheduling constraints — dwell time, platform coverage, atmospheric degradation — with similar scaling issues The author is doing the thing where a writer tries to bamboozle the reader into a conclusion without having to prove it by overwhelming the reader with nouns. Life is too short for shitty gosh gallops.

femiagbabiaka

could use some investigation of the ukranians techniques -- the number of interceptors the U.S. used within the first four days of the war eclipsed the total amount Ukranians have had for the war

energy123

What is the steady state? Assume you have two competent superpowers, both researching missile offense and defense, over the next 1000 years. What are the asymptotics of the interception rate from 0 to 1000?

jmyeet

Pardon the pun but this is an arms race and the defenders are going to lose. There are broadly five classes of missiles (one isn't a missile per se): 1. Ballistic. These are traditional rockets, basically. While rockets are designed to reach orbit or leave the Earth, a ballistic missile basically goes straight up and comes down. The higher it goes, the further away it can get because of the ballistic trajectory and the rotation of the Earth. Ballistic missiles are most vulnerable in the boost phase ie when they're just launched. Since you have little to no warning of that, that's not really helpful. But one weakness of ballistic missiles is you pretty much know the target within a fairly narrow range as soon as they launch. That's the point of early-warning radar: to determine if a launch is a threat so defenses can be prepared. Attackers can confuse or defeat defenses in multiple ways such as making small course corrections on approach, splitting into multiple warheads, using decoys for some of these warheads, deploying anti-radar or anti-heat seeking defenses at key points and breaking into many small munitions, sometimes called cluster munitions on the news but traditionally that's not what a cluster bomb is or was. In more sophisticated launch vehicles, the multiple warheads can be independently targeted. These are called MIRVs (multiple independently targetable reentry vehicles). Economicallky, depending on range and capability, a ballistic missile might cost anywhere from $100k+ to $10M+. 2. Rockets. Militarily this is different to a rocket in a civilian context. It's not much different to a hobby rocket, actually. Often these are "dumb" but some have sensors and guidance capability or might be heat-seeking. These tend to be incredibly cheap to produce and not terribly accurate but that's not really the point. The point is they're cheap and easy to produce and the interceptors are much more expensive. 3. Cruise missiles. Rather than a ballistic trajectory, these have more sophisticated guidance and travel much closer to the ground, usually to avoid radar. The Tomahawk missile is a prime example of this. These tend to be relatively expensive and much slower than ballistic missiles. 4. Hypersonic missiles. This is a relatively new invention that's kind of like a cruise-ballistic hybrid. It flies in the atmosphere for part or all of the time and, unlike cruise missiles, will fly faster than the speed of sound, usually significantly so (eg Mach 4-10). Such high speed makes interception near-impossible currently. The big advantage of a hypersonic missile is that it has the speed of a ballistic missiles without the predictability of the target area. Plus it can be retargeted in-flight. 5. Drones (honorable mention). Not technically a missile but they fit in this space regardless. This is basically a scaled up commercial drone with an explosive payload. These are significantly slower than cruise missiles or rockets but can be live-targeted, re-targeted and have a variety of types ranging from dropping hand grenades from a height (eg as has happened in Ukraine) to suicide-type drones that explode on impact. Drones are typically so slow that you could shoot them down with an shotgun in some cases. But they're incredibly cheap and easy to produce.

captainswirly

This is rocket defense, not missile defense. Pretty much nothing can stop those ICBMs - those aren't rockets. If you dig deeper than mainstream news - Iran is lighting Israel up with those ICBMs, but they don't use them too often.

vaporwario

Not sure if it applies exactly but this discussion brings to mind this saying... "The loser of a knife fight dies in the street. The winner dies in the hospital."

koakuma-chan

Why does a ground based interceptor cost $75M? High idiot index?

fisherwoman

Those rockets are lobbed in high arcs and glow in the sky then slowly fall down - they are so slow they almost look like flares. Your so-called missile defense does nothing at all against a real missile like Iran's supersonic ICBMs which can exceed 24,000+ km/h.

sgtsteaks

What are you gonna do when Iran destroys the missile defense system itself, oops already happened

contravariant

> Note that a more complete model would multiply each term by P(track)_j — the common-mode detection-tracking-classification factor developed in the previous section — but the standard WTA formulation assumes perfect tracking. I'm not sure that is a useful model, or more complete. I don't think you can assign interceptors to undetected missiles, so considering their effect on the value is rather pointless. It's effectively a sunk cost. Multiplying with the probability also makes no sense from an optimisation point of view. Why would you assign lower value to a target about to be hit simply because you were unlikely to detect the missile? The tracking probability only shows up in the meta game described at the end, where one side is trying to optimise their ability to hit valuable targets and the other is trying to optimise their ability to prevent that from happening.

maxglute

>Hence, for one warhead, a defender can launch 4 interceptors and have a 96% chance of successfully intercepting the incoming warhead. >Unfortunately, those numbers are optimistic. This part worth stressing, ceiling for more performant missiles, i.e. faster, terminal maneuvering, decoys are geometrically harder to intercept. Past mach ~10 terminal and functionally impossible because intercept kinematics will break interceptor airframes apart. AFAIK there hasn't been tests (i.e. FTM series) done on anything but staged/choreographed "icbm representative" targets. Iran arsenal charitably pretty shit, including high end. Hypothetical high end missile with 10%-20% single shot probability of kill requires 20-40 interceptors for 98% confidence, before decoys, i.e. 40x6=240 interceptors for 1 missile with 5 credible decoys. The math / economics breaks HARD with offensive missile improvements.

jcul

Really interesting. Forgive my ignorance, but I thought Israel's "iron dome" offered a very effective defense. Is this just from short distance missiles from neighbouring countries? This article seems to indicate it's very difficult to achieve a high success rate against multiple missiles. Admittedly I probably need to read up on this more.