Thursday, October 19, 2017

Tax Cuts and the Stock Markets

The tax system is definitely biased towards the rich. Vox came up with an "explainer" video on how Tax cuts benefit the rich asymmetrically.

I wish to clarify "rich" people as defined here are people who rely solely on investment income. This income is taxed at a much lower rate than earned income. This is already a huge boost to people who seek to play the market as a means to get wealthy. With the proliferation of investment tools, it has become too easy for ordinary people who are otherwise risk averse to be lured into poorly secured investments in the stock market.

The video is pretty instructive in that it tells you that a 5% tax cut results in a lot more actual $ being transferred to a rich person's wallet than your own but it doesn't tell you how this affects the stock markets.

There are two mechanisms by which it can affect the stock market.

1) In anticipation of a large tax cut, rich people will boost speculative pricing bubbles. These bubbles have the benefit of making their income seeing larger. That in turn will allow them to claim a larger dollar amount as a cut.

2) If a tax cut does not materialize then the rich are forced to deflate the stock market. Unless they do this, they will not be able to reduce the amount of money they owe as taxes. They make money by deflating the stock market because they pay less tax.

Here is a simple example.

If I am super rich and I have $1B in a portfolio and the market grows at 20%. Then I have made $200 M as investment income. This should get taxed at 23.8%. I would end up owing Uncle Sam about $47M. If Trump gives me a 10% tax cut, then my earning would be taxed at the 13.8% rate so I would owe only about $27M. I would have "made" $ 20M thanks to Donald Trump.

Now Donald Trump fails to deliver on the tax rate cut, I would still want to "make" $20 M, I would do whatever it takes to drop the value of my income to $113 M. Since my income is directly tied to growth rate of the market, I would have to see the market growth rate drop to 56% of its current 20%  AGR value.

Since my investment income is calculated on an annual basis. To move its net growth rate down to 50% after half of the year is over, I would need to freeze the portfolio value at its current level. If I had to drop the annual growth rate to 50% after 2/3 of the year was over, I would have to drop the value by 10%. As we get closer and closer to the end of the year, my portfolio has to shrink massively in order for me to keep the amount of tax I pay the same (see graph below).


In order to get there, I would need to start selling my own stock at a much lower price than it is currently valued. This should be okay as I deliberately over-valued it in anticipation of a tax cut.

This is why Secy Mnuchin says that if the tax cuts are not passed the market will collapse. [1]

Unfortunately for my toy model, in reality I am not the only player in the stock market. There are others who may seek a very different reduction in the value of their own portfolio, so if I start something, there is no guarantee it will stop when I want it to. This creates a lot of room for political pressures and factional dynamics. You may recall the role of the bankers' pool led by J P Morgan in 1929. They wanted the crash to stop but it didn't and that landed them in a hole they didn't want to be in.

This is obviously overly simplified, but it should give you a snap shot of what is likely in the near future.

Wednesday, October 18, 2017

GW170817 - A truly great day in science

I am sure we have all heard about the astounding discovery revealed two days ago (if not here is a good YouTube vid about it).  

I also managed to find this interesting summary data slide on AMVA4NP . People are saying this is the beginning of "Multi-Messenger Astrophysics". 



This is a really busy slide - but as you can see on it, the neutron star coalescence was observed in a galaxy approx 150 MLY away.  This kind of event releases a lot of energy and its called a Kilonova.

The event generated a massive electromagnetic emission (Gamma Ray Burst, X-ray burst, UV etc...) . You can see what this looked like on various cameras (bottom). The big black spot is the galactic center - there are millions of stars emitting light in there. And the two black lines are where we see light from the kilonova event. You can see it is almost as intense as the galactic center in some images. This really brings out how much energy was released in this event. I am guessing it probably vaporized thousands of star systems in a 100+ LY ball around it.

There is going to be a lot of discussion around this in the months and years to come, but I want to bring up one point which you can all see in the top left part of the slide.

The Gravitational Waves (GW) arrived a full 14 seconds before Gamma Ray Burst (GRB). I am assuming that the time stamps on LIGO and the GRS are well aligned but as both GW and GRB travel at the speed of light, this implies that the space time distortion caused by the event predated the electromagnetic jetting phenomena (which is where a GRB arises) by about 12-14 seconds. The space time distortion peaked a full 2s before the GRB jet developed and escaped the surface of the coalesced stellar mass.

There is some amazing high energy density physics to be modeled here. We are going to learn a lot from the differences in time between these signals.

Some significant developments in digital security this year

We have had a steady stream of bad news on the cyber security front. It is hard to keep all that straight and make sense of where it is all going.  I will attempt to summarize it here.

1) Early in the year, we heard whispers in news reports about RIS led attacks on the electoral systems in 2016. These were later confirmed by DHS officials in Congressional and Senate testimony. This is bad because it means your voter information can be modified and if your state or county uses some form of screening (they all do) to remove suspect voters from their rolls, your voting rights could be terminated.

2) In February of this year, the first SHA-1 collision was calculated. SHA-1 (and similar protocols) are used to sign documents over the internet. These protocols were thought to be unbreakable, but it was found that this is not actually true. Since document signing is at the core of all software updates to your personal devices (mobile, computer etc...) the detection of a SHA-1 collision has massive impact on the apparent security of digital information. While advanced protocols are being used in place of SHA-1, the idea that these may not be as secure as imagined is quite frightening.

3) Last year, there were rumors that Kaspersky AV was penetrated by RIS backed hackers. The rumors have now been reported in the lay press as being sourced to Israel intelligence. Apparently Israeli intelligence penetrated Kaspersky and found out that RIS was using the AV software to open backdoors into every computer on that used it.

4) The credit reporting service Equifax was hacked and the personal information (address, SSN, DOB) etc... of 143 million US residents was compromised. This is the digital equivalent of a Pearl Harbor, but no one seems to have quite figured that out yet. As people went to look at the Equifax site and report incidents of fraud, they were greeted by a large number of fake flash updates. The malware attempted to pass itself off as a Equifax product that customers should install on their computers.

5) WPA2 - a protocol used to secure WiFi communications critical to the functioning of mobile and IoT devices was determined to have a massive vulnerability in it. This is collectively called the "Krack Attack". No patches are available as of today for this. We are flying on a wing and a prayer here.

6) The NSA TAO's tool kit allegedly leaked out on to the internet early this year. The NSA detected a loss of these tools and informed various vendors to patch their breaches but it is unclear how effective the patches have been at containing the threat.

7) Yahoo finally admitted that something like 3 Billion of its accounts had been compromised in a security breach last year. The timing of this admission is important, it suggests something more than the usual level of incompetence is at play.

8) MSFT informed us yesterday that their main server containing information about bugs and hacking attempts/malware was breached about four years ago. Again - it is the timing of this admission that I feel reflects a growing sense of insecurity in MSFT.

9) (Thanks Kevin T). Deloitte was hacked and information pertaining to many government clients was accessed. We know very little about this. This is bad as Deloitte usually performs sensitive accounting services for a variety of big companies. Apparently Deloitte did not have MFA implemented on one of its admin accounts.

I feel two things are still somewhat viable

1) MFA - Multi Factor Authentication - this can get expensive but it may be the only way to secure critical information.

2) PGP - As this is based on the still NP -Hard prime factorization and random key generation problem, it is hoped that separate transmission of encrypted key and data will ensure good security.

That said all the breaches described above reduce the barrier to impersonation attacks.

Neither MFA nor PGP are secure against impersonation.

Thursday, October 12, 2017

Deza - How it really works.

This is a really good article by Micheal Weiss on the use of "Deza" (disinformation) by RIS throughout history. This matter has become quite important especially after the events of 2016. A great deal of the public understanding of these issues can be traced back to the writings of John Barron (NOT Trump's non-existent publicist).

The basic narrative underpinning Deza is the same every time.

1) RU lies
2) Fools believe RU lies.
3) RU lives happily ever after.

Unfortunately that is not how it works IRL.

After RU lies - it pays to have the lie trafficked. That part costs money, and it is usually money RU does not have. So after step 2 in the ideal deza cycle, the "other side" lies back, this sparks an arms race in lies. To win this arms race - RIS must seek out cheaper ways of trafficking its lies than the other side.  The RIS ways need to be a factor of ten or so cheaper because RU is very low on actual resources. If the race goes against the RU's favor, then the RIS will go into "Stalingrad" mode. In this mode - it cannot be said who wins - because even if the RIS "prevails", the cost of "victory" is staggering.

The article offers up the historical example of General Ivan Agayants of the FCD's D Department. This is a spymaster of considerable stature and one must see him in the context of the USSR's disastrous WWII experience. Gen. Agayants grew up in a world where even a morsel of bread was hard to come by. To him the real challenge was how to traffic Soviet lies without running up a huge bill. It is natural that he came up with the scheme Micheal describes.

In my opinion, the choices made by Gen. Agayants reflect the reality of these operations. It is difficult in such an operation to maintain control over the situation for long periods of time. It is akin to starting a fire in the forest, yes the dead wood will burn but I don't think it is possible to make a fire burn selectively. One can even say that there is a physics about these types of jobs, they have to operate withing a very narrow region - the intention of the initiator cannot be exposed, and the actors in this farce should not wander off script. While the exposure of the initiator is not always bad, most spymasters loathe operations that wander out of the zone of control. While the exposure of the originator can be passed off as "necessary" measures put in place by the spymaster to communicate their nation's point of view, the uncontrolled behavior of perceived assets suggest incompetence. No spymaster wants to be thought of as being incompetent.

I feel that when it was clear to Gen. Agayants that the deza campaign was not going to move the needle vis-a-vis German participation in NATO, his zeal for an operation like this would have dropped. As the likelihood of exposure became higher, his actions would have become tempered by the thoughts of a CIA led riposte and when latent anti-semitism began to independently drive the phenomenon, he would have decided to wash his hands off the whole thing. Can you imagine what it would have been like to be known as the Soviet spymaster who reincubated Nazism? - right after WWII? at a time when the USSR was already facing nuclear attack by the United States?... I confess I don't know the man, but I doubt Gen. Agayants craved for such accolades.

The article wisely points out that the internet has lowered the cost of trafficking lies for the RIS but one must remember it has lowered the barrier for counter-lying as well. I think here lies the key to resolving the current crisis.

Some useful links to educate yourself

1) Hamilton 68 Initiative  
2) The KGB Today - by John Barron
3) KGB - The Secret Hand - by John Barron
4) Russian Disinformation Technology - by John Pollock

Tuesday, October 10, 2017

A grim reality has begun to sink in

Among seasoned watchers of troubles (such as yours truly) a grim reality has begun to sink in. As Inspector Pandit once said to Inspector Purohit in the movie Maqbool

Ladki mangali hain, laashon ke dher pey say vida ho key jayegi..
(The bride is cursed, the recessional will walk over a mound of corpses)

Donald Trump insists on playing the Madman when there is no real national security reason to do so. 

As the TrumpRussia probe nears its logical conclusion - Trump's sense of desperation grows. 

Even if the probe does not directly accuse him of treason, it will nail his kids for the same. Trump knows that he will not able to pardon his kids. Once the kids face the prospect of prison, family secrets and skeletons in the cupboard will come crawling out.  These secrets once public will poison his ability to feel any form of joy over the power he apparently enjoys.  A decent and real man would take responsibility for everything and save his family in the process but Donald Trump is none of those things. 

Given how much he has hanging on the sex crimes, the money laundering and treason front, Trump knows there is little hope of him ever functioning as a normal US President would. There is so little for him to get a sense of positive energy there that he routinely retreats to his golf courses where he can avoid thinking about this. 

Trump's only avenue to a sense of empowerment is picking a fight with the GOP and getting something useful (to him) out of them. There is only one thing that would be truly useful - a kind of Nixonian get-out-of-jail-free card. Trump clings to the hope that he will be able to get such a card from the GOP and weasel his personal way out of this. If his family is sacrificed in the process, he seems to be okay with as long as they don't talk about the horrible stuff he has done to them.  He probably believes he can silence them for good. 

Unfortunately no such card exists. The GOP cannot make such a card up. It is already suffering a massive corrosion of public confidence on account of its association with Donald Trump. Even if the GOP was on firm electoral footing, it cannot afford to hand out such a card because no one can truly know how toxic Trump's links to sex crimes, money laundering and Putin's RIS really are. Such a card would become a millstone around the necks of GOP staffers for the rest of eternity. 

Trump cannot get his head around the absence of such a card. His entire sense of self-worth rests on the ability to save his own skin and when it has to be explained to him that no such thing is possible, his narcissistic mind turns to thoughts of a destructive nature. 

It is in this context that one must see his behavior towards North Korea.  It is IMHO foolish to paint what Trump does as a "Madman Gambit" - when it is more correctly simply the actions of a madman!

He is goading KJU into a nuclear war. 

What Trump does not grasp in his feeble mind is that when deterrence breaks down vis-a-vis North Korea (say because KJU felt intense use/lose pressures)  - it breaks down globally - No one will take that idea seriously ever again. This will completely re-write global military balances that rely on nuclear offsets to shortages in conventional deterrence regimes. 

At this time Chinese and Russian national security strategists are wondering how to cope with the inevitable fallout of a failure of the "Madman Gambit". As the idea of deterrence will be badly mauled by that outcome, they must prepare for a nuclear war. 

In 1983 the Russians could not distinguish between Reagan's "Madman" act and the reality of the Able Archer exercise in Europe. They misconstrued the exercise as a prelude to a sudden nuclear strike and brought their entire nuclear arsenal to a state of maximal alert without any of the usual signaling. Out planet stood on the precipice of nuclear annihilation and not even those paid to know about were actually aware of it. 

I feel we are in a similar place. We are extremely close to the edge and there will be no positive resolution time around. The last time around sane people were able to de-escalate and reduce the build up of tension. President Reagan for all his flaws *listened* to his advisers. That is NOT where we are now.  

When major experts in the US are discussing potential ways to interrupt the nuclear chain of command - then you know you are in deep shit.  

Thursday, October 05, 2017

Is Russia's domestic ONG distribution network critical to its political survival?

We know that Russia relies on ONG exports to shore up its GDP. Based on GovRU figures, these exports account about 20% of the GDP.

The general sense among Russia watchers is that profits from these exports go towards shoring up the RU political system - specifically
  1. lining the pockets of the oligarchs (including Putin), 
  2. keeping the RU Military-Industrial complex happy, and 
  3. subsidizing the internal distribution of essential commodities. 
Traditionally political analysis of RU has focused on the first two stabilization mechanisms. I propose we think carefully about the third item on that list.

Geographically speaking Russia is unique - no other country matches it in terms of climate and length of East-West logistical chains. You might be tempted to thing that Canada or Scandinavian countries are similar - but they really do not have the anywhere near the logistical problems. To get a sense of this compare photos of RU at night with other countries. You can see a cluster of lights at the eastern edge of the Northern European plain (where the Grand Duchy of Moscow historically resided) and you can see a small belt of lights lining the Sea of Okhotsk but in between the two (across the expanse of Siberia) you only see a few thin strands of light. One of these is the Trans Siberian railway and the others are the extremely few roads in Siberia. This image reinforces the critical nature of Siberia to Russia. 

I find it helps to think of Russia as an ocean dotted with islands big and small. The islands are connected mainly by railway lines and roads. Under Russian climatic conditions there is a significant amount of thermal cycling which tends to rip up the road and cause railway tracks to become mis-aligned. This raises the cost to maintain each mile of road or railway. The weather also does a number on the rolling stock and vehicle fleets. It appears that the GovRU bears most of the costs associated with the road and rail maintenance and the Russian people bear the cost of maintenance in terms of fuel costs and vehicle repair.

It is no surprise to me that the despite being a major global ONG producer, the average Russian pays 5-10x more than the average Canadian or American for a gallon of gas and that the vehicle repair industry is one of the biggest contributors to the Services portion of the Russian GDP.  

Another point of interest is that while Russia has a GDP that is 5x smaller than the US in PPP terms, its GHG emissions per capita are only 60% of US numbers. This strongly points to the fact that the average Russian consumes much more carbon per unit of productivity than the average American. Add that to the fact that RU life expectancy is much lower than US life expectancy and one realizes that despite burning so much carbon - the Russians don't get a whole lot out of it. 

These subtle comparisons reflect the true scale of the Russian internal distribution problem. Russian ONG is more expensive to mine and more expensive to distribute *within* Russia. As the price of gas finds its way into the cost of every commodity, we see that everything that is derived from ONG is more expensive in RU. As Russian lifestyles evolve to a much higher energy intensive variants we are likely to see the domestic pressures rise. 

I think this sets up some interesting thoughts

1)  The notion that a low international oil price is "something Russia can live with" is not really sustainable. A high international oil price makes it much easier for Russia to transfer the high costs of its own internal distribution on to international buyers. The Russians will be happiest when selling the tiniest possible amount of oil internationally will be enough for them to supply it at a much lower price at the pump locally. 

2) Historically Russia has always managed to keep its populations satisfied by dumping relatively small quantities of ONG, food and coal on the domestic market. But as peoples' expectations of lifestyles change, Moscow will have to dole out more to keep people happy. It is not clear if Moscow's distribution system can keep up with the extra demand. It is also not clear if Moscow can scavenge enough resources to keep this going without a dramatic increase in the exploitation of Siberian reserves. 

3) It may no longer be possible to view Siberia as a place where nothing really happens. Given the resources it possesses and the fact that it sits right in the middle of the East-West supply chain - Siberia will most likely make or break modern Russia. The economics of exploiting Siberian reserves is challenging. You have to put a lot in to get even a little bit out. It is not clear if Russia can raise the capital needed for an economically viable exploitation of Siberia. 

It may be worthwhile to take a closer look at the distribution network for essential commodities inside Russia. It may inform us about the shape of things to come.* 

* I am not discounting the traditional measures like the political temperature of the cities, the shifts in vodka consumption but I suspect risk leaving out a rich vein of knowledge if we completely ignore the economics of internal distribution inside Russia. 

Friday, September 22, 2017

BTC in the Bull Trap

It appears BTC prices are headed for the "Bull Trap". This is a technical term used by people who study speculation or hype cycles [see this article].  A bubble phenomenon (in this case BTC valuation) has a well known shape.

If you pull up the BTC to USD valuation, you will see a similar shape appear every few years.

The trigger for speculative bubbles in the BTC market appear to be FBI seizures of BTC from places like Silkroad, or Hansa/Alphabay. These are illegal markets in proscribed materials which hold large quantities of BTC as escrow. The bulk of the high value transactions on these markets are narcotics related. There is at this time a sizable cash flow from the US to China (mainly purchasing Fentanyl) but every major narcotics player uses these markets.

When the FBI "takes down" a well known market place, it does so (IMHO) because the volume of trade there in illegal narcotics becomes sufficiently high that it starts affecting the traditional price control mechanisms that the DEA and USIC put into place. I think its all part of a larger plan, but obviously I was never read in to what that plan is.

Each "take down" is accompanied by seizure of several hundred thousand BTC. The BTC are usually returned to the owners (if they are not involved in illegal activities) or simply auctioned after a few months. In the immediate term however a major take down produces a sharp rise in demand for BTC, and that drives the price up. In this space speculators jump in and drive the hype cycle/bubble.

At the peaks of the hype cycle, the BTC exchanges come under pressure. The demand is so high that counterfeiting grows and the exchanges are supposed to stop that. If they don't they fall like 'Mt Gox' which creates an added level of scarcity and feeds the bubble.

I feel the recent Chinese move against BTC is driven by concerns about the security of the exchanges themselves. I suspect that the DPRK guys have been gaining off the BTC market in ways that the Chinese don't like very much (and the Chinese don't like anything they can't control anyway - really who does?).

As the exchanges shut down, the transactions displace to other places which can still host them, this loss of trade momentum can cause the price to drop. That price drop is where the Bulls get stuck. It is the panic among the Bulls that really fuels the price plunge. As the exchanges shift and new channels emerge, the trade momentum resumes and we head into the "normal". Beyond that lies the much more complex rationalization process.

We must recognize that just as US or Chinese interventions can cause changes in the price of BTC, other states can affect it too.

As things stand unless the RU can get money back out of Wall Street, the RU banking sector will collapse. There is a partial collapse already on the private side, but the contagion of bad debt will spread to the government side too. RU will not want the price of BTC to fall until they have extracted whatever price they want for their BTC.

DPRK also needs to carry out BTC based transactions. This is the fastest way to get what it wants without having to pay in hard cash. Thanks to BTC, there is no need to send ships filled with Burmese Heroin to Iran and then get "SuperBills" back from there and then use the "SuperBills" along the I-90 corridor in the US ... etc etc etc... all that pain and suffering goes away with BTC.  If KJU is going to keep conducting tests, he needs a less than cumbersome payment options for all the stuff he needs to keep going.

With lots of pressure on BTC from RU and DPRK, I think (despite US and CN moves) we are likely to see new exchanges emerge. Either the PRC government will cave to pressure from the Fentanyl sellers or from its Crypto currency miners (which I will bet you are linked to Chinese intelligence operators) or desperate parts of the RU private banking system will create new exchanges that pull the volume off the Chinese exchanges.

This is IMHO far far far far from over.

DPRK is planning a Juche Bird to remove all doubts about its capability. I think the impact of such a statement by KJU is profound and it will amplify pressures to reignite the BTC valuation.

The battle for control of the BTC price is actually the battle for control over the global economy.

Monday, September 18, 2017

Inertial Measurement Units (IMUs)- Some key issues - IV

The future is hard to predict and the present can only be described partially because we are never fully informed about anything. With that caveat I can make the following guesses about where this is likely to proceed.

As seen in earlier posts, barring major advances in understanding of gravity, defining the accuracy of an IMU will remain a very challenging affair. The precision of an IMU is a relatively simpler affair and we are likely to see Atom optics based gyros used to "clock" the performance of other systems. This kind of bootstrapping will create a deeper understanding of the nature of the error in other systems.

As Atom Optics related technologies become better engineered, we will see a gradual shift in the mission critical side of IMU applications. On the commercial side we will likely see a growth in MEMS based applications. It is not entirely unlikely that these two branches may come to leverage off each other.

I feel we are likely to see the following happen too

1) Role of Sensor Fusion: Using sensors of different types to check on each other offers interesting avenues for reducing noise in measurements of gravity. Schemes involving magnetometers have already been demonstrated, but a number of other schemes may also be possible. Such schemes will improve the precision of any number of existing devices.

2) Clouds help reduce noise: In theory one could have the IMU transmit a signal to a cloud, process it on the cloud and then resend the filtered signal back to the guidance system. This would be too unwieldy to carry out in a military or strategic application, but it may be possible to use this approach with commercial devices.

3) Deep learning will help fish weak signals from noise: It may become possible to implement a deep learning to extract small signals out of the noisy data from a cheap IMU. In the event that a deep learning network is so trained, a version of this network could be deployed on an embedded system attached to the IMU. It is difficult to ascertain how "good" this could be in actual deployment but the idea is plausible.

When speaking about these issues in the context of an actual deployment (as opposed to a "hey check out my Github for my latest Python code" context) - we are looking at a lot of money and hours spent on developing high reliability code and hardware. Those problems easily add decades on to the simplest thing.

N.B.  In order to keep this simple I have left out two other sources of trouble in an IMU - offset and latency. The discussion of these topics is complicated for non-specialists and getting into that will not add anything to what I am attempting to do here.

Inertial Measurement Units (IMUs)- Some key issues - III

We have come a long way since the first mechanical spinning flywheel gyros were made at the beginning of the 19th century. There are three novel techniques available for sensing now

1) Coriolis effect based devices [a nice discussion here] -  These devices are now very popular in commercial cell phones. The most popular versions use Micro Electro-Mechanical Systems (MEMS), and the rotation and acceleration is sensed as a change in the capacitance of a microfabricated circuit. The demands put on fab side are significant although things are getting cheaper as the scale of deployment grows. As the entire device is made in a semiconductor fab, the overhead associated with creating noise control electronics is reduced, as the signal is basically electrical in nature, a number of existing design for low noise signal amplification can be leveraged to improve performance.  Though not terribly good in terms of precision these devices are cheap enough to be deployed on scale. It is possible to remove noise by using a magnetometer or other sensors, but its still pretty bad relative to existing peers. With commercial applications growing, a lot of people are working on ways to fuse the data from multiple sensors and use cloud based big data filtering tools to get intelligence from these devices, but that stuff is still IMHO in its infancy. It is fantastically easy to get hold of a piece of python code that hacks into one of these and gets data out. If you are looking for a place to start learning about these, I recommend playing with the Arduino backed versions of these. I did this with a high school student on the robotics team some years ago - and it was a fantastic pain in the rear but great as a learning tool.

2) Sagnac effect based devices [a good place to start] - These devices are popular in the aerospace side. This effect is used for Ring Laser Gyros and Fiber Optic Gyros (This effect is also used in Atom Optics based systems but that is discussed as a separate topic). One would naively think these systems are the most robust form of sensing possible but there are subtle issues that limit their capabilities and utility [see here]. The main limitation on these devices comes from the fact that to get a very high resolution, one needs a very large path length. Such a path length can only be achieved by incurring penalties in weight and size. The manufacture of these devices is non-trivial and would require significant investment.

3) Atom Optics [See paper by Mark Kasevich etal. in this link] - These devices were originally conceived as sensitive tests of gravitational physics in the atom optics boom years of the last century. These ideas lounged in unwieldy room sized setups in the basements of physics departments for several decades but sustained investment from the NI-24 program by the Navy and a passing interest from the IC enabled the construction of very robust variants of these devices*. Though initially considered too fragile to be used in real world applications, the quality of engineering has steadily improved and I think we may see these on real world aerospace platforms. These devices hold the promise of a significant reduction in noise over current systems and the general thought is that with some effort this will lead to a much better place in the long run. That said the manufacture of these devices is non-trivial, the demands made on associated instrumentation are significantly larger than mechanical devices.

If I were to rate these platforms qualitatively in the order of error (given that hard metrics on this are difficult to come by in context) - I would say that Coriolis systems have the worst noise issues, followed by RLGs and Fiber Optic devices. The Atom Optics systems have the best noise characteristics cited in public sources. I would not take any of these numbers too literally as they are not available for the kinds of application that have spiked public interest,  those numbers are a closely guarded secret for obvious reasons.

As a rule of thumb, if you have a lot of noise on a sensor - you have a large overhead in terms of associated algorithms (and related electronics and software) needed to clean up that mess. IMHO this really limits the ability to use commercial/off-the-shelf stuff in strategic or mission critical applications.

In the next post I will make a few remarks in passing about the way things might change in the future.  (cont'd in next post)

* one of the prime drivers of this effort was the retirement of highly qualified technicians that could make mechanical gyroscopes and gradiometers in the US. Faced with a forced technological regression the S&T guys in the USG gravitated towards the only hope they had at the time of rapid advances. Hence the interest in Atom Optics which had emerged as one of the major candidates for other high impact technologies like Quantum Computation.

Inertial Measurement Units (IMUs)- Some key issues - II

As I indicated in the previous post, the ability to make a "good" IMU is challenged by two basic issues

1) The ability to machine precise parts - such as perfect spheres.
2) The ability to correctly model the behavior of gravity along the IMU's trajectory

The absence of perfect machining creates avenues to add error to the measurement of gravity. This affects the precision of the IMU.

The inability to properly model the local behavior of gravity leads to misinformed notions of accuracy.

There can be a "sweet spot" where acceptable levels of imprecision and inaccuracy coexist in harmony. Under such circumstances, it may be possible to make an IMU that is "good enough" for a particular role. Typically short range ballistic missiles can get away with having "crappier" IMUs simply because they aren't going very far or very high or very fast. However as you get up in speed and altitude, IMUs become quite critical to success.

I suspect the North Koreans are in such a "sweet spot", but I fear they will not be able to stay there very long as their ambitions grow with each passing day.

Here are some ways in which to manage the error in the measurements

1) Comparing measurements on two or more IMUs - If we mount two IMUs on our rocket then we can examine how they differ in the estimates of the height they report. If one IMU is much more sensitive than the other (i.e. able to see differences in height of centimeters as opposed to meters), we could see if it reports a change of 100 units when the coarse IMU reports a chance of 1 m. This kind of thing is pretty common in other measurements. In the published literature you hear words like "Allan Variance" [see this link for more], this refers to way of comparing the performance of two sensors and getting some meaningful measurements of the ARW and drift. In practice, placing multiple IMUs (especially ones with combinations of fine and coarse measurements) on operational platforms is a major manufacturing burden.

2) Error modeling - Once measured there are ways in which one can model the ARW and drift errors in our IMU. Error analysis tools have evolved significantly over the decades. Some really amazing stuff is now available. Most of the methods some variation of "quaternion based filtering". "Quaternions" are a very mathematically compact way of representing the information typically obtained from an IMU. "Filtering" because you are removing noise from the IMU data. Here the community of signal analysts broadly splits into two groups - the DSP guys (who use deep understanding based ideas like Kalman filtering) and the Deep Learning guys (who use techniques like neural networks). It is not clear if either approach gives a clear advantage in terms of accuracy however both approaches require concurrent development of embedded computation systems. That adds large overheads to the manufacturing burden associated with IMUs. You are basically adding a dedicated fab line, firmware development and software validation & testing to the program cost here.

3) RF ranging and other external referencing -You can always use a simple RF signal to correct the accumulation of errors in the IMU. However for extremely long range trajectories, the RF signals run out of line of sight with your rocket. So you have to either use a satellite or do something quite complicated to "get your bearings". If you decide to use a satellite RF beacon, you need to build a really good way of keeping that satellite in a particular spot in space otherwise you can't range off it in any error free way. That part can get really entertaining given all the weird drag effects you have in earth orbit and those gravitational effects I alluded to earlier. Also you are now adding the cost of a satellite beacon program to the cost of your rocket guidance program. This quickly devolves in to a number of chicken-and-egg questions. A highly unpleasant situation but sometimes a way can be found. One of the my favorite ideas in this context is Stellar Navigation. A combined "Astro Inertial Navigation" system was used on the SR-71 and a stellar alignment system was used on Gravity Probe B. These are relatively simple to implement and very robust. The unfortunate side effect of external referencing is that it can be interfered with and that makes its less suitable for nuclear deterrence missions.

In my next post I will discuss some novel gravity sensing systems that are finding application in commercial IMUs and how things might play out for them in the future.

(cont'd in next post).

Inertial Measurement Units (IMUs)- Some key issues - I

The proliferation of Inertial Measurement Units (IMUs) has rightly caused people to become concerned about the likelihood of their misuse by rogue states. There are however physical constraints that limit certain kinds of misuse. I discuss some of the key limitations below.  A good reference to have handy for this is "Inventing Accuracy". If you have problems following what I am saying, please reply to this post in the comments below and I will get back to you asap.

For the purposes of this discussion, let us consider a simplified IMU which consists of a gyroscope and a gradiometer. The gyroscope ensures that the gradiometer is aligned with vertical direction. In our simple model, the gyroscope is a mechanical device- a spinning wheel (the kind you might find in an undergrad physics lab) and the gradiometer is a simple spring which is compressed/stretched by a test mass attached to it. Also let us assume that our IMU is non-ideal in predictable ways and that our IMU is attached to a rocket that behaves in a totally predictable way (these are both over simplifications that do not hold IRL).

In the ideal case, our gryoscope is spun up to a certain angular velocity about its vertical axis and since the entire assembly sits on a gimbal mount, it holds the spring and test weight of the gradiometer perfectly vertical.  The test mass experiences a gravitational field that pulls it downwards and this causes the spring in the gradiometer to extend. If we apply an acceleration to the IMU (as we might if we were to light the rocket engine under it), we see the extension change as the added acceleration also pulls on the test mass.

In the ideal world, our IMU works perfectly, as the rocket engine lights up we see added acceleration add to gravity and the extension increases. As the rocket rises into space, the acceleration due to gravity reduces. A computer attached to the IMU records the change in the extension with time and when the change in extension reaches a particular amount, the computer attributes this change to the rocket reaching a particular height above ground and shuts off the rocket engine. Everyone is happy.

That's not the way it works IRL.

Firstly our gyro experiences friction on its bearings. This leads to a torque that changes its angular momentum. The decline in angular momentum presents in two ways - firstly as a set of random angular deceleration events that cause the angle of the gyro to rattle around (this is called Angular Random Walk or ARW) and secondly as a slow reduction in its angular velocity that causes the angle of the gryo to shift in one direction (this is called "drift"). As the gradiometer is attached to gyro, shifts in the gyro angles propagate to the measurements of acceleration. The exact model of propagation is quite nontrivial but in this way the gradiometer picks up an ARW and Drift of its own.
Errors in the gradiometer reading (i.e. extension) translate into errors in the estimation of the height of the rocket above ground. A large error could significantly alter the trajectory of the rocket.

A mechanical gyro and gradiometer may sound very low tech, but they are based on technologies that are over a hundred years old. They are extremely reliable. If you can machine perfect spheres (turns out that is a lot harder than one might think it is) you can make very high precision and high "accuracy" IMUs. I use "accuracy" in quotes because it turns out that it is quite difficult to define the term in this peculiar context.

As we go up and out from earth, we experience gravitational contributions from poorly characterized terrestrial (such as the non spherical nature of earth) and extraterrestrial sources (the moon, nearby asteroids, tidal effects etc...). These effects make it hard to claim deep knowledge of the gravitational acceleration at various altitudes. This makes it difficult to define "accuracy" in the context of a gradiometer.

(cont'd in next post).