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and here comes my standard question: how can we use this for space? fast detection of natural disasters onboard?

Even on ground. You could for example teach it what nuclear reactors or missiles or other weapons you don't want look like on satellite pictures and automatically scan the world for them (basically replacing intelligence analysts).

In fact, I think this could make a nice ACT project: counting seals from satellite imagery is an actual (and quite recent) thing: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0092613 In this publication they did it manually from a GeoEye 1 b/w image, which sounds quite tedious. Maybe one can train one of those image recognition algorithms to do it automatically. Or maybe it's a bit easier to count larger things, like elephants (also a thing).

In HiPEAC (High Performance, embedded architecture and computation) conference I attended in the beginning of this year there was a big trend of CUDA GPU vs FPGA for hardware accelerated image processing. Most of it orbitting around discussing who was faster and cheaper with people from NVIDIA in one side and people from Xilinx and Intel in the other. I remember of talking with an IBM scientist working on hardware accelerated data processing working together with the Radio telescope institute in Netherlands about the solution where they working on (GPU CUDA). I gathered that NVIDIA GPU suits best in applications that somehow do not rely in hardware, having the advantage of being programmed in a 'easy' way accessible to a scientist. FPGA's are highly reliable components with the advantage of being available in radhard versions, but requiring specific knowledge of physical circuit design and tailored 'harsh' programming languages. I don't know what is the level of rad hardness in NVIDIA's GPUs... Therefore FPGAs are indeed the standard choice for image processing in space missions (a talk with the microelectronics department guys could expand on this), whereas GPUs are currently used in some ground based (radio astronomy or other types of telescopes). I think that on for a specific purpose as the one you mentioned, this FPGA vs GPU should be assessed first before going further.

Q1: For the time being, for what purposes computers are mainly used on-board?

for navigation, control, data handling and so on .... why?

Well, because the point is to identify an application in which such computers would do the job... That could be either an existing application which can be done sufficiently well by such computers or a completely new application which is not already there for instance because of some power consumption constraints... Q2 would be then: for which of these purposes strict determinism of the results is not crucial? As the answer to this may not be obvious, a potential study could address this very issue. For instance one can consider on-board navigation systems with limited accuracy... I may be talking bullshit now, but perhaps in some applications it doesn't matter whether a satellite flies on the exact route but +/-10km to the left/right? ...and so on for the other systems. Another thing is understanding what exactly this probabilistic computing is, and what can be achieved using it (like the result is probabilistic but falls within a defined range of precision), etc. Did they build a complete chip or at least a sub-circiut, or still only logic gates...

Satellites use old CPUs also because with the trend of going for higher power modern CPUs are not very convenient from a system design point of view (TBC)... as a consequence the constraints put on on-board algorithms can be demanding. I agree with you that double precision might just not be necessary for a number of applications (navigation also), but I guess we are not talking about 10km as an absolute value, rather to a relative error that can be tolerated at level of (say) 10^-6. All in all you are right a first study should assess what application this would be useful at all.. and at what precision / power levels

The interest of this can be a high fault tolerance for some math operations, ... which would have for effect to simplify the job of coders! I don't think this is a good idea regarding power consumption for CPU (strictly speaking). The reason we use old chip is just a matter of qualification for space, not power. For instance a LEON Sparc (e.g. use on some platform for ESA) consumes something like 5mW/MHz so it is definitely not were an engineer will look for some power saving considering a usual 10-15kW spacecraft

What about speed then? Seven time faster could allow some real time navigation at higher speed (e.g. velocity of a terminal guidance for an asteroid impactor is limited to 10 km/s ... would a higher velocity be possible with faster processors?) Another issue is the radiation tolerance of the technology ... if the PCMOS are more tolerant to radiation they could get more easily space qualified.....