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Comment by ISL | Hacker News Reader

You can do better than Doppler shift. If the clocks on three ping detectors are well-synchronized and their locations known, you can use the ping arrival times to triangulate. Sound propagation in water is nontrivial, but the people who are good at it are good at it.

Furthermore, as long as the clock on the pinger is fairly good, the ocean environment fairly stable, and you don't drop many pings, you can drive one ping detector around and triangulate from the ensemble of ping measurements.

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You can do better than complete waveform time of arrival.

Sound propagation in water is dispersive (higher frequencies travel faster, but lower frequencies travel farther). With an accurate model if the chirp waveform, you can determine distance more accurately by looking at the amount of signal "spreadding" and the amount of attenuation of specific signal components due to this shifting.

You can do better than that, too. Theoretical accuracy of time of arrival distance approximation is directly related to the wavelength of the transmission signal. If you can model the transmitted signal and its transmission path accurately enough that you can get a strong correlation between the received signal and the modified signal (in this case taking into account Doppler effect and wave dispersion), then you can accurately measure both the time of arrival and the phase of the signal. Assuming a perfect model (HA!) the accuracy of the distance calculation is soon dominated by the various noise components (typically your timer noise, power supply noise, decimation noise from your ADC, and various thermal noise sources in both the transmission path and your measurement equipment).

You can do that with a single moving platform, since the target is not moving. Record the bearings for half an hour, make a 90° turn, and recore another half hour of bearing data. That should give a decent approximate location. Its also basic target motion analysis that a military sonar operator can do in their sleep.

> Its also basic target motion analysis that a military sonar operator can do in their sleep.

Which makes me wonder: Does the US not have military assets in the area? Or do they and they don't want to disclose their capabilities?

EDIT: I'm behind the times; I didn't know the US had a sub-hunter in the area.

I think it's safe to assume that someone(US, Russia, China, etc.) has something in the area, but nobody's going to be talking about it to the public.

It's not so much about disclosing capabilities as much as it's just simply operational secrecy. The entire point of a submarine is that it's hard to find.

>I think it's safe to assume that someone(US, Russia, China, etc.) has something in the area

accidentally, this search may find a lot of that "something"

It's in international waters, the Chinese have no authority here and in any event Australia is coordinating the search. Ocean Shield is an Australian Defence Force ship (although not grey like your typical warship).

http://www.theguardian.com/world/2014/apr/07/mh370-black-box...

The US has a specialist sub-hunter in the area, and they've made extensive use of P3 and P8 aircraft. I doubt they're terribly sensitive about their ability to find a deliberately pinging object 6000m below the surface.

"There are 11 military aircraft, four civilian aircraft and 14 ships taking part in the search on Wednesday."

http://www.theguardian.com/world/2014/apr/09/mh370-search-ar...

>since the target is not moving

assumption

True, but is very likely a correct one.

Not really - underwater currents can be quite strong. If you were creating a model to accurately position this thing, you'd be best to add a v⃗ component for both the transmitter and receiver sides of the equation.

I'm not that familiar with the bathymetry[1] of the area, but I have been seeing reports that the locations are between 3000m and 6000m deep. At that depth, even a strong persistent current is probably only a few cm/sec. For the precision of TMA, that's effectively stationary; the noise in the bearing rate measurement is going to be greater magnitude than the true bearing rate.

[1] Why is "bathymetry" not in Chrome's spelling dictionary?

It's in the 10s of cm per second and up to 1m/s in some places, though not SW Australia

http://hypertextbook.com/facts/2002/EugeneStatnikov.shtml

Sadly the towed pinger locator (TPL-25) is omni directional.

But by analysing the inter-ping interval you can determine a CPA point. Something below I wrote on reddit about this technique:

Due to the pulse length (10ms) there is an inherent 100Hz bandwidth in the signal, which is equivalent to the frequency shift you would expect if moving at 4m/s. In other words, Doppler measurements of a single pulse is NOT going to be useful in attempting to localise.

However, because the pinger has a relatively stable repetition rate (about 1.106s from what I could see) you can do a cool trick to localise it (assuming the source is stationary):

- Perform a pass over the area of interest (ie where the pinger is) - measure the ping times of arrival (either manually with waveform inspection or write an envelope detector) - plot the ping times of arrival versus the time of arrival modulo ping interval. ie in MATLAB: plot(toa, mod(toa, 1.106), '.'); - The plot indicates the relative distance from the source / receiver. Hopefully the plot should contain a local minimum representing a closest point of approach (ie like http://imgur.com/v1ZclaX ). This means that the source lies in a line perpendicular to the vessels course centred at the location of the receiver (ie TPL-25) at CPA time - Perform another pass over the area of interest on a course perpendicular to the first - measure the ping times of arrival and look for CPA as before - You should now have two intersecting lines. Guess what should be at the intersection? :)

This relies on having a stable ping repetition rate.

BTW this is the author of the linked post here :)

Rodney

Edit: @ISL has hit the nail on the head there. Hyperbolic trilateration using multiple simultaneous receivers is the way to go. RAAF will be trying this with sonobuoys deployed from P3-C Orions

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