# Low Frequency Radio Trilateration

In summary: ...need to calculate the power density at the transmitter, the power density loss due to distance, and the lpm of the receiver.
I am simulating a trilateration process that does not require accurate timings to be transmitted as data. The trilateration process uses a known power density, at the transmission source, to within a fine tolerance. Thus, the following equation is the basis for the calculation:

Power Density (Source) = PDs
Power Density (Receiver) = PDr
Power Density Loss = PDl
Loss Per Meter = lpm

PDs - PDr = PDl
PDl / lpm = Distance

I know that additional real-time factors can be considered such, as atmospheric conditions, that may effect the variable lpm and introduce a compound error to the final distance calculation. Thus, I need to create a function ( f(lpm) ) and understand all factors that need to be considered to provide an accurate result.

So, my question is two-fold, what considerations must be made for f(lpm) and what would be your estimate of accuracy? Of course, I would ask that you leave any engineering points to one-side for the moment.

Please provide a few details that are essential to providing an answer.

What frequency will you be using?
How far do you want to be able to measure distance?
What kind of antennas will you be using and how high will they be?
What is f(lpm)?
What accuracy do you need?

I'm not sure about very low frequencies, but my experience with sensor nets at 400-2400MHz indicates that obstructions and multi-path effects make using received signal levels a _very_ approximate and unreliable measure of distance. So your attempt to characterize the error could be futile. Here's a paper I found looking for "RSSI distance measurement" that might lead you to more:

I second schip's comment about multi-path. RSSI is not useful for determining distance in the general case.

What frequency will you be using?

A spread spectrum < 1000Hz.

How far do you want to be able to measure distance?

Ideally, any distance including into orbit.

What kind of antennas will you be using and how high will they be?

Engineering issues should not be raised at this point.

What is f(lpm)?

A function to calculate power density loss per meter. We'd probably need to begin with the power at source and use a function to map the loss until it was equal with the power density received. This would remove compound errors. So, the function is probably better described as distance = f (PDs).

What accuracy do you need?

As close as we can get it.

I'm not sure about very low frequencies, but my experience with sensor nets at 400-2400MHz indicates that obstructions and multi-path effects make using received signal levels a _very_ approximate and unreliable measure of distance. So your attempt to characterize the error could be futile. Here's a paper I found looking for "RSSI distance measurement" that might lead you to more:

Thanks for that, I'm having a read through it now. Just a few points first. First, low frequency radio waves tend to pass through obstructions without interaction. There can be a tendency to follow a ground path, but as we are recording power density and the wavelengths are so long we can establish a filter or noise gate to eliminate signals below a critical power density or with a phase discrepancy. This should eliminate multi-path interference which would be an issue at shorter wavelengths.

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The US Navy used to operate a transmitter in upper Michigan to transmit to submarines. It operated at 10,000 Hz with megawatts of power and miles of antennas.

I used to work with transmitters between 200 & 400 kHz using ferrite rod antennas with about 50 mW of power. We got about 30 meters of range.

schip666!, I've read the document you linked to and I found the following:

The experimental set up consisted of two crossbow motes programmed with count_send and count_receive programs written using visual C#. count_receive program was also designed to read the RSSI value from the mote’s memory and display it in command prompt.

The error appears to be related to the electronics being unable to gauge the signal strength properly. Its probably similar to the iPhone 4 issue where there is no standard to calculate the RSSI.

I used to work with transmitters between 200 & 400 kHz using ferrite rod antennas with about 50 mW of power. We got about 30 meters of range.

Any idea what your f(PDs) function looked like or what factors it considered?

I'm afraid I've long ditched all my stuff pertaining to such systems.

I suggest you do a search for propagation issues in

Oboe
Loran
Decca

There was a book by Laurila that discussed this as well.

I'm trying to figure out the structure of this equation. So, to calculate the power density at the receiver we would use the following formula:

PDr = PDs/ 4 pi R^2

To remove compound errors, we need to account for all the variables over a given distance. Thus, for every meter, we need to account for additional sources of loss (ASL):

PDr = (PDs /4 pi R^2) - ASL

Thus, we can wrap this up in a function and use a lookup table to calculate the losses over a location in 3D space as so:

PDr = f(PDs, distance)

So, rewriting to solve for distance, the formula is:

Distance = f (PDr, PDs)

and the function has a lookup table for the specific loss over a 3D area. We could also use a rough trilateration first to determine which elements of the lookup table to include. This would be useful in a satellite scenario where the atmosphere is in one direction and space in the other, as these vectors will have different associated losses.

Anyone see any problems so far?

RadioEng, I do propagation studies for a living and there are many effects that affect RSSI besides distance. Generally the lower the frequency the less pronounced those effects are. As I said I have worked with systems between 200 kHz and 400 kHz, expressly to determine distance by signal strength and they worked quite well. But they did suffer some unintended effects. One was that the signal strength is quite sensitive to the relative orientation of the Tx & Rx antennas and also to nearby conductors. For instance if you were to use such a system outside and happened to stand over a buried metal pipe, your signal would have a lot less attenuation than if you weren't.

Even though a low frequency is a better choice than a high frequency as far as fading is concerned, the lower the frequency, the more difficult it is to get it to radiate any significant distance. There is an unlicensed band from 160 kHz to 190 kHz where you are allowed to transmit 1 watt with an antenna not to exceed 15 meters.

http://ecfr.gpoaccess.gov/cgi/t/text/text-idx?c=ecfr&sid=0e125035cafa836545a6755115592cf5&rgn=div8&view=text&node=47:1.0.1.1.14.3.241.14&idno=47

This would be my recommendation for the best frequency, power and antenna combination.

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One was that the signal strength is quite sensitive to the relative orientation of the Tx & Rx antennas and also to nearby conductors. For instance if you were to use such a system outside and happened to stand over a buried metal pipe, your signal would have a lot less attenuation than if you weren't.

I understand this. This is why I modified the Power Density calculation and wrapped it up in a function with a lookup table. I needed to account for any source of loss within a given area, so that I didn't end up with large compound errors.

It seems to me that accurate information, of loss over a given path, is the key to obtaining a close result.

I have found the following quote:

The D layer ranges from about 30 to 55 miles. Ionization in the D layer is low because it is the lowest region of the ionosphere. This layer has the ability to refract signals of low frequencies. High frequencies pass right through it and are attenuated. After sunset, the D layer disappears because of the rapid recombination of ions.
http://www.tpub.com/neets/book10/40d.htm

and this:

The D layer reflects vlf waves; is important for long range vlf communications; refracts lf and mf waves for short range communications; absorbs hf waves; has little effect on vhf and above; and disappears at night.
http://www.tpub.com/neets/book10/40h.htm

Now I know that VLF and ELF can be defined differently but I'm assuming, based on the next link, that 3-30KHz is VLF and less than 3KHz is ELF/SLF/ULF.

http://www.vlf.it/frequency/bands.html

Does anyone have wave propagation information for the ELF/SLF/ULF bands through the atmosphere?

Just posting this for future reference. This paper from the US Navy appears to contradict the information supplied about layer D.

LOFTI I is the first of a series of Navy satellite experiments designed for determination of the degree and extent of very-low-frequency (VLF) radio wave penetration of the ionosphere. This investigation has provided unique data on intensity, time delay, echoes, and other characteristics of VLF signals received in the ionosphere from transmitters on the Earth's surface. Theoretical studies carried on concurrently with planning and implementation of the experiment have indicated that VLF radio energy from transmitters operating below the lower atmosphere-ionosphere interface should appear in the ionosphere in useful amount. The LOFTI I telemetry records show relatively strong signals in the ionosphere from 18-kc transmitters on the terrestrial surface. The signals were attenuated less at night and appeared as far away as Australia, 10,000 miles from the transmitter. Statistical treatment of the data so far reduced shows that the attenuation of magnetic field intensity of the 18-kc time pulses from Naval Radio Station NBA, as measured near extreme line of sight distances to the north of the station, was less than 13 db 50 per cent of the time at night and less than 38 db 50 per cent of the time during the daylight hours. The data studied so far shows very little effect of altitude on signal intensity, an observation which agrees with the theoretical treatment based on a model ionosphere.
http://ieeexplore.ieee.org/Xplore/l...066526.pdf?arnumber=4066526&authDecision=-203

So, at orbital distances there is little effect on the electric-field strength, or power density.

At and near the surface, assuming the Tx antenna is at the surface, you have to deal with both groundwave and skywave in several modes. The groundwave amplitude depends on surface conductivity and dielectric constant, which varies wildly from ice to seawater and everything in-between. That would have to be experimentally mapped. The skywaves depend on time of day and ionospheric effects. Please note, the physics doesn't say nothing gets through the reflective layers. It would be a lot simpler if that were just a 1 or a zero, but it's in-between. In daytime it doesn't reflect very well, and at night reflects and refracts somewhat somewhat better. Nobody said nothing gets through, however. So that mix complicates your situation; it's time varying and weather dependent. Finally, if you say you'll only look at one mode, then the problem of time-gating a 1 KHz carrier which is hard-put to effectively modulate at rates above 10 Hz, what happens to your time-gating resolution? Why is the BW so bad? Antennas. You have chosen a wavelength for which there is literally no such thing as an reasonable effective broadband radiator. 300 miles of buried cables in Michigan does not count as practical. To top it all, your Rx noise is lightning from all over the world. The background noise level isn't so great.

Tough problem.

At and near the surface, assuming the Tx antenna is at the surface, you have to deal with both groundwave and skywave in several modes. The groundwave amplitude depends on surface conductivity and dielectric constant, which varies wildly from ice to seawater and everything in-between. That would have to be experimentally mapped. The skywaves depend on time of day and ionospheric effects.

This suggests that the real issue will be an accurate map of the various losses. So, it all comes down to how much money and time you are willing to invest.

Why is the BW so bad? Antennas. You have chosen a wavelength for which there is literally no such thing as an reasonable effective broadband radiator. 300 miles of buried cables in Michigan does not count as practical.

If we forget about Tx modulation for a moment and solely focus on the presence of a signal at a given frequency our Rx antenna can be something like a ball antenna. Any antenna will receive on all frequencies, so its really a DSP issue to detect the presence of a signal on a discreet frequency.

To top it all, your Rx noise is lightning from all over the world. The background noise level isn't so great.

Dealing with RX noise should be pretty straightforward. There will, of course, be certain amount of bad RX readings that would need to be discarded. The other way to deal with such noise is to discard just the data that is corrupted and utilize the rest of the information. A third way, would be to monitor the lightning through a separate system and use a mathematical model to remove the interference from the data you recorded.

As a result, I have been examining Schumann resonances and how this may serve to amplify radio waves in the 3-69Hz spectrum. This would obviously throw off any power calculations and potentially even mask a highly discreet frequency. Again, we have a choice to either discard <70Hz or mathematically account for its effects using readings from a separate system.

Any other factors that need to be considered at low frequency?

OK, so it looks like for a accurate trilateration the formula will be f(PDs) with an experimentally mapped lookup table of losses. Given the scientific papers, this looks as though it could be quite accurate.

So, now for a different different question. I want everyone to keep in mind that we only need to determine the presence of a signal on a given frequency, not demodulate any information.

Which of the following form part of the best solution and why?

1. Satellite or ground-based receivers?
2. Ball antenna, loop antenna or a unique design?
3. Antenna size?

If there is anything you would like to add, feel free.

Looks like we don't have a lot of people here with low frequency experience. No matter, I suppose I can approach it from a different angle and draw upon people's experiences at other frequencies.

I would say this would need to be satellite mounted. Having several large receivers, at different locations on the planet, would introduce a significant amount of problems due to the lack of an efficient waveguide. In addition, skywaves will be subject to less interference and experimental mapping would not be subject to a wide range of transient interactions.

As for antenna design, it needs to in a form factor suitable for satellite deployment and all three options outlined above are quite practical.

As to size, well some of these satellite can be as big as a double-decker bus, so 2mx3m or 3mx3m seems feasible.

Any objections or points I may have missed?

I though that position measurement was usually done using time / phase differences (e.g.LORAN, Decca Navigator and GPS). This is because received power levels are not reliable or predictable whereas timing over a given path length is much more certain.
When you say that you don't want to rely on 'accurate timings' surely they are to be had 'for free' these days from the GPS system. Is there some other factor at work here that caused you to choose an alternative mode of measurement?

I don't think it's that there aren't a lot of people who have low frequency experience, I think they aren't sure you have the competence to do a project like this.

Have you done any experiments to determine the power to distance formula for these frequencies? Are you familiar with the near field effect? How much power do you think it will take to reach a satellite? How well do you understand noise figure and noise power? What will be the sensitivity of your receiver? You need to do a link budget of your system before going any further.

Now that we have opened it up to more "engineering" questions, I have a half-baked suggestion... My actual experience with this is in trying to locate small mobile robots in an area of about 3sqm and I ended up using sonar pings and measuring time delay against a simultaneous radio ping. However I started out with the idea of using three sonar pings with known locations and timing and measuring their arrival time differences. This gives you a screwy sorta-spherical coordinate system, which I tried to plot out (not entirely successfully) here: http://www.etantdonnes.com/TMP/pingrange3.png . I stalled out on how to convert that to a nice cartesian space, and then found that my sensor system couldn't be coerced into receiving all the pings at the same time anyway.

Since it seems you are talking satellites and stuff, you might have enough time/distance to do the same thing with radio. I would be curious to see it work...

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I though that position measurement was usually done using time / phase differences (e.g.LORAN, Decca Navigator and GPS). This is because received power levels are not reliable or predictable whereas timing over a given path length is much more certain.

It depends on the quality of your mapping of losses and how much effect it has on your given frequency.

When you say that you don't want to rely on 'accurate timings' surely they are to be had 'for free' these days from the GPS system. Is there some other factor at work here that caused you to choose an alternative mode of measurement?

You could, but that wouldn't allow me to separate a spread spectrum of signals spatially. I would still need to perform the trilateration to identify the transmitting location. I must point out that I would still be using atomic clock timings in the process, just not an embedded time stamp in the almanac.

I don't think it's that there aren't a lot of people who have low frequency experience, I think they aren't sure you have the competence to do a project like this.

Not really my dept. I'm running a software simulation of wave propagation, as stated at the beginning of the thread. I'm just refreshing my skills, its been a while since I played with the hardware side of things.

But I will answer some of your questions:

Have you done any experiments to determine the power to distance formula for these frequencies?

As long as I know the mathematical approach, its not really my concern. That's an experimental issue outside the scope of work.

Are you familiar with the near field effect?

Near-field coupling has been addressed.

How much power do you think it will take to reach a satellite?

An EM wave will propagate indefinitely, so any power level will reach the satellite. Its a question of what you can detect. In this case, its just whether or not a signal exists. We don't need a lot of transmitting power for that. The final power sensitivity is determined by the choice of receiver. So, not my concern.

How well do you understand noise figure and noise power?

Pretty well, these will be close to ideal as we are not utilizing the bandwidth, just signal presence.

What will be the sensitivity of your receiver?

No idea at this point, but it would form part of an array or big ear. So, perhaps as low as 10^-30 watts, perhaps more.

You need to do a link budget of your system before going any further.

I understand this, I'm just eliminating the obvious first.

A lot of issues here but local effects or even movement have few surprising effects on frequency. You can identify different signals by modulating them differently (labelling).

Power budget is certainly relevant (as always, in fact) because you signals have modulation - which implies finite bandwidth - so signal to noise ratio will affect how well you can get the information off your received signals. Your signal will "always be there" but could be inadequate to use for your purpose. In any case, I feel that the measured power level would be much less easy to use than the timing information that it could carry.

It seems that you have been asked for some input on a project over which you may not have full control or which was defined before you became involved but it may be worthwhile giving some feedback to whoever has asked for your help.

I didn't realize you were only writing the software. I thought this was your project.

Noise power is the power that everything radiates due to it's temperature and is equal to kTB where k is Boltzman's constant (1.38*10-23 Joules/Kelvin), T is the temperature in degrees Kelvin and B is the bandwidth in Hz. At room temperature and a bandwidth of 1 Hz the noise power is equal to -174 dBm. dBm is the ratio of power to that of 1 mW. 10^-30 Watts in dBm is equal to 10*log10(10^-30)+30 or -260 dBm. The received signal will be 86 dB below the theoretical minimum noise floor plus 10log10(BW) dB where BW is the occupied bandwidth. That would be worse than trying to hear a whisper next to a jet engine.

Looks like we don't have a lot of people here with low frequency experience.

I mentioned some of the stuff SophieCentaur listed, way back but you did not deign to answer.

However I will give you the benefit of some of my low frequency experience since I am more skeptical than sceptic about the success of your map.

At any fixed station the received power from such systems varies season to season, day to day hour to hour minute to minute.

This variation occurs for meteorological reasons. Some corrections may be found in publications such as the Admiralty Manual, but they cannot account for every possibility eg propagation through a deciduous forest at different seasons varies dues to leaf presence or abscence.

There seem to be a lot of issues here which, if they haven't been considered, will involve a lot of fruitless expenditure of time and effort. I think you need to consider just why position is, afaik, nearly always measured using timing information and not power measurement. In fact, I think the only application is in the estimation of some cosmological distances - and that's very much ballpark accuracy.
If you have ever been involved in satellite communications, you will realize that there are huge variations in signal strength from place to place and from time to time which are just not predictable to within several dB (representing massive inaccuracy in measurement of distance). I really advise you to think again - or bounce some questions back whence they came.

A lot of issues here but local effects or even movement have few surprising effects on frequency. You can identify different signals by modulating them differently (labelling).

The signals will be unmodulated. That said, there may be patterns in the received pulses.

Noise power is the power that everything radiates due to it's temperature and is equal to kTB where k is Boltzman's constant (1.38*10-23 Joules/Kelvin), T is the temperature in degrees Kelvin and B is the bandwidth in Hz. At room temperature and a bandwidth of 1 Hz the noise power is equal to -174 dBm. dBm is the ratio of power to that of 1 mW. 10^-30 Watts in dBm is equal to 10*log10(10^-30)+30 or -260 dBm. The received signal will be 86 dB below the theoretical minimum noise floor plus 10log10(BW) dB where BW is the occupied bandwidth. That would be worse than trying to hear a whisper next to a jet engine.

As a satellite system, < -230C and no bandwidth is required. I'm not seeking a modulated signal, merely the presence of photons at a given frequency.

At the selected frequency range, the waveguide is the Earth-Ionosphere and we will obtain electrical resonances across the emitted spectrum. Thus, at orbital distances we will have an amplified signal. As such the power density of 10^-30 Watts may represent the expected unamplified source at orbital distances, rather than the real detected power density. To perform the distance calculation, we would need to account for the resonance and subtract as appropriate.

Thus, if the power density at source was 10^-10 Watts, we may detect a signal at 10^-6 Watts at orbital distances.

This variation occurs for meteorological reasons. Some corrections may be found in publications such as the Admiralty Manual, but they cannot account for every possibility eg propagation through a deciduous forest at different seasons varies dues to leaf presence or abscence.

I would expect a real-time map from known ground stations. Something similar to differential GPS.

How can you say that no bandwidth is required? If you can't be sure you've got the right signal, how is it useful for you? It could be interference. There are always "photons of the right frequency" about - it's called background noise and your receiver will also be generating its own noise at that frequency. But, of course, the notion of 'a frequency' is flawed. You need to consider bandwidth in all cases. For a start, there is a small matter of Doppler effect and frequency stability at each end of the link.
The Ionosphere, as a waveguide, is fair enough. The reliability and predictability of the behaviour of this waveguide have been the subject of research for decades. It's at least as bad as the weather for making accurate predictions about what will happen. And disturbances can be very localised.

You might "expect a real time map" but who will be flying a receiver between your source and receiver at all times? Any monitor may give you figures about somewhere else but what use could that be if you need information about our particluar source and receive locations within the order of 1dB? Who would provide these specific monitors, in any case? One per source and always in the right place? How could that be achieved?

The results from simulations are only as good as the original model and the specified conditions. Is this for real?

I would expect a real-time map from known ground stations. Something similar to differential GPS.

I don't think you understood my comment. The problem occurs in the propagation medium ie the atmosphere.

Even much more sophisticated systems, such as the Tellurometer, were subject to this. Hence the reference to the Admiralty Manual. Have you read it?

Another phenomenon that affects phase systems at low level is called 'ground swing'. The A. Manual also describes calibration for this if I remember correctly.

As a matter of interest, what sort of trilateration algorithm are you envisioning?
Hyperbolic or circular (also known as rho-rho)?

How can you say that no bandwidth is required? If you can't be sure you've got the right signal, how is it useful for you? It could be interference. There are always "photons of the right frequency" about - it's called background noise and your receiver will also be generating its own noise at that frequency.

Firstly, you are making it sound as though background noise is magic. Its not. All noise has a source. If you are aware of the source, then you can account for it. Its just a lack of information that creates the problem.

Bandwidth is only required when you want to include information.

Further to this, noise will have a different waveform and its pattern will not be consistent with what you want to monitor. So, this is a signal processing issue, not a detection issue.

But, of course, the notion of 'a frequency' is flawed. You need to consider bandwidth in all cases. For a start, there is a small matter of Doppler effect and frequency stability at each end of the link.

This can be accounted for. Again, its a matter of what information you possess, what resources you have and computational power you are willing to throw at the task.

The Ionosphere, as a waveguide, is fair enough. The reliability and predictability of the behaviour of this waveguide have been the subject of research for decades. It's at least as bad as the weather for making accurate predictions about what will happen. And disturbances can be very localised.

With real-time reference points over a given time period and the motion of a network of satellites, this can be compensated for. Its just a matter of getting the right balance.

You might "expect a real time map" but who will be flying a receiver between your source and receiver at all times?

You do not require an independent receiver, but it could be performed by another network. The simplest solution would be to have an additional antenna, or even the same antenna, examining the reference signals. Of course, the reference signals would be on frequencies not being trilaterated.

Any monitor may give you figures about somewhere else but what use could that be if you need information about our particluar source and receive locations within the order of 1dB?

It depends on the density of reference signals and also historical information. With a network of satellites, say four visible at anyone time, it would be possible to create a 3D map of the disturbances in real-time across a given area.

Who would provide these specific monitors, in any case? One per source and always in the right place? How could that be achieved?

It doesn't need to be in the "right place", you're failing to see what is achievable with a mathematical model over a long time frame.

The results from simulations are only as good as the original model and the specified conditions. Is this for real?

True, but in a practical scenario what resolution could I achieve by taking readings and performing comparisons across days or weeks?

It should be pretty accurate given these conditions.

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"Pretty accurate"
"Zero Bandwidth"
"getting the right balance"
"this can be accounted for"

Have you ever been involved with a real, successful, engineering project?

edit: and are you aware of the noise theory of a certain Mr Shannon? He's ever so well respected.

Have you ever been involved with a real, successful, engineering project?

edit: and are you aware of the noise theory of a certain Mr Shannon? He's ever so well respected.

The Shannon-Hartley theorem relates to noise on a data channel and maximum capacity. As we are not demodulating this signal, we are unconcerned with the channel's capacity. Hartley's law is partially applicable as the receiver must distinguish between amplitude levels.

Thus, to defeat noise we must separate the frequencies very discreetly and examining the pattern received. The pattern will reveal the difference between noise and a signal. Note that I am indicating a definable pattern to the spread spectrum transmission.

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NO.
The information is that the signal is there or not and its level (an analogue quantity which is essential for your purpose which will be varying constantly around a basic downward trend). I do not see how you can think that you have any way of distinguishing between the signal you want and any other signal unless there is some label / modulation. You say that you will 'know about' any other unwanted signals but how? You will "examine the pattern received". How does that not involve bandwidth?

An then you mention a spread spectrum transmission. Are you expecting to track this perfectly - and then treat it as a cw signal? Also, how are you intending to build a receiver with zero bandwidth? If you are making observations over a very long period then this just represents microHz bandwidths or less. But there is still a bandwidth involved which must appear in some calculations.

You have been a bit sparing in your system description but if you are intending to do a measurement over a long period of time, you are dealing with large distances. What about the resulting geometry? You will have a baseline of one Earth Diameter (or possibly some orbit diameter, if your sources are on satellites) what sort of discrimination in range are you expecting between the received signals at even 10 times this distance. What about 100 or 1000 times? How much more accurate could you not get using simple (?! at least well established) Celestial navigation by observing planets and stars. It strikes me that your answers could well come out as "A long way" and then, later "A very long way" and then "Too far away to be sure" but with very few figures.
And on the subject, you actually quote very few figures about a system which relies totally on what are basically very small differences between very big numbers. If it doesn't boil down to Signal To Noise Ratio then it's a unique measuring system.

Seriously - is this your first project or do you have a track record of successful novel measurement methods? This is a very relevant question because I should like to take this seriously but I am struggling.

The information is that the signal is there or not and its level (an analogue quantity which is essential for your purpose which will be varying constantly around a basic downward trend). I do not see how you can think that you have any way of distinguishing between the signal you want and any other signal unless there is some label / modulation.

You are failing to account for the pattern in the spread spectrum. The statistical odds of noise producing the same pattern, over a given time frame, are remote.

So, a label or modulation is not required.

You say that you will 'know about' any other unwanted signals but how? You will "examine the pattern received". How does that not involve bandwidth?

We are not treating the spread spectrum range as a single channel, its broken down into a very discreet range of frequencies and they are treated independently. We are also not looking for a modulated signal. Bandwidth is the amount of information that can be modulated onto a range of frequencies but these signals do not represent symbols. The pattern represents the signals emitted by an array of antennas over a given time period.

An then you mention a spread spectrum transmission. Are you expecting to track this perfectly - and then treat it as a cw signal? Also, how are you intending to build a receiver with zero bandwidth? If you are making observations over a very long period then this just represents microHz bandwidths or less. But there is still a bandwidth involved which must appear in some calculations.

The frequency and temporal spectrums are predicable, thus the pattern is predictable. It will not be treated as a continuous wave. The data will be transferred to a grid that represents a snapshot of time, each square of the grid will represent a highly discreet frequency range. If represented in binary, a 1 will indicate the presence of a signal and a zero the lack of a signal.

In terms of having zero bandwidth, the channels (or discreet frequency ranges) will be as wide as the pulse transmitted. You may call this range bandwidth, but there is no information encoded in this range.

You have been a bit sparing in your system description but if you are intending to do a measurement over a long period of time, you are dealing with large distances. What about the resulting geometry? You will have a baseline of one Earth Diameter (or possibly some orbit diameter, if your sources are on satellites) what sort of discrimination in range are you expecting between the received signals at even 10 times this distance. What about 100 or 1000 times? How much more accurate could you not get using simple (?! at least well established) Celestial navigation by observing planets and stars. It strikes me that your answers could well come out as "A long way" and then, later "A very long way" and then "Too far away to be sure" but with very few figures.

You are not being very clear on this matter. Can you clarify this?

And on the subject, you actually quote very few figures about a system which relies totally on what are basically very small differences between very big numbers. If it doesn't boil down to Signal To Noise Ratio then it's a unique measuring system.

It boils down to pattern analysis to eliminate the effects of noise and experimental mapping to eliminate source of signal loss or gain.

As a measuring system it is rather unique, but it is merely a byproduct of the functionality of the system.

Seriously - is this your first project or do you have a track record of successful novel measurement methods? This is a very relevant question because I should like to take this seriously but I am struggling.

Why should this matter? Should the science not be the same regardless? That's a rather ad hominem approach. So, I will not answer your question at this time.

You are failing to account for the pattern in the spread spectrum. The statistical odds of noise producing the same pattern, over a given time frame, are remote.

But what if the thermal noise is 1 billion times more powerful than your signal (86 dB + 4 dB noise figure)? Will you have 1 billion, 1 Hz receivers?

But what if the thermal noise is 1 billion times more powerful than your signal (86 dB + 4 dB noise figure)? Will you have 1 billion, 1 Hz receivers?

There is no evidence that would be the case. Modern arrays can listen to signals as low 10^-23 W/m^2 , on higher frequencies, with no problems. With the curvature of the Earth-Ionosphere acting as a waveguide, it should be just as effective.

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It boils down to pattern analysis to eliminate the effects of noise and experimental mapping to eliminate source of signal loss or gain.

Actually, SophieCentaur made a very very very good point. The small difference of two very large numbers.

Let us try some specifics

Say your transmitter - receiver distance is 65 kilometres and your desired accuracy is 100 metres.

I see nothing in your proposals that would distinguish between the signal at 65Km and at 65.1Km.

In fact I doubt this has ever been done (or attempted). This is the reason that the measurement systems I referred to use some form of phase comparison. You cannot distinguish 100m in 65Km otherwise.

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