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Low Frequency Radio Trilateration

  1. Sep 23, 2010 #1
    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.
  2. jcsd
  3. Sep 24, 2010 #2
    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?
  4. Sep 24, 2010 #3
    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:
  5. Sep 24, 2010 #4


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    I second schip's comment about multi-path. RSSI is not useful for determining distance in the general case.
  6. Sep 24, 2010 #5
    A spread spectrum < 1000Hz.

    Ideally, any distance including into orbit.

    Engineering issues should not be raised at this point.

    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).

    As close as we can get it.

    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.
    Last edited: Sep 24, 2010
  7. Sep 24, 2010 #6
    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.
  8. Sep 24, 2010 #7
    schip666!, I've read the document you linked to and I found the following:

    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.

    Any idea what your f(PDs) function looked like or what factors it considered?
  9. Sep 24, 2010 #8
    I'm afraid I've long ditched all my stuff pertaining to such systems.

    I suggest you do a search for propagation issues in


    There was a book by Laurila that discussed this as well.
  10. Sep 24, 2010 #9
    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?
  11. Sep 24, 2010 #10
    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: [Broken]

    This would be my recommendation for the best frequency, power and antenna combination.
    Last edited by a moderator: May 4, 2017
  12. Sep 24, 2010 #11
    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:


    and this:


    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.


    Does anyone have wave propagation information for the ELF/SLF/ULF bands through the atmosphere?
  13. Sep 24, 2010 #12
    Just posting this for future reference. This paper from the US Navy appears to contradict the information supplied about layer D.


    So, at orbital distances there is little effect on the electric-field strength, or power density.
  14. Sep 24, 2010 #13
    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.
  15. Sep 26, 2010 #14
    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.

    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.

    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 lightening 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?
  16. Sep 27, 2010 #15
    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.
  17. Sep 28, 2010 #16
    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?
  18. Sep 28, 2010 #17


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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.
    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?
  19. Sep 28, 2010 #18
    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.
  20. Sep 28, 2010 #19
    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 [Broken]. 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...
    Last edited by a moderator: May 4, 2017
  21. Sep 28, 2010 #20
    It depends on the quality of your mapping of losses and how much effect it has on your given frequency.

    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.

    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:

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

    Near-field coupling has been addressed.

    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.

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

    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.

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