Radio based triangulation(Any electrical engineers about?)

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bcglorf
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Radio based triangulation(Any electrical engineers about?)

Post by bcglorf »

I'm wondering if there are any electrical engineers around that can cure my curiosity for me. I'm a comp sci guy, and I've been thinking there are loads of applications for hardware that can get millimeter precision location data for a system of objects.

The best solution I've seen so far is MIT's cricket technology, that combines radio signals and ultrasound time of flight calculations to measure distances. The trouble is it still relies on ultrasound, which interacts heavily with the environment.

Here's my question.

Is there a way to use radio waves in a scheme similar to laser range finders?

I am thinking of the following setup:

1 radio transmitter at a known location sending out a high frequency signal, and then a triplet of receivers to triangulate their relative location to the transmitter. Can I use the signal received by each device, and compare it similarly to how laser range finders work, and get the relative distance between the 3 receivers and the transmitters?

I'm thinking the phase delta from each of the receivers should be able to theoretically get as good of precision as a phase change on a laser reader would.

At the same time, I'm pretty certain hordes of people involved in GPS and other systems have already considered this and have a simple reason it just won't work. I am just very curious what the reason is. Are there physical limitations in translating a radio signal that just leave too much noise to get enough time precision? Or am I missing some obvious and fundamental theoretical problem?

Any help would be greatly appreciated.

D Tibbets
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Post by D Tibbets »

Some mostly ignorant comments. Do laser range finders use phase change to measure distance? I thought it was a simple time of flight there and back again. Phase changes would presumably be significantly longer with radio waves- mocrometers to meters instead of perhaps a few hundred nanometers for a visible wavelength laser. Time of flight measurements would seem more straight forward. Either radar, returning a round trip pulse, or atomic clocks on the sender and receiver that are calibrated should serve. Why a third reciever. I could see how phase changes between the three due to relative distances might derive a distance, but it seams overly complex. I don't know how much tuning drift could be tolorated. Surveyors and GPS uses triangulation. But not just for distance, but also for angular seperatrion so that trig can be used to plot relative position and altitude.
Radars scan in altitude and azimuth to fix the position, the range is simple.
Are you asking if a single non scanning point source radio emitter could do this based of wavelength phase changes at a receiver (or an echo)? I doubt it or the radar designers probably would have not gone through all of the trouble of developing electronically scanned radars. Of course the signil strength of a beamed emission versus an omnidirectional emission is also important...

Dan Tibbets
To error is human... and I'm very human.

bcglorf
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Post by bcglorf »

Do laser range finders use phase change to measure distance? I thought it was a simple time of flight there and back again.

Both. :)

Time of flight measurements would seem more straight forward. Either radar, returning a round trip pulse, or atomic clocks on the sender and receiver that are calibrated should serve.

The clocks are the trick. Light is of course stupidly fast, so if you want millimeter precision on a time of flight calculation for something like light, synched atomic locks just don't cut it. You need sub pico-second accuracy.

The way laser ranger finders get around this are two-fold. First, the light is sent and received from the same spot, so no need for synching. Secondly is the phasing. By modulating the laser signal at a very high frequency, you can compare the phase of the light coming back to the phase you are currently sending and thus measure smaller time slices than any oscillator can manage.

The trick is I have applications where line of sight is too limiting. So on to radio waves. The transmitter sends a signal that's oscillating at some frequency to be read at each receiver. The receivers then will each have three signals offset by the difference of time of flight to each of them. I'm wondering if you can compare those signals the way a laser range finder does and get out a useful distance measurement that can be used for accurate triangulation...

I'm sure the GPS guys will have considered this though, and my guess is something about the radio signal processing hoses the idea, but I really want to know what it is. The applications for it are just really tempting.

ladajo
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Post by ladajo »

GPS is all about the clocks. The atomic synch clocking is how the trangulation is determined. This is some other stuff that goes into it to account for atmospherics, frame drag, and what not, but the core idea is that you know when the signal is sent (encoded in the signal), and you know the timing offset of when you recieve it. Thus the Delta gives you the distance. Three distance arcs give you a position. The other magic of the system is in that the satellite positions are kept in an almanac, and courtesy of Kepler, we know the bird positions, the atomic clocking gives the distances, cut the arc intersects, and viola, you know where you are in 4D. Simple, and silli-accurate. The accuracy is a primary function of the clocks.

In you system, it would be possible to do something similar. It is a multi-static radar application. If you encode the transmission timing into your emitted signal, developed a way to seperate tranmitted pulse from reflected (timing estimates), and then used your multiple recievers (also clocked), you could certainly easily track object position in your monitored space volume.

When you say you are line of sight limited, what do you mean?
Also, there is another means to develop tracking information from "reverb" reflections in a volume, but that is math and horsepower heavy. It can, and has been done though.

bcglorf
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Post by bcglorf »

ladajo wrote:GPS is all about the clocks. The atomic synch clocking is how the trangulation is determined. This is some other stuff that goes into it to account for atmospherics, frame drag, and what not, but the core idea is that you know when the signal is sent (encoded in the signal), and you know the timing offset of when you recieve it. Thus the Delta gives you the distance. Three distance arcs give you a position. The other magic of the system is in that the satellite positions are kept in an almanac, and courtesy of Kepler, we know the bird positions, the atomic clocking gives the distances, cut the arc intersects, and viola, you know where you are in 4D. Simple, and silli-accurate. The accuracy is a primary function of the clocks.

In you system, it would be possible to do something similar. It is a multi-static radar application. If you encode the transmission timing into your emitted signal, developed a way to seperate tranmitted pulse from reflected (timing estimates), and then used your multiple recievers (also clocked), you could certainly easily track object position in your monitored space volume.

When you say you are line of sight limited, what do you mean?
Also, there is another means to develop tracking information from "reverb" reflections in a volume, but that is math and horsepower heavy. It can, and has been done though.
The clocks are the trouble. Even the absolute fastest clocks you can get still allow light travel nearly a meter between ticks. Laser range finders, the millimeter accurate ones, don't use clocks or oscillators to measure time, they modulate the laser at a high frequency, and use THAT to measure time over shorter bursts than any clock in existence.

I am basically looking at GPS, but without the clocks. I want mm accuracy, and clocks don't cut it then.

What I'm really wanting is a GPS like device to track location in real-time with mm accuracy, ideally one that isn't hindered by environmental obstacles. MIT has basically what I want, but it uses ultrasound making it's accuracy very dependent on environment, and inherently less accurate than I really want too.

I am thinking of transmitting a radio signal with a modulating signal ala laser range finders. Then the trick is how can a remote device see that signal, and figure out TOF. If 3 receivers each see the signal, I can compare each signal and pick out how much longer the signal traveled to each receiver, but not the total flight time. I'm just wondering if i can work that backwards to get the original signal(I think that's doable, and pretty straightforward at that). I'm more wondering if there's any problems in receiving a radio signal with precision and accuracy I'm going to need.

Finally, in the event that it should all work, why can't I find anyone that's already using it? GPS could easily be running with 100-1000X the accuracy it is now.

D Tibbets
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Post by D Tibbets »

Mostly speculation, but if you need mm precision and accuracy. Then the wavelengths of the radio signal needs to be perhaps 1/2 that length(or with phase shift measurements perhaps several mm wavelengths would serve(?). Phase shifts are I assume variant over one wavelength. If the timing signal is only good for ~ 1 meter, then how do you know which wave you are measuring. The phase shift may give you the fractional wavelenth, but is it the fraction plus one wave length, minus 8 wavelengths...?

There was a clever setup where experimenters measured the speed of light to a fair degree of accuracy by using a mechanical setup, so there may be tricks.
Perhaps having a series of radio wavelengths, each a little longer than the previous, over a time frame that adds up to the clock limits, then perhaps this would somehow allow you to determine which wavelength, or the fraction of which wavelength you were measuring.

Also, even changes in air density would change the transmission speed. I assume that for meter accuracy this is trivial. Could it be ignored over mm accuracy ranges?

Light speed is ~ 300,000,000 meters/s. So I would think that a modest timing interval ~ 1/30 billionth of a second would come close to mm flight distance measurements. What am I missing?

Dan Tibbets
To error is human... and I'm very human.

bcglorf
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Post by bcglorf »

D Tibbets wrote:Mostly speculation, but if you need mm precision and accuracy. Then the wavelengths of the radio signal needs to be perhaps 1/2 that length(or with phase shift measurements perhaps several mm wavelengths would serve(?). Phase shifts are I assume variant over one wavelength. If the timing signal is only good for ~ 1 meter, then how do you know which wave you are measuring. The phase shift may give you the fractional wavelenth, but is it the fraction plus one wave length, minus 8 wavelengths...?

There was a clever setup where experimenters measured the speed of light to a fair degree of accuracy by using a mechanical setup, so there may be tricks.
Perhaps having a series of radio wavelengths, each a little longer than the previous, over a time frame that adds up to the clock limits, then perhaps this would somehow allow you to determine which wavelength, or the fraction of which wavelength you were measuring.

Also, even changes in air density would change the transmission speed. I assume that for meter accuracy this is trivial. Could it be ignored over mm accuracy ranges?

Light speed is ~ 300,000,000 meters/s. So I would think that a modest timing interval ~ 1/30 billionth of a second would come close to mm flight distance measurements. What am I missing?

Dan Tibbets
Thanks for the feedback, it's helping me if nothing else in communicating what I want to try and why.

The idea behind phase variations is to bypass any measurement of time by instead comparing two phases to each other, and deriving the time delta by how much the phases are offset from one another. Wave lengths don't so much matter. As for which wave your measuring, you just work in the range where you only have a single wave to worry about, which is on the order of miles if need be.

As for environment, I'm not sure if how much it plays in at mm levels. I know that laser range finders manage well enough. I'm anticipating and hoping that the way I'm using it environment affects signal strength more than travel time and won't be too big a problem. For my own use though I can overcome it by just working within 200 yards of the transmitter and then it shouldn't matter too much anyway.

1/30 billionth of a second would come close to mm

That's the trick though, 1/30 billionth of a second is cm, 1/300 billionth is mm. Even high end experimental crystal oscillators die out in the double digit GHZ range. The real killer though is those oscillators won't stay in synch at the precision for any length of time anyways, even if cm was good enough I want to stay synched for a good many minutes and preferably hours.

The big thing I think you might be missing is that TOF for lightspeed signals is hard capped well short of even cm precision with the use of oscillators as clocks. Oscillators additionally limit you to bounce(there and back) measurements, or else your accuracy drops off with every tick that you run the system, which becomes useless in seconds.

Aero
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Post by Aero »

1 radio transmitter at a known location sending out a high frequency signal, and then a triplet of receivers to triangulate their relative location to the transmitter. Can I use the signal received by each device, and compare it similarly to how laser range finders work, and get the relative distance between the 3 receivers and the transmitters?
I think we are getting a little off-track in our replies. I know I was thinking "position location or navigation" but that isn't what you asked. To the point of your question, as quoted above, no. The only thing you can determine (to more or less accuracy) is the range or distance from the transmitter to each receiver. If the 3 receivers communicate the distance data to a central processor, then the central processor can calculate the differences in distance but can't determine direction and so cannot triangulate their relative location to the transmitter. There is simply not enough information in the 3 range signals. Try an example using pencil and paper, with a ruler to measure ranges.

Now, if the situation were reversed, with 3 transmitters and one receiver, then yes, you could triangulate the location of the receiver, and could in fact triangulate the location of as many receivers as you cared to use. Note though, that calculating the relative locations, the range measurement error would be multiplied by a geometric factor, so you need to keep the transmitters well separated. This geometric factor is known as "Geometric Dilution Of Precision," and is described here http://en.wikipedia.org/wiki/Dilution_o ... _%28GPS%29
The dilution of location accuracy can be very large, or said another way, geometry can introduce large errors in location calculations.
Aero

bcglorf
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Post by bcglorf »

Aero wrote:
1 radio transmitter at a known location sending out a high frequency signal, and then a triplet of receivers to triangulate their relative location to the transmitter. Can I use the signal received by each device, and compare it similarly to how laser range finders work, and get the relative distance between the 3 receivers and the transmitters?
I think we are getting a little off-track in our replies. I know I was thinking "position location or navigation" but that isn't what you asked. To the point of your question, as quoted above, no. The only thing you can determine (to more or less accuracy) is the range or distance from the transmitter to each receiver. If the 3 receivers communicate the distance data to a central processor, then the central processor can calculate the differences in distance but can't determine direction and so cannot triangulate their relative location to the transmitter. There is simply not enough information in the 3 range signals. Try an example using pencil and paper, with a ruler to measure ranges.

Now, if the situation were reversed, with 3 transmitters and one receiver, then yes, you could triangulate the location of the receiver, and could in fact triangulate the location of as many receivers as you cared to use. Note though, that calculating the relative locations, the range measurement error would be multiplied by a geometric factor, so you need to keep the transmitters well separated. This geometric factor is known as "Geometric Dilution Of Precision," and is described here http://en.wikipedia.org/wiki/Dilution_o ... _%28GPS%29
The dilution of location accuracy can be very large, or said another way, geometry can introduce large errors in location calculations.
Thanks for answering down into the core of the question.

I think I might've been unclear about the receivers, the design is to have the receivers all at known positions relative each other, so if I had a distance to transmitter for each I can triangulate the transmitter's location.

My trouble is if I can have enough information between the receivers to even get the distance. Since I really need to be measuring time by comparing a modulated signal, here's what I can get.
Receiver A: TOF = x, completely unknown
Receiver B: Comparing phase of signals at A&B I can get TOF=x+y, where y is the difference in TOF to B vs. A
Receiver C:Similar to B, comparison to A gives TOF=x+z, where z is the difference in TOF to C vs. A

I'm pretty sure if I know x,y and the relative positions of A,B and C I can work my way back and solve for x where
Transmitter to A = x
Transmitter to B = x+y
Transmitter to C = x+z

I'm more worried about the accuracy I might lose along the way. More importantly, I am worried about if I can receive the radio signal in a way that I can still compare the phase offsets at a useful precision.

Does that make any sense? If it's ambiguous I'll take another crack at the description.

Aero
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Post by Aero »

That's an unusual set-up but it should be solvable, theoretically. Signal timing is still a problem though. How big is your system? Room size or geographically big. I mean, is it feasible to run the whole system from a single clock by distributing a timing signal? Say a few meters cable run? You might have to get exotic with your ranging signal structure, too.
Aero

bcglorf
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Post by bcglorf »

Aero wrote:That's an unusual set-up but it should be solvable, theoretically. Signal timing is still a problem though. How big is your system? Room size or geographically big. I mean, is it feasible to run the whole system from a single clock by distributing a timing signal? Say a few meters cable run? You might have to get exotic with your ranging signal structure, too.
The receivers are planned to be soldered,glued or welded to the same device, with the device ideally being pda sized. The transmitter can be within a hundred yards, though a larger range would be ideal. The feasibility of running off the same clock though just isn't there, clocks don't exist that tick fast enough.

It's the limitation of clocks that forces the time to be measured by having the radio signal itself modulate at a high frequency and comparing the phase offset of the signal at different locations.

If the basic math is quite solvable, which I already figured on, it's the accuracy of comparing phase offsets of radio waves that is the limit on accuracy. I know doppler uses radio waves and phase offsets just as I intend, but it compares a signal bouncing back, mine is one way. What kind of precision does doppler get and how much of that limitation is related to the bouncing and how much inherent in the electronics?

ladajo
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Post by ladajo »

bcglorf wrote:
Aero wrote:That's an unusual set-up but it should be solvable, theoretically. Signal timing is still a problem though. How big is your system? Room size or geographically big. I mean, is it feasible to run the whole system from a single clock by distributing a timing signal? Say a few meters cable run? You might have to get exotic with your ranging signal structure, too.
The receivers are planned to be soldered,glued or welded to the same device, with the device ideally being pda sized. The transmitter can be within a hundred yards, though a larger range would be ideal. The feasibility of running off the same clock though just isn't there, clocks don't exist that tick fast enough.

It's the limitation of clocks that forces the time to be measured by having the radio signal itself modulate at a high frequency and comparing the phase offset of the signal at different locations.

If the basic math is quite solvable, which I already figured on, it's the accuracy of comparing phase offsets of radio waves that is the limit on accuracy. I know doppler uses radio waves and phase offsets just as I intend, but it compares a signal bouncing back, mine is one way. What kind of precision does doppler get and how much of that limitation is related to the bouncing and how much inherent in the electronics?
Now you are at the heart of GPS. The timing issue as stated is handled by Atomic clocks. These colocks are silly accurate, and keep the entire system in synch. It is why they are used. That "the US owns time" is one of my favorite quotes. The world uses GPS timing to run. And the US owns GPS. As for the phasing, yes it can be done, and is done. I mentioned this above, but probably not clearly. The accuracies achievable are impressive. I am not able to say what the absolute accuracy of current generation GPS is, but there is a reason the military owns and maintains the constellation. The next generation of GPS on the boards right now, (at MIT ironically for you) is even another leap in accuracy. I recently got a look at it in conjunction with a seminar by arguably the smartest guy in the world on GPS. It involves clock improvements again, as well as signal processing.

Your problem seems straight forward enough, but you still have n ot answered the questions: How big is the monitored space? How fast (often) do you need updates? What are your issues with Line of Sight?

Aero
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Post by Aero »

What kind of precision does doppler get and how much of that limitation is related to the bouncing and how much inherent in the electronics?
Two way doppler can be quite accurate but as I understand it, doppler measures velocity (along the line of sight), not distance. It is accurate because the clock errors are eliminated by using the same clock for signal transmission and signal reception. Clock drift occurring during the signal time of flight is negligible for short distances.

I'm still confused about your set-up, though. If I understand correctly, the distance between receivers is much, much less than the distance to your transmitter. If that is the case, go back up-thread and read the reference on GDOP to understand why that won't work with any reasonable tech.
Aero

bcglorf
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Post by bcglorf »

The timing issue as stated is handled by Atomic clocks. These colocks are silly accurate, and keep the entire system in synch.

Yep, the problem is my application needs better than silly accurate, I need an impossibly accurate clock. Not even the most expensive atomic clocks available right now go much past a billion ticks per second, I need 300 billion.

The next generation of GPS on the boards right now, (at MIT ironically for you) is even another leap in accuracy. I recently got a look at it in conjunction with a seminar by arguably the smartest guy in the world on GPS. It involves clock improvements again, as well as signal processing.

Any links, I've really never seen any GPS get lower than 1 meter precision, and unless they switch to signal processing in place of clocks they simply physically can not with today's atomic clock tech.

How big is the monitored space?
100 cubic meters would work well enough.


How fast (often) do you need updates?

60 per second minimum(reliably), but the more the better.

What are your issues with Line of Sight?
It needs to work as a wearable device in a building with plenty of walls and moving objects.

It is accurate because the clock errors are eliminated by using the same clock for signal transmission and signal reception.

Hmmm, I thought it was like laser range finders where in essence the signal IS the clock. My idea is right out if you can't do something similar with radio or other em waves.


I am basically looking to eliminate the clock errors by letting the clocking in essence be in the signal. My first receiver only knows it's got a signal. The second further on uses that as a base signal, and compares it to what it see's itself to know how much further/closer it is relative to the first. Then repeat for as many receivers as needed to get out something accurate.

If I understand correctly, the distance between receivers is much, much less than the distance to your transmitter. If that is the case, go back up-thread and read the reference on GDOP to understand why that won't work with any reasonable tech.

My receivers would absolutely be much, much closer. That has been used though in other location systems, MIT's cricket does it and gets good results still. Are you seeing problems with accuracy errors being multiplied?

Aero
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Post by Aero »

I looked at the Cricket system - position locating receivers inside an instrumented building is something different to me. I don't have any experience with it.
Aero

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