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Non-directional tracking solution?
Hello,
I'm not certain this is the appropriate newsgroup for this question, but if it isn't, I'd appreciate any referrals to other forums. In many posts dealing with "foxhunts" and radio tracking situations, I hear directional antennas discussed, or triangulation via a moving receiver. But what are the relevant parameters if the receiving stations are fixed? Partly for the fun of it, and also for practical uses, I'd like to design a receiving system whereby a small transmitter could be located. This would not technically be a "tracking" situation, since the transmitter would not always be on. I'm imagining something like a garage door opener, where pushing the button can send a brief (but very strong if necessary - this may have power implications?) signal. The reason I ask about the non-directional solution is because I have access to a plot of land approx. 300 x 300 feet square, with no restrictions on building antennas on the four corners of the property. I'm guessing such a system could be more accurate than a directional system at a given power level, but the technical aspects of the situation are beyond me. I am a mathematician by trade, but know a smattering of electronics. It would seem, at least in theory, that the relevant parameters here are the distances between the 3-4 antennas (would a 4th help?), and the strength and frequency of the signal. I also realize that some processing of the signal would need to be done at the receiving end. Perhaps the triangulation can be handled by software? Any advice, direction, URLs, or discussion is much appreciated. -wp |
Washed Phenom wrote:
Partly for the fun of it, and also for practical uses, I'd like to design a receiving system whereby a small transmitter could be located. This would not technically be a "tracking" situation, since the transmitter would not always be on. I'm imagining something like a garage door opener, where pushing the button can send a brief (but very strong if necessary - this may have power implications?) signal. Try this one: http://members.aol.com/BmgEngInc/Adcock.html 73, Markus HB9BRJ |
Washed Phenom wrote:
Partly for the fun of it, and also for practical uses, I'd like to design a receiving system whereby a small transmitter could be located. This would not technically be a "tracking" situation, since the transmitter would not always be on. I'm imagining something like a garage door opener, where pushing the button can send a brief (but very strong if necessary - this may have power implications?) signal. Try this one: http://members.aol.com/BmgEngInc/Adcock.html 73, Markus HB9BRJ |
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Do you have any frequency ranges in mind? A VHF system would be vastly
different in size than shortwave for example. jw K9RZZ |
Do you have any frequency ranges in mind? A VHF system would be vastly
different in size than shortwave for example. jw K9RZZ |
Zack Lau wrote:
(Washed Phenom) wrote in message om... Partly for the fun of it, and also for practical uses, I'd like to design a receiving system whereby a small transmitter could be located. This would not technically be a "tracking" situation, since the transmitter would not always be on. I'm imagining something like a garage door opener, where pushing the button can send a brief (but very strong if necessary - this may have power implications?) signal. The reason I ask about the non-directional solution is because I have access to a plot of land approx. 300 x 300 feet square, with no restrictions on building antennas on the four corners of the property. I'm guessing such a system could be more accurate than a directional system at a given power level, but the technical aspects of the situation are beyond me. I am a mathematician by trade, but know a smattering of electronics. It would seem, at least in theory, that the relevant parameters here are the distances between the 3-4 antennas (would a 4th help?), and the strength and frequency of the signal. I also realize that some processing of the signal would need to be done at the receiving end. Perhaps the triangulation can be handled by software? Any advice, direction, URLs, or discussion is much appreciated. Accurate signal strength measurements are surprisingly difficult. Ground reflections can combine to to double the signal strength, or nearly cancel it out. Hams and broadcasters often use the term "picket fencing" to describe the rapid fluctuations in signal strength that occurs with fixed to mobile signal paths. Not that your task is impossible, just hard. Perhaps a sufficient number of signals can be simultaneously processed to statistically reduce the signal combination/cancellation effect to an acceptable error. Zack Lau W1VT Doing it by carrier phase would be better, if you could arrange a phase reference. With hard-mounted receivers (or with a 2nd transmitter in a known location) you can broadcast a time reference and do a reverse-GPS sorta thing. The higher the carrier the better the measurement, but with a lot 100 meters on a side you probably also want to send some sort of time reference (you do get to design the transmitter as well, right?). -- Tim Wescott Wescott Design Services http://www.wescottdesign.com |
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Tim Wescott wrote:
Doing it by carrier phase would be better, if you could arrange a phase reference. With hard-mounted receivers (or with a 2nd transmitter in a known location) you can broadcast a time reference and do a reverse-GPS sorta thing. I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. So what am I missing? -- Mike Andrews Tired old sysadmin |
Tim Wescott wrote:
Doing it by carrier phase would be better, if you could arrange a phase reference. With hard-mounted receivers (or with a 2nd transmitter in a known location) you can broadcast a time reference and do a reverse-GPS sorta thing. I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. So what am I missing? -- Mike Andrews Tired old sysadmin |
Mike Andrews wrote:
Tim Wescott wrote: Doing it by carrier phase would be better, if you could arrange a phase reference. With hard-mounted receivers (or with a 2nd transmitter in a known location) you can broadcast a time reference and do a reverse-GPS sorta thing. I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. So what am I missing? OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com |
Mike Andrews wrote:
Tim Wescott wrote: Doing it by carrier phase would be better, if you could arrange a phase reference. With hard-mounted receivers (or with a 2nd transmitter in a known location) you can broadcast a time reference and do a reverse-GPS sorta thing. I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. So what am I missing? OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com |
Tim Wescott wrote:
Mike Andrews wrote: I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... While I do computer science now, rather than math, my degree is the 5-year Bachelor's in math, for what _that's_ worth. Every now and again I get to actually use a bit of real math at work, generally to the amazement of the in-juh-nears here at WeBuildHighways. My point here is definitely not to wave my degree, as I'm quite sure that others here have degrees more advanced than mine, or do math for a living instead of as a hobby, etc., but to point out that having a math background didn't make it any easier for me. It's still fun, though. Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. Seems to me that N+1 receivers gives you an unambiguous fix in (min(N-1,3))-space: 2 receivers locate the transmitter on a line, 3 locate it on a plane, and 4 locate it in 3 dimensions. Since we only get to sense 3 spatial dimensions, more than 4 receivers are useful only to provide an overdetermined solution, which may permit more precision. Of course, the "closer" the receivers are to one another as seen by the transmitter (think of the solid angle that the receiver array subtends from the transmitter), the more ill-conditioned the matrix of coefficients that one uses to determine the position. An interesting variation on the problem would be one in which the receivers also received or derived some precise time signal, such as GPS time, and the transmitter to be located transmitted a signal which contained a precise time referenced to the same standard. This turns out to provide a good location for the transmitter, I believe. -- Mike Andrews Tired old sysadmin |
Tim Wescott wrote:
Mike Andrews wrote: I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... While I do computer science now, rather than math, my degree is the 5-year Bachelor's in math, for what _that's_ worth. Every now and again I get to actually use a bit of real math at work, generally to the amazement of the in-juh-nears here at WeBuildHighways. My point here is definitely not to wave my degree, as I'm quite sure that others here have degrees more advanced than mine, or do math for a living instead of as a hobby, etc., but to point out that having a math background didn't make it any easier for me. It's still fun, though. Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. Seems to me that N+1 receivers gives you an unambiguous fix in (min(N-1,3))-space: 2 receivers locate the transmitter on a line, 3 locate it on a plane, and 4 locate it in 3 dimensions. Since we only get to sense 3 spatial dimensions, more than 4 receivers are useful only to provide an overdetermined solution, which may permit more precision. Of course, the "closer" the receivers are to one another as seen by the transmitter (think of the solid angle that the receiver array subtends from the transmitter), the more ill-conditioned the matrix of coefficients that one uses to determine the position. An interesting variation on the problem would be one in which the receivers also received or derived some precise time signal, such as GPS time, and the transmitter to be located transmitted a signal which contained a precise time referenced to the same standard. This turns out to provide a good location for the transmitter, I believe. -- Mike Andrews Tired old sysadmin |
Mike Andrews wrote:
Tim Wescott wrote: Mike Andrews wrote: I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... While I do computer science now, rather than math, my degree is the 5-year Bachelor's in math, for what _that's_ worth. Every now and again I get to actually use a bit of real math at work, generally to the amazement of the in-juh-nears here at WeBuildHighways. My point here is definitely not to wave my degree, as I'm quite sure that others here have degrees more advanced than mine, or do math for a living instead of as a hobby, etc., but to point out that having a math background didn't make it any easier for me. It's still fun, though. Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. Seems to me that N+1 receivers gives you an unambiguous fix in (min(N-1,3))-space: 2 receivers locate the transmitter on a line, 3 locate it on a plane, and 4 locate it in 3 dimensions. Since we only get to sense 3 spatial dimensions, more than 4 receivers are useful only to provide an overdetermined solution, which may permit more precision. Of course, the "closer" the receivers are to one another as seen by the transmitter (think of the solid angle that the receiver array subtends from the transmitter), the more ill-conditioned the matrix of coefficients that one uses to determine the position. An interesting variation on the problem would be one in which the receivers also received or derived some precise time signal, such as GPS time, and the transmitter to be located transmitted a signal which contained a precise time referenced to the same standard. This turns out to provide a good location for the transmitter, I believe. But if you put GPS into the transmitter for the time signal why not just have it get it's own position and transmit it, ala APRS locators? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com |
Mike Andrews wrote:
Tim Wescott wrote: Mike Andrews wrote: I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... While I do computer science now, rather than math, my degree is the 5-year Bachelor's in math, for what _that's_ worth. Every now and again I get to actually use a bit of real math at work, generally to the amazement of the in-juh-nears here at WeBuildHighways. My point here is definitely not to wave my degree, as I'm quite sure that others here have degrees more advanced than mine, or do math for a living instead of as a hobby, etc., but to point out that having a math background didn't make it any easier for me. It's still fun, though. Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. Seems to me that N+1 receivers gives you an unambiguous fix in (min(N-1,3))-space: 2 receivers locate the transmitter on a line, 3 locate it on a plane, and 4 locate it in 3 dimensions. Since we only get to sense 3 spatial dimensions, more than 4 receivers are useful only to provide an overdetermined solution, which may permit more precision. Of course, the "closer" the receivers are to one another as seen by the transmitter (think of the solid angle that the receiver array subtends from the transmitter), the more ill-conditioned the matrix of coefficients that one uses to determine the position. An interesting variation on the problem would be one in which the receivers also received or derived some precise time signal, such as GPS time, and the transmitter to be located transmitted a signal which contained a precise time referenced to the same standard. This turns out to provide a good location for the transmitter, I believe. But if you put GPS into the transmitter for the time signal why not just have it get it's own position and transmit it, ala APRS locators? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com |
Tim Wescott wrote:
Mike Andrews wrote: [snip] An interesting variation on the problem would be one in which the receivers also received or derived some precise time signal, such as GPS time, and the transmitter to be located transmitted a signal which contained a precise time referenced to the same standard. This turns out to provide a good location for the transmitter, I believe. But if you put GPS into the transmitter for the time signal why not just have it get it's own position and transmit it, ala APRS locators? (Shhhhhh! Pay no attention to the man behind the curtain.) That, of course, is an elegant solution to the problem, but I didn't consider it because it appeared to be outside the postulates given. -- Mike Andrews Tired old sysadmin |
Tim Wescott wrote:
Mike Andrews wrote: [snip] An interesting variation on the problem would be one in which the receivers also received or derived some precise time signal, such as GPS time, and the transmitter to be located transmitted a signal which contained a precise time referenced to the same standard. This turns out to provide a good location for the transmitter, I believe. But if you put GPS into the transmitter for the time signal why not just have it get it's own position and transmit it, ala APRS locators? (Shhhhhh! Pay no attention to the man behind the curtain.) That, of course, is an elegant solution to the problem, but I didn't consider it because it appeared to be outside the postulates given. -- Mike Andrews Tired old sysadmin |
If you want to build something that will locate the roving transmitter on
your plot of land that is 300 foot by 300 foot it might not be too hard to do if you can get your four receivers to do a little bit of timing computations for you. Set the roving unit up to send a pulse on a regular basis. It doesn't have to carry any data or anything like that and it wouldn't have to be too powerful either. There are a few assumptions that can be made that are pretty definate. 1. The distance from two diagonal corners of the square is the maximum distance the transmitter can be from the receiver and still be in the area that is designated as home. 2. The transmitter should be home. If the calculations are coming out wrong then the transmitter has violated the bondary of home. 3. All four of the receivers must be set to a very accurate clock so that they are all using the same reference. I don't have a calculator with me that will let me do the calculation to find the diagonal distance across the square so I will use 450 feet as the rough number for the maximum distance from any receiver. The first receiver detects the transmit pulse and it is known that the transmitter is within 450 feet of that receiver. That starts a clock. The second receiver detects the transmit pulse and the time since the clock started is noted. The third receiver detects the transmit pulse and the time since the first receiver detected the signal is noted. With this much information the position of the transmitter can be determined on a two dimensional plot. The fourth receiver could be used for a sanity check to make certain that the transmitter is in the expected location and it would allow better coverage for when only three receivers can detect the signal. The space between clock start and second receive detect is the difference in distance between these two receivers. The next detect is the difference in distance between the first receiver and the third. And lastly the fourth detect sets the distance between the fourth receiver and the first. If the math is done right there will be four circles drawn each has the center at the corner of your property. When the drawings are made they will all cross in only one place. There will be other places where two or three circles cross. The nice thing about doing it this way is that there is nothing mechanical and with todays computing power that is available a solution can be had within milliseconds of the transmitter putting out a pulse. An idea for the accurate clock could be to use a receiver at each receiver in the square to receive a local TV station and use the synch pulses as a reference. Just don't forget the propagation delay is from one side of the square to the other and figure that in. Another option would be to put a GPS receiver at each corner and use the clock from these as your reference. Or you could use a common receiver site and one clock feeds all four detectors. Just remember that there will need to be four receiver antennas and corresponding feed lines to take care of. |
If you want to build something that will locate the roving transmitter on
your plot of land that is 300 foot by 300 foot it might not be too hard to do if you can get your four receivers to do a little bit of timing computations for you. Set the roving unit up to send a pulse on a regular basis. It doesn't have to carry any data or anything like that and it wouldn't have to be too powerful either. There are a few assumptions that can be made that are pretty definate. 1. The distance from two diagonal corners of the square is the maximum distance the transmitter can be from the receiver and still be in the area that is designated as home. 2. The transmitter should be home. If the calculations are coming out wrong then the transmitter has violated the bondary of home. 3. All four of the receivers must be set to a very accurate clock so that they are all using the same reference. I don't have a calculator with me that will let me do the calculation to find the diagonal distance across the square so I will use 450 feet as the rough number for the maximum distance from any receiver. The first receiver detects the transmit pulse and it is known that the transmitter is within 450 feet of that receiver. That starts a clock. The second receiver detects the transmit pulse and the time since the clock started is noted. The third receiver detects the transmit pulse and the time since the first receiver detected the signal is noted. With this much information the position of the transmitter can be determined on a two dimensional plot. The fourth receiver could be used for a sanity check to make certain that the transmitter is in the expected location and it would allow better coverage for when only three receivers can detect the signal. The space between clock start and second receive detect is the difference in distance between these two receivers. The next detect is the difference in distance between the first receiver and the third. And lastly the fourth detect sets the distance between the fourth receiver and the first. If the math is done right there will be four circles drawn each has the center at the corner of your property. When the drawings are made they will all cross in only one place. There will be other places where two or three circles cross. The nice thing about doing it this way is that there is nothing mechanical and with todays computing power that is available a solution can be had within milliseconds of the transmitter putting out a pulse. An idea for the accurate clock could be to use a receiver at each receiver in the square to receive a local TV station and use the synch pulses as a reference. Just don't forget the propagation delay is from one side of the square to the other and figure that in. Another option would be to put a GPS receiver at each corner and use the clock from these as your reference. Or you could use a common receiver site and one clock feeds all four detectors. Just remember that there will need to be four receiver antennas and corresponding feed lines to take care of. |
In article , Tim Wescott
writes: Mike Andrews wrote: Tim Wescott wrote: Doing it by carrier phase would be better, if you could arrange a phase reference. With hard-mounted receivers (or with a 2nd transmitter in a known location) you can broadcast a time reference and do a reverse-GPS sorta thing. I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. So what am I missing? OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. This sort of thing was attempted in 1960-1961 by Ramo-Wooldridge Corporation (the corporation that spun off what was to become TRW) on HF direction finding using "time of arrival." Essentially that project failed due to a need of absolute group-delay control in the receivers, specifically in the IF chain. While the same local oscillator could feed the mixers and be well isolated from one another to prevent signal coupling around the wrong path, the group-delay or relative phase shift of the various IF chains defeated the theoretical concept. To stay within a 100m (or so) square, one has to work with the phases of the wavefronts so a superheterodyne type of receiver is not too swift unless each IF section is an absolute duplicate of the others. It might be possible with a DC (Direct Conversion) or "zero-IF" type, working with a specific audio tone (as an example), but that's more stuff for analysis. Group delay in tuned amplifiers is not normally measured, nor was it a factor in the military R-391 receivers used for this project at R-W. My body was involved to the extent of others' wants to set up equal group delays but still others' wants had me on the short list for what is now termed "downsizing." [R-W eventually went kaput despite being the origin of STL and, eventually the space factory of TRW] As far as I know the project never made it to full promise. Len Anderson retired (from regular hours) electronic engineer person |
In article , Tim Wescott
writes: Mike Andrews wrote: Tim Wescott wrote: Doing it by carrier phase would be better, if you could arrange a phase reference. With hard-mounted receivers (or with a 2nd transmitter in a known location) you can broadcast a time reference and do a reverse-GPS sorta thing. I thought about the reverse-GPS approach, but couldn't figure out how to determine absolute position. The most I could come up with was that you'd know times-of-arrival at the various receivers, and that would give you deltas from the earliest time-of-arrival. But until you know the distance of the transmitter from any one of the receivers, you can't determine position w.r.t. _any_ of them. As soon as you have distance from one of the receivers and N deltas, you have a fix in (min(N-1,3)) dimensions -- assuming that the processor knows where all the receivers (or antennas, at least) is in that space. So what am I missing? OK, maybe reverse LORAN. If you know the difference in the times of arrival between two stations you can plot the hyperbolic surface where your transmitter must lie. With four stations you should have six different surfaces. The intersections won't agree, but you can get a maximum likelihood estimation of the transmitter's position in three-dimensional space. Being a mathematician by trade would make this easier, and more fun... Actually three receivers would do it unambiguously most of the time, but four would be more accurate at the cost of a bunch more math. This sort of thing was attempted in 1960-1961 by Ramo-Wooldridge Corporation (the corporation that spun off what was to become TRW) on HF direction finding using "time of arrival." Essentially that project failed due to a need of absolute group-delay control in the receivers, specifically in the IF chain. While the same local oscillator could feed the mixers and be well isolated from one another to prevent signal coupling around the wrong path, the group-delay or relative phase shift of the various IF chains defeated the theoretical concept. To stay within a 100m (or so) square, one has to work with the phases of the wavefronts so a superheterodyne type of receiver is not too swift unless each IF section is an absolute duplicate of the others. It might be possible with a DC (Direct Conversion) or "zero-IF" type, working with a specific audio tone (as an example), but that's more stuff for analysis. Group delay in tuned amplifiers is not normally measured, nor was it a factor in the military R-391 receivers used for this project at R-W. My body was involved to the extent of others' wants to set up equal group delays but still others' wants had me on the short list for what is now termed "downsizing." [R-W eventually went kaput despite being the origin of STL and, eventually the space factory of TRW] As far as I know the project never made it to full promise. Len Anderson retired (from regular hours) electronic engineer person |
Allan Butler wrote:
[snip preconditions] The first receiver detects the transmit pulse and it is known that the transmitter is within 450 feet of that receiver. That starts a clock. The second receiver detects the transmit pulse and the time since the clock started is noted. The third receiver detects the transmit pulse and the time since the first receiver detected the signal is noted. With this much information the position of the transmitter can be determined on a two dimensional plot. The fourth receiver could be used for a sanity check to make certain that the transmitter is in the expected location and it would allow better coverage for when only three receivers can detect the signal. The space between clock start and second receive detect is the difference in distance between these two receivers. The next detect is the difference in distance between the first receiver and the third. And lastly the fourth detect sets the distance between the fourth receiver and the first. If the math is done right there will be four circles drawn each has the center at the corner of your property. When the drawings are made they will all cross in only one place. There will be other places where two or three circles cross. But for this to work, as I pointed out in another post, you need to know the true distance from the transmitter to any one or more of the receivers already, or (equivalently) you need to know the exact time of transmission relative to the receiver clock. Otherwise all you have is the delta-Time Of Arrival (TOA) from the receiver that gets the pulse first to the other receivers, and that's not sufficient to locate the transmitter. Even where the maximum distance is known, you still need the true distance from the transmitter to any one receiver at a minimum. If you don't have that, you can't draw any circles. Or I'm missing something obvious. I really don't think I am, but if someone can point out what I'm missing I _will_ be grateful. -- Mike Andrews Tired old sysadmin |
Allan Butler wrote:
[snip preconditions] The first receiver detects the transmit pulse and it is known that the transmitter is within 450 feet of that receiver. That starts a clock. The second receiver detects the transmit pulse and the time since the clock started is noted. The third receiver detects the transmit pulse and the time since the first receiver detected the signal is noted. With this much information the position of the transmitter can be determined on a two dimensional plot. The fourth receiver could be used for a sanity check to make certain that the transmitter is in the expected location and it would allow better coverage for when only three receivers can detect the signal. The space between clock start and second receive detect is the difference in distance between these two receivers. The next detect is the difference in distance between the first receiver and the third. And lastly the fourth detect sets the distance between the fourth receiver and the first. If the math is done right there will be four circles drawn each has the center at the corner of your property. When the drawings are made they will all cross in only one place. There will be other places where two or three circles cross. But for this to work, as I pointed out in another post, you need to know the true distance from the transmitter to any one or more of the receivers already, or (equivalently) you need to know the exact time of transmission relative to the receiver clock. Otherwise all you have is the delta-Time Of Arrival (TOA) from the receiver that gets the pulse first to the other receivers, and that's not sufficient to locate the transmitter. Even where the maximum distance is known, you still need the true distance from the transmitter to any one receiver at a minimum. If you don't have that, you can't draw any circles. Or I'm missing something obvious. I really don't think I am, but if someone can point out what I'm missing I _will_ be grateful. -- Mike Andrews Tired old sysadmin |
Mike Andrews wrote:
Allan Butler wrote: [snip preconditions] The first receiver detects the transmit pulse and it is known that the transmitter is within 450 feet of that receiver. That starts a clock. The second receiver detects the transmit pulse and the time since the clock started is noted. The third receiver detects the transmit pulse and the time since the first receiver detected the signal is noted. With this much information the position of the transmitter can be determined on a two dimensional plot. The fourth receiver could be used for a sanity check to make certain that the transmitter is in the expected location and it would allow better coverage for when only three receivers can detect the signal. The space between clock start and second receive detect is the difference in distance between these two receivers. The next detect is the difference in distance between the first receiver and the third. And lastly the fourth detect sets the distance between the fourth receiver and the first. If the math is done right there will be four circles drawn each has the center at the corner of your property. When the drawings are made they will all cross in only one place. There will be other places where two or three circles cross. But for this to work, as I pointed out in another post, you need to know the true distance from the transmitter to any one or more of the receivers already, or (equivalently) you need to know the exact time of transmission relative to the receiver clock. Otherwise all you have is the delta-Time Of Arrival (TOA) from the receiver that gets the pulse first to the other receivers, and that's not sufficient to locate the transmitter. Even where the maximum distance is known, you still need the true distance from the transmitter to any one receiver at a minimum. If you don't have that, you can't draw any circles. Or I'm missing something obvious. I really don't think I am, but if someone can point out what I'm missing I _will_ be grateful. If you know the positions of any two receivers, and the time delta between the reception of the pulses from the transmitters, the set of possible positions of the transmitter lies on a hyperbola that intersects the line between the two receivers. With two pairs of receivers you get two hyperbolas and two intersections -- and three receivers gives you three pairings to calculate with. So you don't need to know the absolute time of the transmitted pulse, just the difference. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com |
Mike Andrews wrote:
Allan Butler wrote: [snip preconditions] The first receiver detects the transmit pulse and it is known that the transmitter is within 450 feet of that receiver. That starts a clock. The second receiver detects the transmit pulse and the time since the clock started is noted. The third receiver detects the transmit pulse and the time since the first receiver detected the signal is noted. With this much information the position of the transmitter can be determined on a two dimensional plot. The fourth receiver could be used for a sanity check to make certain that the transmitter is in the expected location and it would allow better coverage for when only three receivers can detect the signal. The space between clock start and second receive detect is the difference in distance between these two receivers. The next detect is the difference in distance between the first receiver and the third. And lastly the fourth detect sets the distance between the fourth receiver and the first. If the math is done right there will be four circles drawn each has the center at the corner of your property. When the drawings are made they will all cross in only one place. There will be other places where two or three circles cross. But for this to work, as I pointed out in another post, you need to know the true distance from the transmitter to any one or more of the receivers already, or (equivalently) you need to know the exact time of transmission relative to the receiver clock. Otherwise all you have is the delta-Time Of Arrival (TOA) from the receiver that gets the pulse first to the other receivers, and that's not sufficient to locate the transmitter. Even where the maximum distance is known, you still need the true distance from the transmitter to any one receiver at a minimum. If you don't have that, you can't draw any circles. Or I'm missing something obvious. I really don't think I am, but if someone can point out what I'm missing I _will_ be grateful. If you know the positions of any two receivers, and the time delta between the reception of the pulses from the transmitters, the set of possible positions of the transmitter lies on a hyperbola that intersects the line between the two receivers. With two pairs of receivers you get two hyperbolas and two intersections -- and three receivers gives you three pairings to calculate with. So you don't need to know the absolute time of the transmitted pulse, just the difference. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com |
"Tim Wescott" wrote in message
... Mike Andrews wrote: Allan Butler wrote: [snip preconditions] Withoug the previous parts of the thread this may be duplication since I don't know the original constraints...but I have always wanted to build a model rocket altitude transponder using this concept: On-board the rocket we have a "transponder"... a one transistor superregen Rx on, say 10 or 6 Meters. I hae a schematic around here somewhere for a one tranny FM broadcast receiver from Pop Tronics. Have it's demodulated signal modulate a 2 meter TX. This can be a 9 or 12 Mhz. xtal osc and 2 meter tuned circuit (gets you a few miles on the ground from a tower receiver). On the ground you have the "Ground Station" 10 or 6 meter mobile. Since you can have lots of power, the crummy Rx onboard the rocket is no problem. From the mobile, transmit a tone. Measure the time delay of a zero crossing of the transponded tone. A simple freq counter can be made to do this if it had (I forget the official name--triggered event counter maybe??) the ability to start counting on the TX tone's edge and stop on the RX tone's edge. Just a few chips for this. You pick the frequency that the counter is counting to display feet or whatever units you like. What's-it, something like a nano second per foot? You also need a delay in the proper place to account for the "zero distance" delay of the receivers & transmitters. Seems like one other "Ground" receiver is all that's needed to triangulate the location horizontally... There was an article in QST within the last year or so where some fellas measured the delay through a, I think, 2M repeater versus distance...same concept, 'cept they just used a dual trace scope.. -- Steve N, K,9;d, c. i My email has no u's.. |
"Tim Wescott" wrote in message
... Mike Andrews wrote: Allan Butler wrote: [snip preconditions] Withoug the previous parts of the thread this may be duplication since I don't know the original constraints...but I have always wanted to build a model rocket altitude transponder using this concept: On-board the rocket we have a "transponder"... a one transistor superregen Rx on, say 10 or 6 Meters. I hae a schematic around here somewhere for a one tranny FM broadcast receiver from Pop Tronics. Have it's demodulated signal modulate a 2 meter TX. This can be a 9 or 12 Mhz. xtal osc and 2 meter tuned circuit (gets you a few miles on the ground from a tower receiver). On the ground you have the "Ground Station" 10 or 6 meter mobile. Since you can have lots of power, the crummy Rx onboard the rocket is no problem. From the mobile, transmit a tone. Measure the time delay of a zero crossing of the transponded tone. A simple freq counter can be made to do this if it had (I forget the official name--triggered event counter maybe??) the ability to start counting on the TX tone's edge and stop on the RX tone's edge. Just a few chips for this. You pick the frequency that the counter is counting to display feet or whatever units you like. What's-it, something like a nano second per foot? You also need a delay in the proper place to account for the "zero distance" delay of the receivers & transmitters. Seems like one other "Ground" receiver is all that's needed to triangulate the location horizontally... There was an article in QST within the last year or so where some fellas measured the delay through a, I think, 2M repeater versus distance...same concept, 'cept they just used a dual trace scope.. -- Steve N, K,9;d, c. i My email has no u's.. |
(Washed Phenom) wrote in message om...
Any advice, direction, URLs, or discussion is much appreciated. I'm still following this thread with interest and looking up things that I don't understand. The recent exchanges of the past day have gone quite over my head, but I'm reaching. In my travels, I found this link. It seems this setup is using two antennas, but I'm wondering if a similar 4-antenna solution could be used for what I am trying to do. It would seem that the ability to use a common PC audio card and readily available software would be a big bonus. Comments welcome, particularly if this idea is way-off what I'd need! The URL: http://www.vlf.it/rdfsoftware/rdf.html |
(Washed Phenom) wrote in message om...
Any advice, direction, URLs, or discussion is much appreciated. I'm still following this thread with interest and looking up things that I don't understand. The recent exchanges of the past day have gone quite over my head, but I'm reaching. In my travels, I found this link. It seems this setup is using two antennas, but I'm wondering if a similar 4-antenna solution could be used for what I am trying to do. It would seem that the ability to use a common PC audio card and readily available software would be a big bonus. Comments welcome, particularly if this idea is way-off what I'd need! The URL: http://www.vlf.it/rdfsoftware/rdf.html |
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