PerSonal Security System - PSST

Actual Operation

This is the Theory and Equipment Design description page for the PSST Rape Prevention system. For a description of the device and the system, please go to the PerSonal Security Transmitter Home Page.

The PSST system operates as follows:

The nearest existing system is the LORAN-C marine navigation system. The PSST system is somewhat of an inverse of that system. LORAN-C uses a fixed, known-location, land-based transmitter and repeater, with the analysis being done AT the unknown location on a boat, by determining the intersection point of two or more hyperbolas. The similarity of PSST and LORAN-C is in that they are the only two position locating systems which use hyperbolas in the analysis. The PSST system uses an UNKNOWN location transmitter (the girl's pendant), a fixed, known-position repeater, and the position analysis being done at various (at least three) fixed, known receiver locations, by determining the intersection point of two or more hyperbolas.

LORAN-C signals are generally sent as a short pulse on a carrier frequency of around 2 MHz. Radio waves travel at the speed of light, so they travel around 150 meters (or 500 feet) during one oscillation at that 2 MHz frequency, which has the effect of limiting LORAN-C position determination accuracy to roughly that range. For identifying the position of a boat in the ocean, that accuracy is generally sufficient. The PSST system is designed for a carrier frequency of around 900 MHz. During one oscillation at that frequency, the radio waves travel around 1/3 meter (or one foot), which permits position determination of approximately that precision. A girl in trouble could be identified and located within about one foot, X, Y and Z, in a fraction of a second.

The repeater receiver/transmitter, the final receivers, the signal processing, and the intersecting hyperbola analysis are all fairly similar to LORAN-C components, relatively standard equipment, except for the much higher carrier frequency.

Text Font Face
Text Size
(for printing)

An Analogy

Imagine that you are in a canyon, which is very echoey. You notice two large flat areas of the canyon walls. During the night, somewhere in the canyon, a very valuable meteorite crashes down, making a single impact sound. You left a tape recorder on all night, and it recorded that direct sound, and then shortly later, it recorded the two echoes off of those two canyon walls. It might seem amazing, but by simply analyzing the recording, you could walk directly to where the meteorite had fallen (while you were asleep and in pitch darkness) and pick it up!

The RELATIVE TIMING of the direct sound and the echoes is all that is actually required! The ACTUAL precise time when it fell is irrelevant, so no precise clock is required for that. The TIME BETWEEN the three sounds on the tape is all that is necessary. By accurately knowing where those reflective canyon wall areas areas were (as from an accurate map), you could calculate three different hyperbolic curves, for each only needing to know the TIME INTERVAL between any two of the three sounds recorded. (Three hyperbolas result because there are three different pairs of sounds where the time interval is known, first-second, first-third, and second-third.) These hyperbolas are then drawn on a map of the canyon, and the three curved lines will intersect/cross at the point where the sound had originally come from! You then just walk to that location and pick up the meteorite! The meteorite did not have any sophisticated electronics on board, but a cheap and simple tape recording of the three sounds still permitted very accurate location of it. In that situation, if the recorder was a modern digital recorder, and it recorded at 6600 bits per second, and the speed of sound was 1100 feet per second, the intersection of the hyperbolas should be accurate to around FOUR INCHES! Incredible precision for a system that only needed a cheap tape recorder!

That is essentially the premise of the PSST system!

PSST uses microwave radio waves, which travel at the speed of light (roughly a billion feet per second) and a frequency resolution of around one foot due to using a carrier frequency of around 900 MHz (or roughly one billion cycles per second). A one-foot precision of position location is unheard of with any other approach. The public generally is not aware of it, but the commercial version of GPS only has an accuracy of around 100 feet in any direction. Other systems such as triangulation or RDF often have even worse accuracy. Regarding trying to prevent a rape from occurring or proceeding, a location that might be 100 feet off in any direction might mean that the girl is twelve stories higher or lower in a hi-rise dormitory, or in or outside of several different houses. It is not possible for Police to locate and apprehend the criminal under those conditions. But with the PSST system, the Police would immediately know EXACTLY where she is, such that they could quickly go to that exact location. In fact, if the girl was able to keep the PSST device transmitting, then each second, another signal is sent out, and the PSST system would then again calculate where she is. If she was now five feet away from the previous second's location, that implies that she is WALKING in a known direction! If the speed was higher, she may have been taken into a vehicle and it is moving. In any case, the one-foot precision is critically important in locating her FAST!

Basic Theory

The PSST invention is based on several simple and well-established premises. A simplest possible (hand-held) transmitter, which can produce an un-modulated carrier wave, is merely turned on, very briefly, for less than a millionth of a second, which permits battery life to be good even while sending out a very strong radio signal. Four fixed-location receiving antennas each listen for that distinctive signal. One of those receivers (which we will call a repeater) also has a transmitter of its own, and it immediately sends out a transmitted signal of its own whenever it senses a received signal from a hand-held transmitter.

The result is that each of the other three receivers receive TWO signals, one directly from the hand-held transmitter and a slightly later one from the repeater transmitter. As in our canyon analogy, those three receivers do not have to care about the precise TIME of reception of either signal, but only the time interval BETWEEN receiving the two, which is generally less than one-millionth of a second. Many other systems, including GPS, require every GPS device and all of their orbiting satellites to know PRECISELY the exact time and to agree, in order for their system to function. But the clocks on the satellites each continuously change rates, as they get hotter and cooler from being in the sun or behind the earth. And all GPS devices also have clocks which constantly change their rate and must constantly be corrected. PSST does not need those complications, and the simpler approach is expected to be much more reliable and accurate. That measurement of the INTERVAL between the two received signals is ALL that any of the three PSST receiving antenna systems needs! As in our canyon analogy, each receiving station then can determine an hyperbola, on a city map, somewhere upon which the girl is located.

Each receiving station actually does NOT do that analysis of the hyperbola. Instead, each of the three receiving stations simply sends a single bit of data to a central analysis station, that bit of data being the NUMBER OF NANOSECONDS IN THE INTERVAL BETWEEN THE TWO RECEIVED SIGNALS at that station. So this is simply an integer number, generally between 0 and 50,000. This can be sent as a standard two-byte data message. (These values permit PSST to protect a community about ten miles in diameter, a distance which was selected to reduce the necessary transmitting power of the transmitter and its small battery.) The analysis station receives the three time differentials, where it can then generate the three hyperbolas, and the point of intersection can be either plotted on a map or the location can be converted into a street address and displayed on a computer screen.

This entire process occurs amazingly fast. The computer time in generating the hyperbolas and then converting the intersection point into a street address is what takes the longest, but with modern computers, that occurs is well under 1/100 second. So the Police would see the street address of where the girl is being attacked, essentially at the same time she pressed the button on the PSST device!

It then only depends on where the nearest Police car might be before the Officers arrive to aid the girl. Hopefully, that should be just a minute or two at most.

That is essentially all there is to the PSST system! The receivers do NOT have to maintain precise clock timings, as the actual moment of signal reception is not needed. The transmitter does not need any timing circuitry, either, and ONLY needs to create a "sharp-edged" transition from off to on!

The analysis is what is unique in PSST. A boat captain using LORAN-C notes the time of signal reception from an onshort LORAN-C transmitter and an onshore repeater station, and then he can plot an hyperbola on his chart. He does the same for a different LORAN-C transmitter to get a second hyperbola, and where the two curves cross, that is (roughly) where he is! So even though LORAN-C is similar in using hyperbolas for the analysis, it is done in a cumbersome and time-consuming manner. PSST is FAST, because a modern high-speed computer does nearly everything.

This time-difference results for each of the three receivers is sent (by conventional data transmission means, even phone lines are fine) to a central office. By taking any two (say A and B) of these time-differences, we can define and calculate a hyperbolic line as being the only possible locus of locations of the source transmitter. By then taking a different pair of these time-differences (say A and C), a DIFFERENT hyperbola is determined. The point where the two hyperbolas cross MUST BE the exact location of the transmitter! As a confirmation, the remaining pair of results (here B and C) are then also analyzed to provide a third hyperbola. If the signal and data are valid, then all three hyperbolas cross at exactly the same point. In reality, they generally cross such that there is a tiny triangle between the three lines, a triangle which is generally smaller than one foot in size, and often is far smaller than that.

A real application of this has a variety of complications, but the above description is the entirety of the concept of this PSST invention! The full practical system would have five or six receiving stations. If power goes out or something fails at any one station, the other operating stations will still determine the precise location. Additionally, having SIX hyperbolas all intersect at one specific location is additional confirmation of knowing EXACTLY where the girl is! If something bizarre would happen where the six hyperbolas intersected at locations that were far apart, that would imply that the location was not reliable. We do not see how that could ever happen, but it is nice to know that PSST has a self-check capability.

In addition, PSST would operate a storefront where each girl would bring her PSST device in once every three months to have the battery checked and possibly replaced. While there, HER device would be placed on a specific spot on a specific table and triggered. The entire PSST system then operates and generates a location as being on that specific table. The analysis system would be instructed to NOT alert the Police when the location is on that table! But this represents another reassurance that PSST was always fully operational. IF a hundred girls each brought her PSST device in for the battery maintenance each day, then the entire PSST system would also be checked a hundred times every day. And IF the location is determined to be anywhere except on that table, even tiny problems with PSST's accuracy would be immediately known!


A very small and simple hand-held transmitter emits a signal for a very brief period of time, on the scale of a millionth of a second. If the carrier frequency is at 1 GHz and the signal length is one-millionth of a second, then 1000 oscillations of the carrier wave would be included in the transmitted pulse train.

Such a very simple pulse train would be very hard to identify as being part of the PSST system, and a system based on such a crude transmitter would be extremely susceptible to false signals, such as by lightning. In addition, because very high frequency signals do not "instantly" turn on but gradually "ramp up", there would be no precise instant in time identified for the later analysis to use. Therefore, about one-third of the way through that millionth-of-a-second long pulse train, we electronically plan to invert the carrier wave signal once. Being a carrier sine wave, the effect of inverting it is to shift it half a wavelength later (when compared to an indexing pulse train).

The transmitter would then be silent (off) for nearly the entire following second. After about one full second, and if the girl was still pressing the button on her PSST device, the simple (inversion) signal pulse train would be repeated. Between these very brief pulse trains, the transmitter does not emit any signal, for two main reasons. (1) With the PSST approach, the receiving/analyzing apparatus is not tied up with signals from this specific transmitter, so the system could receive and process signals sent from a second, different transmitter. It seems remote that a second rape could be occurring at the exact same instant, but if it ever does, PSST would detect and monitor BOTH events. In fact, we believe it could simultaneously analyze more than 50,000 events in different parts of the city, and provide the results to the Police. (2) By only operating the transmitter for such extremely brief intervals, the transmitter's battery is not rapidly depleted, and the transmitter could continue to send out relatively powerful pulses until the police apprehend the perpetrator.

Each inversion pulse train is a separate event in time, so normally the receiving/analysis system will process and identify the location of any active PSST transmitter about once every second. With this known interval spacing, the ongoing position analysis can even determine the speed and direction of any motion of the transmitter during that active period. This allows real-time tracking of a moving transmitter, at the one-second intervals.

If the length of each transmitted pulse train was one-millionth of a second, with no signal transmitted between the one-second-apart repetitions, the clear-channel frequency is nearly always available for signals from other transmitters. It seems certain that more than 50,000 PSST transmitters could be simultaneously activated, and the system could determine the precise locations of all of them!

Seeing that there would probably be little need for responding to 50,000 simultaneous crimes, and that handling even 5,000 would be far more than ever actually necessary, the length of the pulse train could be extended, to say, one-hundred thousandth of a second. This could allow two advantages. (1) The initial transmitter operation would have a longer time to stabilize on its natural carrier frequency. (2) In the end of the pulse train, two bytes of data (16 bits) could be embedded (modulated) on the signal. These two bytes could uniquely identify up to 65,500 individual transmitters, so the analysis processing could add a person's name and description to the precise location information already generated. Most of the PSST descriptions include this feature.

The simplicity of the transmitted signal is central to the concept of this system. Each transmitter is extremely simple AND INEXPENSIVE. Also durable and reliable.


A basically very simple receiver is also a main part of this system. It has two functions. The second (and actually less important) is a reception and recognition of the 16-bit (or two byte) sequence that identifies the unique code of that particular transmitter. (This length sequence allows the identification of 65,500 unique transmitters, enough for most communities.)

The FIRST function of the receivers is to receive the carrier wave and identify extremely accurately the exact instant the event of the inversion of the signal is received. This is actually done from TWO copies of the original transmitted signal (explanation below). These two copies generally arrive at each receiver antenna less than a microsecond apart in time. When the first copy arrives, an internal pulse-counter/timer in that receiver is started. When the second copy arrives, the timer is stopped. The RESULTS of this timer, the INTERVAL of time between the reception of the two signals is all that is needed to precisely locate the transmitter's location, as explained further on. Interestingly, even if that receiver takes a significant amount of time to analyze the signal to determine that it had received a signal, it will take virtually the exact same amount of time to process both of the signals processed. The INTERVAL or difference in time between the two receptions would not significantly be affected. Any flaws or variations in the operation of a receiver circuit therefore do not affect the desired timing result. Once this interval is determined, a standard digital signal could be sent over modem/phone lines to a central office to be analyzed there.

There must be at least three (identical) receivers located near the perimeter of the protected area. Their exact locations are moderately flexible, with an ideal arrangement being an equilateral triangle. The following discussion will consider three receivers, and the final notes will comment on the benefit from having additional receivers installed.

Repeater Transmitter Facility

At an separate (somewhat optional) location somewhere near the center of the protected area, a fourth receiver is necessary. This one is different from the others. In this discussion, we will call it the "repeater." Any PSST signal it receives is just amplified and immediately re-transmitted, to be received by the three other receivers. The effect will almost seem like an "echo" signal because this signal will always arrive later than the original direct signal from the hand-held transmitter.

There are a wide range of ways that this transmitter could be configured.

Summary So Far

A receiver gets two copies of the transmitted signal. The first arrives directly from the hand-held transmitter. The second comes from a duplicate version of this signal from our Repeater Facility. That signal always arrives later. The delay is due to two reasons.

This will all become clearer below. It is now appropriate to discuss more fully the theory of why this system works.


The transmitted waves of any radio or microwave transmitter travel at the speed of light. The speed of light is actually very slightly affected by the presence of the atmosphere and humidity, but since we are only interested in differences in arrival times, for relatively short distances (less than a few miles), this effect is negligible for this application.

For the directly received signal, this means that the direct signal will arrive at the receiver's antenna a time Tdirect later. Tdirect is simply determined by (the straight line Distance from the hand-held transmitter to the receiver antenna) divided by the speed of light.

The signal that was received by the Repeater Facility and then re-transmitted was delayed by a total of three consecutive time intervals. The first could be called T1 and is the time taken for the signal to travel from the hand-held transmitter to the antenna of the Repeater Facility. The second (Trepeater) is the total delay caused by the equipment of the Repeater Facility, including the times taken for the signal to travel down and up the cables and wires and the time to amplify the signal for re-transmission. The third delay (T2) is the time taken for the re-transmitted signal to travel from the Repeater's transmitting antenna to the Receiver's antenna. This path's total delay is therefore
T1 + Trepeater + T2.

The system under consideration does not ever need to determine the precise value of any of these individual variables. The ONLY measurement taken is the interval of time (at the receiver) between the arrival of the two copies of the signal. Using the terminology above, that is
T1 + Trepeater+ T2 - Tdirect.

This procedure eliminates any possible errors due to variations or fluctuations in the operation of the transmitter, because any such changes are cancelled out by the PSST method of only measuring the DIFFERENCE of time or reception based on a single signal inversion event of the hand-held transmitter signal. This is an important reason why very inexpensive transmitters may be used in the PSST System.

Systems such as GPS are extremely sensitive to the temperature of the device, as the on-board clock changes speed with temperature (as well as with humidity and other variables). Therefore, GPS must constantly be correcting its on-board clock to be precise enough and to agree with the time as determined by the satellites. Each satellite must send out constant updates of its position and the time it thinks it is, and there are many sources of possible error or failure. PSST avoids most of that by not needing to know the actual time!

Once this time difference is determined in a receiver, the resultant number of nano-seconds of this delay is transferred by any conventional means to an office somewhere in the community. This 'difference-number' will generally be different for each of the (three) receivers, and all three resultant difference-numbers will arrive at the office.

Let's call the three receiving antennas A, B, and C. Let us now pick any two of the receivers (say A and B) and subtract one reading from the other. This is now the difference between two numbers that were already differences of signal reception times! This second level of 'differencing' in this manner of processing eliminates even MORE potential sources of errors! For example, any variations or fluctuations in the operation of the equipment of the Repeater antennas, cables, receiver, amplifier, or transmitter are eliminated from being sources of errors in the location analysis.

This DIFFERENCE is now T1A + TrepeaterA + T2A - TdirectA - T1B - TrepeaterB - T2B + TdirectB.

The delay caused by the repeater MUST always be the exact same value (because they were really one and the same event), so those two terms always perfectly cancel out. Two other terms are dependent on the physical distance between the Repeater transmitting antenna and the final Receiver antennas. These distances never change because our equipment is fixed in position, so these time intervals never change, T2A and T2B. These are the time delays caused by the Repeater signal traveling to each of our two fixed Receiver antennas. Both of these dimensions are fixed when the system is installed. Therefore, those time delays can be calculated precisely and then removed from the above equation. The following discussion includes a (K) term for this constant.

This leaves T1A - TdirectA - T1B + TdirectB + K. The intervals T1A and T1B are by definition exactly identical (being the time interval for the propagation of the original signal from the transmitter to get to the Repeater antenna), so they will also cancel out of this equation, which leaves TdirectB - TdirectA + K. Since we know the precise value of the constant K (from above), this means we now have a very accurate value of the difference in time reception of the Direct signal from the hand-held transmitter to each of two Receiving antennas! In the process, our differencing approach has eliminated any possible variations or fluctuations in the inexpensive hand-held transmitter and in any of the equipment involved in the Repeater installation.

There have been other approaches previously used to attempt to accurately get this difference. Unfortunately, those approaches have always had numerous sources of potential error that are very difficult to overcome. Usually, such systems rely on extremely accurate on-board clocks at each receiving station to determine the ACTUAL time of reception. Unfortunately, such clocks have both long-term and short-term variations in their performance. Under normal circumstances, these variations would not seem significant. But, in the context of determining the location of the source transmitter precisely, it is necessary to determine timing to a billionth of a second! It is extremely difficult to provide a receiver's clock (and other internal signal processing equipment) to consistently identify a precise time better than to about 20 billionths of a second. Since the difference between two such readings (at different receiver locations) is actually needed, an error amount as great as 40 billionths of a second could exist in the results. This could represent an error in the actual position calculated of well over 100 feet! And that's with absolute state-of-the-art timing equipment!

The PSST system does NOT rely on such potentially fluctuating clocks. As mentioned above, our processing method has eliminated any possible errors due to fluctuations in the transmitters and in the entire Repeater system, and now also in the individual receiver antennas and circuits (using the same-frequency configuration described above).

Since the speed of light is constant, knowing the difference in TIME of the signal propagating on a direct straight line path from transmitter to receivers means that we also know the difference in DISTANCE between the hand-held transmitter and the two Receiving antennas.

It may not be obvious, but this 'difference' equation is actually a mathematical definition of a unique half-hyperbola as being the ONLY possible locus of locations where the hand-held transmitter could possibly be. (That 'difference' equation is actually one of the basic mathematical definitions of a hyperbola, where the two PSST Receivers are located at the two foci of the hyperbola). Nearly all of the possible sources of error have earlier been eliminated by the two levels of differencing of the time intervals involved.

Using identical logic, but using the difference of the time result values from Receivers A and C, we can get a new and DIFFERENT half-hyperbola as the locus of the ONLY locations possible for the hand-held transmitter. Plotting both of these half-hyperbolas on a map of the community, there is (generally) only one point of intersection and that point therefore uniquely defines the precise location of the hand-held transmitter!

Near the perimeter of the area between the Receiver antennas, and outside of the protected area, it is sometimes possible for there to be a maximum of two points of intersection, and therefore two solutions. In real situations, these two solutions are generally physically extremely close to each other. Whether or not that is true, it is possible for the computer to also use Receivers B and C results to plot yet another half-hyperbola. The three half-hyperbolas will all cross at one unique, unambiguous location. This would eliminate any ambiguity in the actual location of the hand-held transmitter.

Therefore, the final result is an amazingly accurate location of the hand-held transmitter. This is accomplished while using extremely simple and inexpensive hand-held transmitters and relatively inexpensive receivers and analysis equipment. If the time differences are determined to the nearest nano-second, a position determination accuracy of a few inches is possible in the center of the protected area, which increases to a foot or two at the very perimeter of the city area. This is considering an area of around 10 miles in diameter. If the time differences are only determined to an accuracy of a several nano-seconds, the accuracy of position determination increases to a foot or two in the center of the protected area.

In the computer analysis of these results, the intersection point of the three hyperbolic curves would never be precisely one point in practice. There would invariably be a small triangular shaped area between the three lines. The center of this area would probably represent the absolutely most precise position determination, and the dimensions of that triangle would give some idea of the possible error factor. In practice, this refinement of an inch or two of better accuracy should be irrelevant when the Police are trying to locate a person.

There are some very important other benefits of this system. Nearly all of the possible sources of errors are minimized in this system. The Repeater Transmitter Facility could slightly vary the amount of time delay as a result of warmth of the day or cool of the night or for a number of other reasons. ALL of these effects are eliminated in our differencing processing, because the Repeater Facility delay interval is necessarily precisely the same for each Receiver and that interval is cancelled out (as described above) since we only use the DIFFERENCE between the results of different Receivers.

The clocks and timers in each of the Receivers are also susceptible to slight variations of rates. If we were depending on comparing the ACTUAL times of reception at the various Receivers, there would be a number of potential timing errors as a result. GPS systems are necessarily very complicated (and expensive) because they have to do this, and to continuously deal with possible variations and fluctuations of the clocks on the various satellites and the GPS receiver. The PSST system does not need to be concerned with that problem. Each receiver only measures an interval on the scale of one-millionth of a second long. With even a 'moderately stable' (inexpensive) on-board clock, this short of an interval can be measured extremely accurately.

The transmitter does not need ANY accurate timing circuitry or any analysis circuitry of any kind. This also eliminates many possible sources of error in the system. (Some previous attempts at this kind of location determining system have relied on an extremely accurate clock installed in each transmitter. This made for rather complicated and expensive transmitters, and also introduced several serious sources of potential timing errors).

Practical Application


An off the shelf 1 GHz generic transmitter circuit board could be used with two modifications. (1) A timer circuit would limit the pulse train to a specific length, probably around one microsecond, and it would also repeat that pulse train at approximately one-second intervals, with no transmissions between those brief pulse trains. (2) A provision must be made to invert the carrier wave pulse train a few hundred nano-seconds after the carrier wave is initiated. This is not as easy as it sounds. At low frequencies, it would be easy to electronically invert such a signal. But, at such very high frequencies, even the initiation of the wave train is not instantaneous. Rather, the amplitude of the sine waves gradually increases, so there is no obvious instant in time that can be identified as the moment when the carrier wave was turned on. This is why the front or trailing edge of the wave train cannot be used for timing purposes. The precise moment when the signal was actually "on" would be somewhat uncertain, on the time scale we are interested in.

That's why we decided to initiate the carrier wave and then, after it has stabilized, to invert it. We think the most straightforward way of doing this is to just switch in an additional amplification stage in the signal path of the transmitter amplifier, which has a gain of 1. This would act to invert the signal. Again, the result would not be an instantaneous action, and the wave train will take a number of cycles before the transition is completed.

This is not the only possible way to create an identifiable instant in time in the wave train. We have not discussed using the modulation circuitry in the transmitter, because the PSST usage of the transmitter is so basic that we don't think we actually even need to modulate the carrier with an information signal, at least for position determination. IF such a modulation signal was introduced, the total pulse train length would be necessarily much longer (possibly affecting the number of simultaneous transmitters that could be located). It would make sense that the starting sequence of that modulation pulse train be a known sequence of signals, so receiver circuits would recognize the signal. With this being the case, a receiver could be programmed to look for such a specific sequence with a matched sequence onboard the receiver demodulating circuitry. A wave train matching circuit in the receiver, similar to that used in GPS receivers, would create an EPIC (instantaneous spike of output signal) when the timing of the identical sequences matched exactly. This is a more complicated and sophisticated way for the receiver to unambiguously identify the precise moment of time that the signal is received. This would ensure extremely accurate starting and stopping of the interval timer onboard the Receiver installation.


In the receiver (when using the unmodulated carrier approach), each of the two received carrier wave trains would be sent to an analysis circuit. Each wave train received (the Direct signal and the Repeater signal) would be continuously beat against (electronically subtracted from) a pulse train from a standard demodulator onboard oscillator, and then checked with a pulse train summer, for a fixed (short) interval (say, 100 wavelengths). When the carrier wave train is first received, the absolute value of this sum quickly drops to near zero, because the on-board oscillator is designed to quickly synchronize with the incoming carrier frequency, and all the incoming wavefronts would exactly match the on-board oscillator's waves, and all the individual wave subtractions would result in zeroes, so the sum total would be zero. Well AFTER the inverting transition has passed, the sum will again be zero, because the on-board oscillator would again have re-synchronized with the incoming carrier frequency. Between these points in time, however, before any re-synchronization could occur, a moment occurs when half of the comparison pulse train (that already went by) would match perfectly and cancel out as before, but there would be the NEW half of the comparison pulse train, where the result of the pulse subtraction would be twice the pulse amplitude. When this is summed over the total of the comparison pulse train, a maximum amplitude of that summation will occur as the inversion point passes by. This maximum in this comparison summation will be a very well defined instant, even for an inversion transition that is not very well defined as a precise event. It therefore identifies the precise time of the reception of the desired signal.

This is similar to the approach of circuitry in GPS receivers that look for an EPIC, or highest summation value of a sequence of such comparisons of pulses. The only difference is that we are actually looking for a zero-crossing point in the original signal, but the processing logic and the time determination is the same.

In the case of the more complicated transmitter, which uses the modulated signal with a known modulation pulse sequence (to reduce the possibility of false triggering of the system), that identical sequence could be installed onboard the receivers. Once de-modulated, the received pulse sequence would be matched against the known expected sequence. In this case, an EPIC would be identified. At the exact instant when the pulse train precisely matched the onboard sequence, the summation circuit would momentarily attain an extreme maximum value (spike), being the desired EPIC, and unambiguously identifying the desired instant in time.

The main difference between these two approaches is that the first is intended to not need to demodulate the received signals and works directly with the received carrier signals. The second demodulates the signal and then uses the resultant modulation signal for analysis. The first seems purer and less susceptible to additional timing error sources. The second uses accepted and proven circuitry from GPS equipment development analysis designs.


Any one Receiver installation only develops a SINGLE piece of data as a result of capturing a valid signal from a hand-held transmitter, the DIFFERENCE in time of reception of the two incoming signals, the original signal and that from the Repeater. It is not possible for any position determination to be done at any of the Receiver installations. The (digital) value of that time interval must be sent to an Office location, for comparison to the results from other Receiver installations. This data transfer can be done in any of a multitude of conventional ways. All that is necessary is for a 2-byte (16-bit) numerical value be transferred. It would represent the number of carrier pulses that passed between the reception of the two received (inversion) signals. If the carrier frequency is around 1 Ghz, this result will be approximately the number of nano-seconds between the two signals being received.

Once received at the Office location, any pair of the incoming time differential results from two Receiving installations can then be used (along with the locations and separation of the two specific fixed Receivers) to easily generate a half-hyperbola that represent the ONLY possible solutions of the location of the hand-held transmitter (as described above more specifically). A second pair of Receiving antennas can generate a second half-hyperbola, which will necessarily intersect in at least one place with the half-hyperbola of the first solution. We refer to HALF-hyperbolas rather than hyperbolas, because our method of differencing analysis lets us know which antenna received the signal first, which specifies which half-hyperbola would represent valid solutions.

Applications in Larger Areas

That intersection point unambiguously identifies the location of the hand-held transmitter, with VERY few possible sources of error that could introduce inaccuracies. With even moderate quality, essentially "off-the-shelf" components and a 1 GHz carrier frequency, a location determination accurate to within one foot is consistently possible anywhere in an extended area of up to five to ten miles across.

For larger areas, additional Receiver locations could be added, much like cellular phone towers. Each 'triangle' of protected area would have its own central office analysis setup. Each analysis would then proceed as before. Whenever a calculated location is outside the triangle formed by the three local Receivers, that would indicate that the hand-held transmitter had been activated inside of a DIFFERENT protected 'triangle' of protected area. A very simple analysis step could quickly eliminate further analysis of that result within THIS Office's processing equipment. This means that only transmitter triggering events inside of THIS protected 'triangle' would be processed for determination of the position.

Additional Receiver Installations In A Protected Area

Even in a single area, there can be advantages of having more than three Receiving installations connected. In the event that an equipment malfunction or electrical disruption occurred at one Receiver, a position determination could still be accomplished. Similarly, if a hand-held transmitter's signal was somehow not received by a particular Receiver antenna, there would still be three (or more) remaining Receivers to generate the necessary time differential results.

Another advantage of additional Receiving installations in a single area is the ability to achieve even more precision in position determination. With three Receivers, it is possible to generate three different hyperbolic curves (A-B, A-C, and B-C). Generally, the three half-hyperbolas will not precisely intersect in the exact same point. The three curves usually cross very near each other, establishing a triangle-shaped shape, which dimensions indicate the accuracy of the determination. With four Receivers, it is possible to generate SIX different hyperbolic curves (A-B, A-C, A-D, B-C, B-D, C-D). These six curves will again intersect in nearly the same location, and analysis of these results can accomplish even more precise results than with just three Receivers. The same is true for five Receivers (10 hyperbolas) or six Receivers (15 hyperbolas) or more.

Having extra receivers also minimizes the effect of any spurious results. If six Receivers are used, and 14 hyperbolas intersect at virtually the same point and one does not, the outlier could be dismissed as spurious.

Very little difference would be involved in any other parts of the PSST system in adding an additional Receiver. The hand-held transmitters and the Repeater installation would not be affected at all. The central Office analysis would only have to be slightly modified to accept additional input and to calculate additional half-hyperbolas.

Advanced Processing

The presentation so far has discussed the situation of relatively rare single stationary hand-held transmitter events. Many extensions of this technology are available, and are effectively already built in. The most obvious is to record the readings generated from a specific hand-held transmitter each second, and then to plot them on a map. A stationary transmitter would show each result at the exact same location. A moving transmitter would show the direction, speed and path followed by the transmitter. If, for example, each second, the result is 44 feet east of the previous result, it can reasonably be concluded that the transmitter is in a vehicle that is traveling east at 30 mph, on a street that is easily identified by its location. Therefore, even if an assault or rape victim was being kidnapped in a car, the PSST system would be able to track the progress. Since the hand-held transmitter could be quite small and would NOT make any audible indication of its triggering, the attacker would not even know that the transmitter was continuously allowing the tracking of his progress.

The PSST System concept is designed to only use very brief transmission pulses. This greatly extends the battery life in the transmitter. It also leaves the receiving system open to respond to a separate emergency at a different location from a different PSST transmitter. This means that several individual signals can be received and processed simultaneously in a multi-plexing type of method, all automatically. If transmission intervals could be kept shorter than one one-hundred-thousandth of a second and the repetition interval maintained at about one second, then it should be possible to have the system respond to more than 10,000 simultaneous emergencies! (No city has enough Police to respond to 10,000 simultaneous crimes being committed!)

Additional Applications for PSST

Considering this capability, of being able to handle over 10,000 simultaneous PSST transmitters' signals, a broad range of additional applications become practical. Since each PSST transmitter sends out a 16-bit pulse string that identifies itself, many additional benefits are available.

A number of specialty uses are also available: All of the discussion so far has considered identifying locations on the (flat) surface of the earth. It is easily possible to add an additional PSST Receiver installation above or below the plane of the surface of the earth. By using similar Differentials between this Receiver's result and that of any other Receiver's result, it is possible to generate an accurate vertical position as well. In areas where there are high-rise buildings, or in rugged terrain areas, this could be beneficial. No special additional technology or equipment is necessary.

This page - - - - is at
This subject presentation was last updated on - -

Link to the Public Services Home Page

E-mail to:

C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago