Tracking a radio beacon from a moving device

Abstract

A method and devices are disclosed, for tracking a radio beacon from a moving device, while the beacon transmits periodic signals, which the device detects at least at two different locations, and the device provided with information enabling determining the time difference between transmissions of these periodic signals. The method discloses a formula for estimating the angle between the course of the moving device and the beacon: arccos [c*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12]; wherein the moving device detects signal 1 and signal 2 respectively at location 1 and location 2, the distance between these locations defined as baseline.sub.12, TDOA.sub.12 is the Time Difference of Arrival of the signals at the two locations, TDOT.sub.12 is the time difference between transmission of these signals, and c is the speed of light.

Claims

1. A method for tracking a radio beacon from a moving device, comprising the steps of: a. at said radio beacon transmitting periodic signals; b. providing said device with information enabling determining at least a time difference TDOT.sub.12 between a transmission time instant of a first signal and a transmission time instant of a second signal, said first and second signals been part of said periodic signals; c. at said device, at a first location, determining location coordinates, and a receiving time instant of said first signal; d. at said device, at a second location, determining location coordinates, and a receiving time instant of said second signal; e. at said device, determining a time difference TDOA.sub.12 between the receiving time instant of said first signal and the receiving time instant of said second signal, and a distance baseline.sub.12 between said first and second locations; f. at said device, determining a direction to said radio beacon, from said TDOT.sub.12, TDOA.sub.12 and baseline.sub.12.

2. The method according to claim 1, wherein said information is associated with at least one of: a. data configured in advance at said beacon and at said device; b. data communicated from said beacon to said device; c. data specifying TDOT.sub.12; d. minimum time difference (T) between permitted values of TDOT.sub.12; e. time of transmission with respect to a beacon time reference; f. time of transmission with respect to a time reference known to said device; g. time between a predefined phase of said time reference known to said device and time of transmission; h. maximum operating range; i. maximum length of baseline.sub.12.

3. The method according to claim 1, at said device, estimating the direction from said second location to said beacon, relatively to the direction from said first location to said second location, as an angle of: arccos [c*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12]; wherein c is the speed of light.

4. The method according to claim 1, at said device, for moving towards the beacon, at said first location, determining the direction to a second location such that [baseline.sub.12c*(TDOA.sub.12TDOT.sub.12)] is zero.

5. The method according to claim 1, at said device, further comprising the steps of: a. providing information enabling determining a time difference TDOT.sub.34 between transmission of a third signal and a forth signal, of said periodic signals; b. at a third location, determining location coordinates, and a receiving time instant of said third signal; c. at a forth location, determining location coordinates, and a receiving time instant of said forth signal; d. determining a time difference TDOA.sub.34 between said receiving time instant of said third signal and said receiving time instant of said forth signal, and determining a distance baseline.sub.34 between said third location and said forth location; e. determining the location of said radio beacon, from said TDOT.sub.12, TDOA.sub.12, baseline.sub.12, TDOT.sub.34, TDOA.sub.34 and baseline.sub.34.

6. The method according to claim 1, wherein the period of said periodic signals is an integer number multiplied by T, wherein T is greater than at least one of: a. the maximum operating range divided by the speed of light; b. the maximum length of baseline.sub.12 divided by the speed of light.

7. The method according to claim 1, wherein said transmission time instants and receiving time instants are determined with respect to a same time reference.

8. The method according to claim 7, further comprising the steps of: a. at said beacon, determining the transmission time of said first signal and second signal with respect to a predefined phase of said same time reference; b. at said device, determining the location of said radio beacon from: said coordinates at said first and second locations, and the receiving time instant of said first and second signal, and said predefined phase of said same time reference.

9. A portable device for tracking a radio beacon, said device comprising: a first receiver, a GNSS receiver, a computer and an indicator; said device configured with at least two operating modes: acquisition and tracking; in acquisition mode, said device configured to determine initial geolocation coordinates of said beacon, and in tracking mode said device configured to determine a direction to said beacon while moving substantially in said direction; said device configured to detect signals periodically transmitted by said radio beacon and to accurately measure time of reception of said signals, and provided with information enabling determining at least a time difference TDOT.sub.12 between transmission of a first signal and transmission of a second signal, of said periodic signals; and determine, at a first location, location coordinates, and a receiving time of said first signal; and determine, at a second location, location coordinates, and a receiving time of said second signal; and determine a time difference TDOA.sub.12 between said receiving time of said first and said second signal, and determine a distance baseline.sub.12 between said first location and said second location; and determine a direction to said radio beacon, based on said TDOT.sub.12, TDOA.sub.12 and baseline.sub.12; and indicate said direction to a user.

10. The device according to claim 9, wherein said information is associated with at least one of: a. data configured in advance at said beacon and at said device; b. data communicated from said beacon to said device; c. data specifying TDOT.sub.12; d. minimum time difference (T) between permitted values of TDOT.sub.12; e. time of transmission with respect to the beacon time reference; f. time of transmission with respect to a time reference known to said device; g. time between a predefined phase of said time reference known to said device and time of transmission; h. maximum operating range; i. maximum length of baseline.sub.12.

11. The device according to claim 9, further configured to estimate the direction from said second location to said beacon, relatively to the direction from said first location to said second location, as an angle of: arccos [c*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12]; wherein c is speed of light.

12. The device according to claim 9, further configured, in tracking mode, for a given first location, to determine the direction to a second location such that [baseline.sub.12c*(TDOA.sub.12TDOT.sub.12)] is zero.

13. The device according to claim 9, further in acquisition mode, provided with information enabling determining a time difference TDOT.sub.34 between transmission of a third signal and a forth signal, of said periodic signals; and configured to determine, at a third location, location coordinates, and receiving time of said third signal; and to determine at a forth location, location coordinates, and receiving time of said forth signal; and determine a time difference TDOA.sub.34 between said receiving time of said third signal and forth signal, and a distance baseline.sub.34 between said third location and said forth location; and determine a location of said radio beacon, from said TDOT.sub.12, TDOA.sub.12, baseline.sub.12, TDOT.sub.34, TDOA.sub.34 and baseline.sub.34.

14. The device according to claim 9, wherein the period of said periodic signals is an integer number times T, wherein T is greater than at least one of: a. a maximum operating range divided by the speed of light; b. the maximum length of baseline.sub.12 divided by the speed of light.

15. The device according to claim 9, wherein said transmission time instants and receiving time instants are determined with respect to a same time reference.

16. The device according to claim 15, wherein said transmission time of said first signal and second signal are determined with respect to a predefined phase of said same time reference, and said device configured to determine a location of said radio beacon, from coordinates at said first and second locations, and the receiving time instant of said first and second signal, and said predefined phase of said same time reference.

17. A radio beacon comprising an accurate clock generator, a data processor and a carrier frequency generator, enabling tracking by a moving device, the beacon configured to transmit periodic signals at timing controlled by said clock generator, wherein a time difference between transmissions of at least two of said signals configured substantially equal to m times T, and wherein m is an integer number, and T is greater than at least one of: a. a maximum specified range between said beacon and said device, divided by the speed of light; b. a maximum distance between locations where said two signals are detected, divided by the speed of light; enabling said device determining a direction to said beacon from said m and T, and from time measured between detecting said two signals, each signal detected at a different location, and from distance measured between said different locations.

18. The radio beacon according to claim 17, said signals modulated according to a direct sequence spread spectrum (DSSS) scheme.

19. The radio beacon according to claim 17, further comprising a GNSS receiver, and configured to determine the transmission time of said two signals with respect to a predefined phase of a clock synchronized with said GNSS clock.

20. The radio beacon according to claim 19, wherein the time period of said clock synchronized with said GNSS clock is not shorter than a maximum specified range between said beacon and said device, divided by the speed of light.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above and other characteristics and advantages of the invention will be better understood through the following illustrative and non-limitative detailed description of preferred embodiments thereof, with reference to the appended drawings, wherein:

(2) FIG. 1 illustrates a GPS Trilateration based on TOA. Three Space Vehicles (satellites) marked SV1, SV2 and SV3 are shown, from each a TOA is measured at a receiver by the earth. In reality each [SV+related TOA] define a sphere, however for simplicity the picture depicts a circle, wherein these circles are shown to intersect at a unique point, at which the receiver is placed. Down in the picture, the three navigation equations that describe this trilateration method are presented (wherein C represents the speed of light):
[(x-x.sub.1).sup.2+(y-y.sub.1).sup.2+(z-z.sub.1).sup.2]=CTOA.sub.1
[(x-x.sub.2).sup.2+(y-y.sub.2).sup.2+(z-z.sub.2).sup.2]=CTOA.sub.2
[(x-x.sub.3).sup.2+(y-y.sub.3).sup.2+(z-z.sub.3).sup.2]=CTOA.sub.3

(3) FIG. 2 illustrates the concept of 2 D Hyperbolic Navigation based on TDOA. Two reference transmitters are depicted by a beacon tower icon, respectively placed at (x.sub.1, y.sub.1) and (x.sub.2, y.sub.2), and a receiver in form of a triangle, at point (x, y). The time difference of arrival of signals from those transmitters to the receiver is marked as TDOA.sub.12. The distance between the receiver and the transmitters is [(x-x.sub.1).sup.2+(y-y.sub.1).sup.2] and [(x-x.sub.2).sup.2+(y-y.sub.2).sup.2], respectively, so the receiver is placed on a hyperbola, illustrated and defined by the equation presented at the bottom of the picture:
[(x-x.sub.1).sup.2+(y-y.sub.1).sup.2][(x-x.sub.2).sup.2+(y-y.sub.2).sup.2]=c*TDOA.sub.12.

(4) FIG. 3 illustrates the concept of 3D Hyperbolic Navigation based on TDOA. Two reference transmitters are depicted, placed at (x.sub.1, y.sub.1, z.sub.1) and (x.sub.2, y.sub.2, z.sub.3) respectively, and a receiver in form of a triangle at point (x, y, z), to measure the time difference of arrival of signals from those transmitters, marked as TDOA.sub.12. The distance from the receiver to transmitters 1 is [(x-x.sub.1).sup.2+(y-y.sub.1).sup.2+(z-z.sub.1).sup.2] and to transmitter 2 is [(x-x.sub.2).sup.2+(y-y.sub.2).sup.2+(z-z.sub.2).sup.2], so the receiver is placed on a hyperboloid, illustrated and defined by the equation: [(x-x.sub.1).sup.2+(y-y.sub.1).sup.2+(z-z.sub.1).sup.2][(x-x.sub.2).sup.2+(y-y.sub.2).sup.2+(z-z.sub.2).sup.2]=c*TDOA.sub.12 presented at the bottom of the picture.

(5) FIG. 4 presents a Moving Receiver Measuring TDOA of Signals Transmitted by Radio Beacon. A helicopter is depicted, assumed to have a tracking receiver onboard, and flying on a line passing at points R1, R2, and R3. At these points, it is assumed that TDOA measurements are made, in relation to consecutive signals 1, 2 and 3 transmitted from a beacon depicted by a triangle at point T(x, y), at time intervals: TDOT.sub.12=time difference of transmission between signals 1 and 2; and TDOT.sub.23=time difference of transmission between signals 2 and 3. Two hyperbolas are depicted according to these TDOA readings, respectively relating to baseline.sub.12 and baseline.sub.23, wherein the beacon at point T(x, y) is depicted on the intersection of these hyperbolas. At the bottom of the picture, the equations that define these hyperbolas are presented (wherein c represents the speed of light):
[(x-x.sub.1).sup.2+(y-y.sub.1).sup.2][(x-x.sub.2).sup.2+(y-y.sub.2).sup.2]=c*(TDOA.sub.12TDOT.sub.12);
[(x-x.sub.2).sup.2+(y-y.sub.2).sup.2][(x-x.sub.3).sup.2+(y-y.sub.3).sup.2]=c*(TDOA.sub.23TDOT.sub.23).

(6) Further are depicted sides and angles in triangle TR.sub.2R.sub.3: TR.sub.2=c; R.sub.2R.sub.3=d=d1+d2; TR.sub.3=e; .sub.2=angle(TR.sub.2R.sub.3); 180.sub.3=angle(TR.sub.3R.sub.2).

(7) FIG. 5 presents Low GDOP Hyperbolic Navigation with Moving Receiver. A helicopter is depicted, assumed to have a tracking receiver onboard, and flying on a line marked as X-axis, passing at points R.sub.1 and R.sub.2, then flying on another line marked as X-axis, passing at points R.sub.3 and R.sub.4. A beacon to be tracked is depicted by a triangle at point T(x, y), assumedly transmitting signals 1 and 2 at a time difference of TDOT.sub.12, and also transmitting signals 3 and 4 at a time difference of TDOT.sub.34. It is also assumed that TDOA measurements are made at points R.sub.1, R.sub.2, R.sub.3 and R.sub.4, related to baseline R.sub.1R.sub.2 formed by points R.sub.1 and R.sub.2, and to baseline R.sub.3R.sub.4 formed by points R.sub.3 and R.sub.4. The Y-axis and Y-axis are respectively perpendicular to the X-axis and X-axis, wherein the origin of the XY frame is on baseline R.sub.1R.sub.2 and the origin of the XY frame is on baseline R.sub.3R.sub.4. Two hyperbolas (each having two branches symmetrically mirrored over the Y and Y axis) are depicted, respectively related to the TDOA.sub.12 and TDOA.sub.34 measurements, and as expected, T(x, y) is shown at the intersection of said two hyperbolas. At the bottom of the picture, the equations that define these hyperbolas are presented (wherein c represents the speed of light):
x.sup.2/0.5*c*(TDOA.sub.12TDOT.sub.12).sup.2y.sup.2/[(0.5*R.sub.1R.sub.2).sup.2(0.5*c*(TDOA.sub.12TDOT.sub.12).sup.2]=1
x.sup.2/0.5*c*(TDOA.sub.34TDOT.sub.34).sup.2y.sup.2/[(0.5*R.sub.3R.sub.4).sup.2(0.5*c*(TDOA.sub.34TDOT.sub.34).sup.2]=1

(8) FIG. 6 shows Determining Direction to a Radio Beacon from a Moving Receiver. A helicopter is depicted, assumed to have a tracking receiver onboard, and flying on a line passing at points R.sub.1 and R.sub.2, at point R.sub.2 changing course by an angle of .sub.2, then moving on a line passing at point R.sub.3, in the direction of a beacon placed at point T(x, y). The beacon, depicted by a triangle, assumedly transmitting signal 1 and signal 2 at a transmission time difference of TDOT.sub.12, said signals detected at points R.sub.1 and R.sub.2 respectively at a time difference of TDOA.sub.12. At the bottom of the picture, an equation estimating the angle .sub.2 by which the helicopter should turn at point R.sub.2 in order to fly towards the beacon at T(x, y) is presented (C is the speed of light; R.sub.1R.sub.2 is the distance between R.sub.1 and R.sub.2):
cos(.sub.2)(ac)/b=C*(TDOA.sub.12TDOT.sub.12)/R.sub.1R.sub.2

(9) Also, in triangle TR.sub.1R.sub.2, side TR.sub.1 is marked a, side R.sub.1R.sub.2 is marked b, and side TR.sub.2 is marked c.

(10) FIG. 7 shows Receiver Directed to Radio Beacon based on TDOA Measurements. A helicopter is depicted, assumed to have a tracking receiver onboard, and flying on a line passing at points R.sub.1 and R.sub.2, substantially at the direction of a beacon depicted by a triangle at point T(x, y). The beacon is assumed to transmit signal 1 and signal 2 at a transmission time difference of TDOT.sub.12, those signals detected at points R.sub.1 and R.sub.2 respectively at a time difference of TDOA.sub.12. At the bottom of the picture, shown is an equation estimating the criterion indicating that the helicopter is substantially in a direction towards the beacon (wherein c represents the speed of light and R.sub.1R.sub.2 is the distance between R.sub.1 and R.sub.2):
[R.sub.1R.sub.2c*(TDOA.sub.12TDOT.sub.12)]0

(11) FIG. 8 presents a Block Diagram of Device for Beacon Tracking According to a Preferred Embodiment. The picture shows a computer coupled to: a first receiver, a GPS receiver and an indicator, and further having an I/O interface to the external world. A PLL (Phase Locked Loop) block is also shown, fed from a TCXO (Temperature Compensated Crystal Oscillator), and controlled by a time signal provided by the GPS receiver. The PLL output is shown to be routed to the computer and to the first receiver. Each of the first receiver and GPS receiver is depicted with an antenna on top. The schematic I/O block represents any kind of wired or wireless interface, such as standard USB, Bluetooth or customized I/O.

(12) FIG. 9 illustrates a Flow Chart of Beacon Tracking Process, depicting the following events/steps at the receiver (unless indicated otherwise):

(13) Define min ();

(14) Acquire initial radio beacon coordinates; determine initial distance; determine initial direction;

(15) Move in the initial direction to the Radio Beacon, and indicate .sub.0;

(16) Set i=1;

(17) Input from the beacon: Radio Beacon Transmission i;

(18) In reaction, at the receiver: Define point R.sub.i and Measure receiving time & self position.

(19) [Loop]Input from the beacon: Radio Beacon Transmission i+1;

(20) In reaction, at the receiver: Define point R.sub.i+1 and Measure receiving time & self position.

(21) Determine cos .sub.(i+1)=C*(TDOA.sub.i(i+1)TDOT.sub.i(i+1))]/R.sub.iR.sub.(i+1); Indicate .sub.(i+1)

(22) Check: Is |.sub.(i+1)|<min()?

(23) If the answer is Yes, then indicate: Keep Current Course;

(24) If the answer is No, then indicate: Change Course by .sub.(i+1);

(25) End if initial distance made good; otherwise update: i=i+1 and go to [Loop].

(26) FIG. 10 shows Transmission and Receiving Timing of periodic signals transmitted by the beacon and detected by the receiving device. The diagram at the upper part of the picture shows the transmitted signals vs. the transmitter time (clock). Shown are a first signal and a second signal, and the time (TDOT.sub.12) between the transmission thereof, as measured by the transmitter clock. A later third signal is also shown.

(27) The diagram at the bottom part of the picture shows the transmitted signals as detected at the moving receiving device, and time tagged according to the receiving clock. A helicopter is depicted under the time axis, indicating that the receiving device is moving from left to right. The first signal is shown to be detected at a first location, and the second signal is shown to be detected at a second location, as well as the time (TDOA.sub.12) between detection thereof, as measured at the receiver. Also shown is the third signal as detected at a third location. For the 2.sup.nd signal, the difference between transmission time according to the transmission clock and receiving time according to the receiving clock is indicated as (pseudo-range)/c, wherein c means speed of light.

(28) FIG. 11 shows Transmission and Detection Synchronized with GPS Clock. The diagram at the upper part of the picture shows the transmitted signal vs. the transmitter time (clock) and the diagram at the bottom part of the picture shows the transmitted signal as detected at the moving receiving device, according to the receiving clock. On both diagrams, 1 PPS and 1000 PPS pulses synchronized with the GPS clock are depicted, obviously aligned in time. The Transmitted signal is shown exactly aligned with a 1000 PPS pulse, and at the lower diagram, the time between the receiving time of the signal and the nearest past 1000 PPS pulse is indicated as range/c, wherein c means the speed of light.

(29) FIG. 12 illustrates the Beacon Block Diagram According to a first embodiment of the present invention. From left side, a master clock block is depicted, based on a TCXO (Temperature Compensated Crystal Oscillator) generating a basic frequency of 12.68875 MHz. This master clock is employed, via multiplication (PLL) and/or division, to generate other clock waves at the beacon, synchronized with each other: the carrier frequency at 406.04 MHz (upper branch), the PRN code at 80.31 KHz (center branch), and the Data (beacon message) clock at 400 Hz (lower branch). In particular it is important according to the present invention to control the Time Difference between Transmissions [TDOT], which is illustrated by the SYNC block coupled to the PRN Code Generator. The beacon message is provided by the Data block, coupled to the Data Processing Message block which clocks out the message bits. The serial bits output from the Data processing Message block and the serial chips output from the PRN Code Generator are coupled to inputs of a circular depicted block with an internal plus sign illustrating an exclusive-or (XOR) function employed on the data and PRN code. Finally, a PSK Modulator block illustrates the modulation of said XOR product on the UHF carrier, resulting with a signal to be transmitted, via the antenna shown at the upper-right side of the picture.

(30) FIG. 13 illustrates the Beacon Block Diagram According to a second embodiment of the present invention. This figure comprises all the building blocks depicted in FIG. 12 (the first embodiment), and in addition: a GPS receiver+antenna is depicted by the upper-left corner, from which a 1 Hz, i.e. 1 PPS signal is output, coupled to a PLL block generating a 1 KHz (1000 PPS) clock. That 1 KHz clock is routed to the SYNC block that controls the phase of the PRN sequence, consequently controlling the time of transmission and TDOT.

DETAILED DESCRIPTION

(31) The above examples and description have of course been provided only for the purpose of illustration, and are not intended to limit the invention in any way. As will be appreciated by the skilled person, the invention can be carried out in a great variety of ways, employing more than one technique from those described above, all without exceeding the scope of the invention.

(32) The present invention discloses a method for tracking a radio beacon from a moving device, comprising the steps of: a. at said radio beacon transmitting periodic signals; b. providing said device with information enabling determining at least the time difference (TDOT.sub.12) between transmission time of a first signal and transmission time of a second signal, said first and second signals been part of said periodic signals; c. at said device, at a first location, determining the location coordinates, and a receiving time of said first signal; d. at said device, at a second location, determining the location coordinates, and a receiving time of said second signal; e. at said device, determining the time difference (TDOA.sub.12) between the receiving time of said first signal and the receiving time of said second signal, and the distance (baseline.sub.12) between said first and second locations; f. at said device, determining a direction to said radio beacon, from said TDOT.sub.12, TDOA.sub.12 and baseline.sub.12.

(33) FIG. 10 shows two time diagrams illustrating the periodic signals transmitted by the beacon and detected by the receiving device, according to a first embodiment of the present invention. The upper diagram shows three signals transmitted by the beacon, part of more signals that are not shown, related to a time scale defined by the beacon clock. The lower diagram shows the transmitted signals as detected at the moving receiving device, related to a time scale defined by the receiving clock. A helicopter depicted under the receiving time axis illustrates that the receiving device (assuming carried onboard) is moving, and indicating that each signal is detected at a different location. Preferably, the beacon is assumed to be substantially stationary during the transmission of these signals. FIG. 10 also indicates the time (TDOT.sub.12) between the transmission of a first signal and a second signal, as measured by the transmitter clock, and the time (TDOA.sub.12) between detection of these first and second signals as measured at the receiver. At the lower diagram, the difference between transmission time according to the transmission clock and the receiving time according to the receiving clock is indicated as (pseudo-range/c), wherein c means speed of light.

(34) FIG. 4 illustrates the scenario of FIG. 10, but from a spatial (2D) view. The beacon is depicted as a triangle at point T(x, y) and the Moving Receiver is shown as a helicopter flying from right to left on a line passing at points R.sub.1, R.sub.2, and R.sub.3. At points R.sub.1 and R.sub.2, two transmitted signals are detected (the first signal or signal 1 detected at R.sub.1, and the second signal or signal 2 detected at R.sub.2) and the difference in time of arrival (TDOA.sub.12) of these signals is determined, as well as determination of the distance (baseline.sub.12) between R.sub.1 and R.sub.2. Then, at point R.sub.3 signal 3 (or the third signal) is detected, and the difference in time of arrival (TDOA.sub.23) between signal 2 and signal 3 is determined, as well as the distance (baseline.sub.23) between R.sub.2 and R.sub.3.

(35) Then, assuming that TDOT.sub.12 and TDOT.sub.23 can be determined at the receiver, the location of the beacon can be determined at the intersection of two hyperbolas, according to the two equations depicted at the bottom of FIG. 4. Another method to determine the beacon location T(x, y) based on triangle TR.sub.2R.sub.3 will be disclosed later.

(36) The present invention also discloses a portable device for tracking a radio beacon, said device comprising: a first receiver, a GNSS receiver, a computer and an indicator; said device configured with at least two operating modes: acquisition and tracking; in acquisition mode, said device configured to determine initial geolocation coordinates of said beacon, and in tracking mode said device configured to determine a direction to said beacon while moving substantially on said direction; said device configured to detect signals periodically transmitted by said radio beacon and to accurately measure time of reception of said signals, and provided with information enabling determining at least the time difference (TDOT.sub.12) between transmission of a first signal and of a second signal, of said periodic signals; and determine, at a first location, the location coordinates, and a receiving time of said first signal; and determine, at a second location, the location coordinates, and a receiving time of said second signal; and determine the time difference (TDOA.sub.12) between said receiving time of said first and second signal, and determine the distance (baseline.sub.12) between said first location and said second location; and determine a direction to said radio beacon, based on said TDOT.sub.12, TDOA.sub.12 and baseline.sub.12; and indicate said direction to a user.

(37) FIG. 8 presents a Block Diagram of a receiving Device for Beacon Tracking according to a preferred embodiment of the invention. The picture shows a computer coupled to: a first receiver, a GPS receiver and an indicator, and in addition an I/O interface to the external world. This first receiver is capable of detecting DSSS signals and capable of accurately determining the receiving time instant of this signals. The receiving device also comprises, as shown in FIG. 8, a PLL (Phase Locked Loop), fed by a TCXO (Temperature Compensated Crystal Oscillator), e.g. at 20 MHz, and controlled by a timing signal provided by the GPS receiver. This timing signal is preferably the 1 PPS clock commonly provided by GPS receivers; the output of the PLL is preferably a 1 KHz clock phased locked to the GPS 1 PPS, and this PLL output is routed to the first receiver and to the computer, the latter also configured to read the GPS TOD via the bus coupling between those blocks.

(38) The indicator is preferably a display, capable of showing, among other functions and data, the direction to the beacon in degrees or graphically on a background of a compass dial, with respect to the magnetic or geographical north. Nevertheless, though preferably the indicator is configured to serve a human user, it is also possible that the computer output will interface a machine, in addition or instead of interfacing a human user.

(39) According to a first embodiment of the invention, the radio beacon is configured to broadcast signals every 502.5 seconds, so 47.5 s<TDOT.sub.12<52.5 s; however the actual time of transmission, and the time [TDOT] between successive transmissions is not required to be determined in advance, and can even be pseudo-randomly distributed. Preferably, the basic clock used at the beacon to determine the transmission time, and therefore the TDOT, obtains a resolution not worse than 0.1 s (10 MHz), for example 20 MHz, the latter equivalent to 15 m in pseudo-range.

(40) Preferably, the transmitted signal is modulated according to a predefine DSSS scheme, enabling to accurately determine the receiving time instant. The chip rate of the spreading sequence in this DSSS scheme is preferably 100 Kc/s, which may provide a receiving time determination resolution of approximately 1%* 1/100 Kc/s=0.1 s, i.e. 30 m in pseudo-range.

(41) According to the first embodiment of the invention, the beacon clock is independent, yet according to the second embodiment of the invention, the beacon clock is synchronized to the GPS clock, as will be elaborated later.

(42) Providing the detecting device with information enabling determining TDOT.sub.12 may be done in several ways, as already discussed, wherein the information is associated with: a. data configured in advance at said beacon and at said device; b. data communicated from said beacon to said device; c. data specifying TDOT.sub.12; d. minimum time difference (T) between permitted values of TDOT.sub.12; e. time of transmission with respect to the beacon time reference; f. time of transmission with respect to a time reference known to said device; g. time between a predefined phase of said time reference known to said device and time of transmission; h. maximum operating range; i. maximum length of baseline.sub.12.

(43) According to the first embodiment of the present invention, TDOT.sub.12 is not specifically determined in advanced; neither it is explicitly communicated to the detecting device. Rather, it is agreed in advanced that a minimum difference (T) between permitted values of TDOT.sub.12 will be employed, i.e. the time between any two consecutive signal transmissions is configured in T=1 ms steps (practically, a tolerance of 0.1 s is expected, due to the clock resolution and other factors). Specifically, permitted TDOTs are set to: 50 s1 ms*n, where n=0, 1, 2, . . . , 2500. So TDOT is an integer number of T's, wherein T is greater than at least one of: a. the maximum operating range divided by the speed of light; b. the maximum length of baseline.sub.12 divided by the speed of light.

(44) So according to the first embodiment of the invention, either: [max operating range]<1 ms*c=300 Km; or baseline.sub.12<300 Km. Practically, even baseline.sub.12<30 Km can be easily assumed accounting for maximum TDOT of 52.5 s and speed limit of detecting device of 2,000 Km/h, since at this speed and during this time interval the detecting device makes (2000/3600)Km/s*52.5 s=29.2 Km. Quantizing TDOT this way, T=1 ms enables determining TDOT.sub.12 at the receiving device, just by identifying the permitted TDOT nearest to the measured TDOA.sub.12. Then, by subtracting [TDOA.sub.12TDOT.sub.12], the detecting device normalizes the TDOA measured by a single receiver at two locations referring to two different signals, to a TDOA that theoretically would have been measured simultaneously by two receivers at said two locations referring to a single signal.

(45) Now some mathematical aspects of the invention will be elaborated, considering FIG. 6.

(46) FIG. 6 illustrates Determining Direction to a Radio Beacon from a Moving Receiver. A helicopter is depicted, assumedly with a tracking receiver onboard, flying on a line passing at a first location R.sub.1 and a second location R.sub.2, then at R.sub.2 changing its flight course by an angle of .sub.2, and further moving on a line passing at point R.sub.3, in the direction of a beacon placed at point T(x, y). The beacon, depicted by a triangle, assumedly transmitting a first signal detected at R.sub.1 and a second signal detected at R.sub.2, from which the detecting device determines TDOA.sub.12, and also TDOT.sub.12, assuming TDOT=T*n, wherein n is integer and T=1 ms. The detecting device is configured with a GPS receiver and determines the coordinates at R.sub.1 and R.sub.2, then able to determine the distance between R.sub.1 and R.sub.2, defined as baseline.sub.12. At the bottom of the picture, an equation estimating the angle .sub.2 by which the helicopter should turn at point R.sub.2 in order to fly towards the beacon at T(x, y) is presented (R.sub.1R.sub.2 is the distance between R.sub.1 and R.sub.2, sometimes marked as baseline.sub.12 in this document): cos(.sub.2)(ac)/b=C*(TDOA.sub.12TDOT.sub.12)/R.sub.1R.sub.2; C representing the speed of light. Still, as skilled persons understand, the angle of .sub.2 also complies with that equation, since cos(.sub.2)=cos(.sub.2), so there is an ambiguity in the solution of the direction based on TDOA measurements. That alternative solution for the position of the beacon based on .sub.2, which may be marked as T(x, y), is mirrored over to the X-axis with respect to T(x, y), and not shown in the picture. However, as skilled persons appreciate, this ambiguity can be removed in several ways, e.g. with TOA measurements, further TDOA measurements (on different baselines), dead reckoning or other inputs.

(47) Triangle TR.sub.1R.sub.2 will be now observed, using the designation: TR.sub.1=a; R.sub.1R.sub.2=b=baseline.sub.12; TR.sub.2=c; and also replacing: (TR.sub.1TR.sub.2)=(ac)=C*[TDOA.sub.12TDOT.sub.12]; wherein C=speed of light. It should be noted that in this part of the document, the speed of light is marked by a capital C, to distinguish it from the triangle side c=TR.sub.2.

(48) First, the equation (ac)=C*[TDOA.sub.12TDOT.sub.12] will be proved.

(49) Assuming a time difference of (positive or negative or zero) between the transmitter clock and the receiver clock, then:
a=range between T and R.sub.1=C*[rx.sub.1(tx.sub.1+)];
c=range between T and R.sub.2=C*[rx.sub.2(tx.sub.2+)];
wherein:

(50) rx.sub.1 is the receiving time of signal 1 according to the receiver clock and tx.sub.1 is the transmission time of signal 1 according to the transmitter clock;

(51) rx.sub.2 is the receiving time of signal 2 according to the receiver clock and tx.sub.2 is the transmission time of signal 2 according to the transmitter clock;
then: (ac)=C*[(rx.sub.1rx.sub.2)(tx.sub.1tx.sub.2)]=C*[TDOA.sub.12TDOT.sub.12].

(52) Next, according to the law of cosines in triangle TR.sub.1R.sub.2:
a.sup.2=c.sup.2+b.sup.22*c*b*cos(180.sub.2); then:
a.sup.2=c.sup.2+b.sup.2+2*c*b*cos(.sub.2);
cos(.sub.2)=(a.sup.2c.sup.2b.sup.2)/2bc=[(acb)*(a+c+b)+2bc]/2bc=[(ac)b]*(a+c+b)/2bc+1; so:
cos(.sub.2)=1[b(ac)]*(a+c+b)/2bc.(3)

(53) According to the triangle inequality, (a+c+b)>2*max(a, b, c), and [b(ac)]>0, so:
[b(ac)]*(a+c+b)/2bc>[b(ac)]*2c/2bc=1(ac)/b;
(ac)/b>1[b(ac)]*(a+c+b)/2bc; so:
cos(.sub.2)<(ac)/b, or:
cos(.sub.2)<C*(TDOA.sub.12TDOT.sub.12)]/baseline.sub.12;(4) and if .sub.2<180, then:
.sub.2>arccos {[C*(TDOA.sub.12TDOT.sub.12)]/baseline.sub.12}.

(54) Looking again at the general equation (3), some special cases will be now analyzed.

(55) If the detecting device is far away from the beacon, compared to the length of baseline.sub.12, i.e. b<<a, then due to the triangle inequality also b<<c, and ac, so in this case:
cos(.sub.2)=1[b(ac)]*(a+c+b)/2bc1[b(ac)]*2c/2bc=1[b(ac)]/b=(ac)/b, so:
if b<<a,then: cos(.sub.2)C*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12=(ac)/b;so:(5)
.sub.2arccos [C*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12]

(56) In order to examine the scope of the estimation expressed in equation (5), the difference [ cos( cos(.sub.2)] between the accurate cos(.sub.2) according to equation (3) and the estimated cos(.sub.2) according to equation (5) will be studied:
cos(.sub.2)=(a.sup.2c.sup.2b.sup.2)/2bc(ac)/b=(a.sup.2c.sup.2b.sup.22ca+2c.sup.2)/2bc=[(a.sup.2+c.sup.22ca)b.sup.2]/2bc, or:
cos(.sub.2)=[(ac).sup.2b.sup.2]/2bc.(6)

(57) Still according to the triangle inequality: b<(ac)<b, so |ac|<b, and [(ac).sup.2b.sup.2]<0. Hence cos(.sub.2) is negative (or zero in the degenerated case of a triangle which is a line, when .sub.2 is 0 or 180), i.e. the real=accurate cos(.sub.2) is smaller than (or equal to) the estimated cos(.sub.2), and (for .sub.2<180) the real=accurate (.sub.2) is larger than (or equal to) the estimated (.sub.2), as taught by equation (4).

(58) Since cos(.sub.2) is not positive, then the maximal error of the estimated equation (5) is reached when | cos(.sub.2)|= cos(.sub.2)=[b.sup.2(ac).sup.2]/2bc is at maximum, i.e. when a=c, then the error is b/2c, and finally: b/2c cos(.sub.2)0.

(59) Some practical examples of the estimation of .sub.2 according to equation (5) will be reviewed below.
if c=10b then:(7)
cos(.sub.2)=[(ac).sup.2b.sup.2]/2bc=[(a10b).sup.2b.sup.2]/20b.sup.2=(a/b).sup.2/20(a/b)+99/20.

(60) Due to the triangle inequality, (c+b)=11b>a>(cb)=9b, i.e. 11>(a/b)>9.

(61) Some computed figures of cos(.sub.2) in this range are:
if a/b=9.0, then: cos(.sub.2)=0;
if a/b=9.2, then: cos(.sub.2)=0.018;
if a/b=9.4, then: cos(.sub.2)=0.032;
if a/b=9.6, then: cos(.sub.2)=0.042;
if a/b=9.8, then: cos(.sub.2)=0.048;
if a/b=10.0, then: cos(.sub.2)=0.05;
if a/b=10.2, then: cos(.sub.2)=0.048;
if a/b=10.4, then: cos(.sub.2)=0.042;
if a/b=10.6, then: cos(.sub.2)=0.032;
if a/b=10.8, then: cos(.sub.2)=0.018;
if a/b=11.0, then: cos(.sub.2)=0.

(62) The above figures show that for c=10b the maximum estimation error | cos(.sub.2)| is at a=c, i.e. when the triangle TR.sub.1R.sub.2 is isosceles, which occurs when the estimated .sub.2 is 90; the minimum estimation error is zero, when a=11b or a=9b, i.e. when b=|ac|, i.e. when the course to the beacon is 0 or 180. As skilled persons appreciate, a small deviation in cos(.sub.2) means also a small deviation in .sub.2.

(63) Further for example, if c=10b and a=10.8b, then:

(64) According to the general equation (3): cos(.sub.2)=10.2*21.8/20=0.782, so .sub.2=38.6;

(65) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0.8, so .sub.2=36.9;

(66) and the difference (.sub.2) between (3) and (5) is: 38.636.9=1.7.

(67) Checking with equation (6): cos(.sub.2)=[(ac).sup.2b.sup.2]/2bc=[(0.8).sup.21]/20=0.018=0.7820.8.
if c=10b the maximum estimation error is at a=10b,then:(8)

(68) According to the general equation (3): cos(.sub.2)=121/20=0.05, so .sub.2=92.9;

(69) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0, so .sub.2=90;

(70) and the difference (.sub.2) between (3) and (5) is: 92.990=2.9.
if c=5b then according to (3): cos(.sub.2)=(a.sup.226b.sup.2)/10b.sup.2=a.sup.2/10b.sup.22.6.(9)

(71) For example, if c=5b and a=5.8b, then:

(72) According to equation (9): cos(.sub.2)=5.8.sup.2/102.6=0.764, so .sub.2=40.2;

(73) [Checking] According to equation (3): cos(.sub.2)=(5.8.sup.25.sup.21.sup.2)/10=0.764, so .sub.2=40.2;

(74) According to equation (5): cos(.sub.2)=(ac)/b=0.8, so .sub.2=36.9;

(75) and the difference (.sub.2) between the real angle (3) and the estimated angle (5) is: 40.236.9=3.3.
if c=5b the maximum estimation error is at a=5b,then:(10)

(76) According to the general equation (3): cos(.sub.2)=111/10=0.1, so .sub.2=95.7;

(77) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0, so .sub.2=90;

(78) and the difference (.sub.2) between (3) and (5) is: 95.790=5.7.
If [b(ac)]=[baseline.sub.12C*(TDOA.sub.12TDOT.sub.12]=0,then: cos(.sub.2)=1 and .sub.2=0(or 180),(11)
indicating that the device is exactly on course towards (or away from) the beacon. Distinguishing between moving towards or away from the beacon can be done, as skilled persons understand, by TOA measurements, or additional TDOA measurements, or dead reckoning or other inputs.

(79) Furthermore, as seen from equation (3), the closer to zero is [baseline.sub.12C*(TDOA.sub.12TDOT.sub.12], closer to 1 is cos(.sub.2), and the smaller is angle .sub.2, indicating a closer course towards the beacon.

(80) Some cases of small .sub.2 at short range between beacon and detecting device will be now considered.
if c=b,a=1.9b,then:(12)

(81) According to the general equation (3): cos(.sub.2)=10.1*3.9/2=0.805, so .sub.2=36.4;

(82) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0.9, so .sub.2=25.8;

(83) and the difference (.sub.2) between (3) and (5) is: 36.425.8=10.6.
if c=b,a=1.95b,then:(13)

(84) According to the general equation (3): cos(.sub.2)=10.05*3.95/2=0.901, so .sub.2=25.7;

(85) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0.95, so .sub.2=18.2;

(86) and the difference (.sub.2) between (3) and (5) is: 25.718.2=7.5.
if c=b,a=1.98b,then:(14)

(87) According to the general equation (3): cos(.sub.2)=10.02*3.98/2=0.960, so .sub.2=16.2;

(88) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0.98, so .sub.2=11.5;

(89) and the difference (.sub.2) between (3) and (5) is: 16.211.5=4.7.
if c=b,a=1.995b,then:(15)

(90) According to the general equation (3): cos(.sub.2)=10.005*3.995/2=0.990, so .sub.2=8.1;

(91) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0.995, so .sub.2=5.7;

(92) and the difference (.sub.2) between (3) and (5) is: 8.15.7=2.4.

(93) Finally the case of large .sub.2 at short range between beacon and detecting device is considered.
if c=b=a,then:(16)

(94) According to the general equation (3): cos(.sub.2)=13/2=0.5, so .sub.2=120;

(95) According to the estimation equation (5): cos(.sub.2)=(ac)/b=0, so .sub.2=90;

(96) and the difference (.sub.2) between (3) and (5) is: 12090=30.

(97) Hence at these conditions the estimation equation (5) is not accurate.

(98) As a conclusion, it can be seen that equation (5) estimates the angle .sub.2 in better than 3 when the beacon is about 10 times baseline.sub.12 away from the detecting device (cases 7, 8 above); and in better than 6 when the beacon is about 5 times baseline.sub.12 away from the detecting device (cases 9, 10 above); when the distance between the beacon and the detecting device is short, such that the distance to the beacon is about 1 baseline.sub.12 from the detecting device, equation (5) provides an estimation for the angle .sub.2 to the beacon accurate to about 5 when the real course is about 15 (case 14 above).

(99) So preferably, the detecting device is configured to employ equation (5), i.e. estimate the direction from said second location to said beacon, relatively to the direction from said first location to said second location, as the angle .sub.2=arccos [c*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12], when the beacon is about 5 times baseline.sub.12 away or more, at any direction, or when the beacon is closer and already moving in the direction of the beacon, about plus or minus 15 degrees.

(100) In tracking mode, for a given first location, the detecting device is configured to determine the direction to a second location such that [baseline.sub.12c*(TDOA.sub.12TDOT.sub.12)] is substantially small. In terms of triangle TR.sub.1R.sub.2, this condition means that [b(ac)] is substantially small, where ultimately the smallest is the case of [b(ac)]=0 (a negative value is not permitted due to the triangle inequality).

(101) From the above cases (12)-(15) it can be seen that as [baseline.sub.12c*(TDOA.sub.12TDOT.sub.12)]=[b(ac)] gets smaller, so is .sub.2 smaller, i.e. the detecting device course is closer to the direction of the beacon, and equation (5) better estimates that direction:

(102) According to (12): at [b(ac)]=0.1b, .sub.2=36.4 and (.sub.2)=10.6;

(103) According to (13): at [b(ac)]=0.05b, .sub.2=25.7 and (.sub.2)=7.5;

(104) According to (14): at [b(ac)]=0.02b, .sub.2=16.2 and (.sub.2)=4.7;

(105) According to (15): at [b(ac)]=0.005b, .sub.2=8.1 and (.sub.2)=2.4.

(106) So the preferred operational tracking strategy would be, upon acquiring the initial beacon coordinates, to move directly towards the beacon, and confirm that direction while still been away from the beacon.

(107) This tracking scenario is illustrated in FIG. 7, showing a Receiver Directed to a Radio Beacon based on TDOA Measurements, according to the first embodiment of the invention. The good old helicopter is depicted, assumed to have a tracking receiver onboard, and flying on a line passing at a first location R.sub.1 and a second location R.sub.2, substantially at the direction of a beacon depicted by a triangle at point T(x, y). The beacon is assumed to transmit a first signal and a second signal at a transmission time difference of TDOT.sub.12, and those signals are respectively detected at points R.sub.1 and R.sub.2, at a time difference of TDOA.sub.12. The disclosed criterion for indicating been on a substantially direct course to the beacon is [R.sub.1R.sub.2c*(TDOA.sub.12TDOT.sub.12)]0, wherein c represents the speed of light and R.sub.1R.sub.2 is the distance between R.sub.1 and R.sub.2, i.e. baseline.sub.12.

(108) Before entering the tracking mode, where the device is configured to determine the direction to the beacon, as discussed above, it preferably enters an acquisition mode, where the device determines the beacon location. This acquisition phase can be merely a process of getting the location coordinates of the beacon from an external source, such as the Cospas-Sarsat system, through the I/O interface shown in FIG. 8, or independently acquiring the beacon location by TDOA measurements.

(109) According to the first embodiment of the invention, the detecting device determines initial coordinates of the beacon by measurements providing two LOPs (referring to 2D navigation), preferably at Geometry obtaining good (low) Dilution of Precision (DOP or GDOP). This process is illustrated in FIG. 5, titled: Low GDOP Hyperbolic Navigation with Moving Receiver. Our helicopter, assumed to have a tracking receiver onboard, is depicted making two sets of TDOA measurements, each set on a different baseline, to provide two independent LOPs. According to a rough estimation of the beacon location, two lines are selected, the depicted x-axis and x-axis, on which baseline.sub.12 and baseline.sub.34 are formed, according to the locations where a first (R.sub.1) and a second (R.sub.2) signal, then a third (R.sub.3) and a forth (R.sub.4) signal, are detected. The beacon to be tracked is depicted by a triangle at point T(x, y), assumedly transmitting signals 1 and 2 at a time difference of TDOT.sub.12, and also transmitting signals 3 and 4 at a time difference of TDOT.sub.34. Preferably, in order to have low GDOP, said X-axis and X-axis are substantially perpendicular with each other, and determined so that a line connecting the estimated position of the beacon with a point approximately in the middle of each baseline, is perpendicular to that baseline. On each baseline TDOA is measured, TDOT is determined, and the baseline length is also determined. As already discussed, each set of said measurements provides a hyperbolic LOP, and at the crossing of these LOPs the beacon position is determined.

(110) The equations that define these hyperbolas are:
x.sup.2/0.5*c*(TDOA.sub.12TDOT.sub.12).sup.2y.sup.2/[(0.5*R.sub.1R.sub.2).sup.2(0.5*c*(TDOA.sub.12TDOT.sub.12).sup.2]=1;(17)
x.sup.2/0.5*c*(TDOA.sub.34TDOT.sub.34).sup.2y.sup.2/[(0.5*R.sub.3R.sub.4).sup.2(0.5*c*(TDOA.sub.34TDOT.sub.34).sup.2]=1;(18)

(111) wherein R.sub.1R.sub.2 is baseline.sub.12 and R.sub.3R.sub.4 is baseline.sub.34.

(112) As a skilled person understands, the use of different X-Y frames for the different baselines in FIG. 5 was made for explanation purposes, however in fact, a common X-Y (or X-Y-Z) frame should be used at both sets of measurements in order to have a common basis to solve the two quadratic equations.

(113) In details, the steps to follow in order to determine a second LOP, in addition to the first LOP, then fix the beacon position, are: a. providing information enabling determining the time difference (TDOT.sub.34) between transmission of a third signal and of a forth signal, part of the periodic signals transmitted by the beacon; b. at a third location, determining the location coordinates, and a receiving time of said third signal; c. at a forth location, determining the location coordinates, and a receiving time of said forth signal; d. determining the time difference (TDOA.sub.34) between said receiving time instant of said third signal and said receiving time instant of said forth signal, and determining the distance (baseline.sub.34) between said third location and said forth location; e. determining the location of said radio beacon, from TDOT.sub.12, TDOA.sub.12, baseline.sub.12, TDOT.sub.34, TDOA.sub.34 and baseline.sub.34.

(114) It is possible, according to the present invention to configure TDOT.sub.12=TDOT.sub.34.

(115) Another method to determine the location of the beacon will be now disclosed, related to FIG. 4.

(116) Looking back at FIG. 4, a skilled person can see that triangle TR.sub.2R.sub.3 can be solved, from one side: R.sub.2R.sub.3=d=(d1+d2)=baseline.sub.23, and two angles: .sub.2=angle(TR.sub.2R.sub.3) and (180.sub.3)=angle(TR.sub.3R.sub.2). baseline.sub.23 can be determined upon determining the coordinates at R.sub.2 and R.sub.3, and the angles .sub.2 and .sub.3 can be estimated from equation (5):
.sub.2arccos [C*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12];
.sub.3arccos [C*(TDOA.sub.23TDOT.sub.23)/baseline.sub.23];

(117) then, looking at triangle TR.sub.2R.sub.3, and assuming that R.sub.1-R.sub.2-R.sub.3 are on the X-axis, it is clear that:

(118) (yy.sub.2)=d2*tan(.sub.2); and (yy.sub.3)=d1*tan(180.sub.3); and since (d1+d2)=d=baseline.sub.23, then:
baseline.sub.23=(y-y.sub.2)/tan(.sub.2)+(y-y.sub.3)/tan(180.sub.3).

(119) From this equation the coordinate y of the beacon can be resolved.

(120) According to the coordinate system depicted in FIG. 4, y.sub.1=y.sub.2=y.sub.3=0, then equation (19) turns to be: baseline.sub.23=y/tan(.sub.2)+y/tan(180.sub.3)=y/tan(.sub.2)y/tan(.sub.3), so: y=baseline.sub.23/(1/tan(.sub.2)1/tan(.sub.3)].

(121) And the coordinate x of the beacon can be also resolved according to:
tan(.sub.2)=y/(x.sub.2-x).(20)

(122) According to the coordinate system depicted in FIG. 4, x.sub.2=0, then equation (20) turns to be: x=y/tan(.sub.2)=baseline.sub.23/[tan(.sub.2)/tan(.sub.3)1]1.

(123) Equations (19) and (20) are not applicable when moving directly to the beacon, i.e. when .sub.2 or .sub.3 are zero, however can be employed when equation (5) indicates that .sub.2 is not zero, in order to estimate the distance to the beacon.

(124) According to a second embodiment of the present invention, the transmission time instants and the receiving time instants are determined with respect to a substantially same time reference. Specifically, both the beacon and detecting device are embedded with a GPS receiver, and synchronize their internal clock to the GPS time, in frequency and in phase. As already discussed, FIG. 8 presents the structure by which the detecting device generates an internal clock phased locked to the GPS 1 PPS signal. This internal clock, at the detecting device, is preferably configured at a frequency of 20 MHz, providing approximately 0.1 s in resolution (due to the clock frequency and other factors) for determining the receiving time at the tracking device. In addition, both the beacon and the detecting device read the GPS TOD, so read the present calendar year, month, day, hour, minute and second, with respect to the GPS time.

(125) For determining the location of the beacon, typically in the acquisition mode, according to this second embodiment of the invention, measurements at two locations (i.e. single baseline) are sufficient, since each of these measurements provides a LOP, so the beacon position can be fixed following the steps of: a. at said beacon, determining the transmission time of said first signal and second signal with respect to a predefined phase of said same time reference; b. at said device, determining the location of said radio beacon, from: said coordinates at said first and second locations, and the receiving time instant of said first and second signal, and said predefined phase of said same time reference.

(126) FIG. 11 shows Transmission and Detection Synchronized with GPS Clock according to the second embodiment of the present invention. The upper diagram showing the transmitted signal vs. the transmitter time (clock) and the lower diagram showing the transmitted signal as detected at the moving receiving device, according to the receiving clock. On both diagrams, 1 PPS (1 Hz) and 1000 PPS (1 KHz) pulses synchronized with the GPS clock are depicted, obviously aligned in time, hence synchronizing the receiving clock with the transmission clock. The Transmitted signal at the upper diagram is exactly aligned with a 1000 PPS pulse, and at the lower diagram, the time between the receiving time of the signal and the nearest past 1000 PPS pulse is indicated as range/c, wherein c means the speed of light.

(127) According to this second embodiment of the invention, the transmission time of all periodic signals transmitted by the beacon are synchronized with the GPS clock, referring to the phase of the rising edge of a 1 KHz clock phased locked to the GPS 1 PPS (1 Hz) clock. The resolution for configuring time intervals between consecutive signal transmissions at the beacon is set to T=1 ms, and permitted TDOTs are: 50 s1 ms*n, where n=0, 1, 2, . . . , 2500.

(128) Then, according to the second embodiment of the invention, as the receiving time is also determined according to the GPS clock, the TOA is determined as the receiving time instant minus the time reading of the nearest past 1 KHz rising edge. If the distance to the beacon is 300 Km or less, then the TOA can be uniquely determined, this way, since the difference between successive 1 KHz pulses is 1 ms, equivalent in range to 300 Km.

(129) Using any of the 1000 PPS pulses as a phase reference for transmission is actually specifying the maximum time between a predefined phase of the time reference known to the device and time of transmission to 1 ms, since the time difference between successive 1000 PPS pulses is 1 ms. Assuming maximum range to beacon of 300 Km, then the maximum propagation time of that signal is 300 Km/c=1 ms, so there is no ambiguity at the detecting device in associating the detected signal with a specific (nearest past) 1000 PPS pulse, at which the signal was transmitted. Thus, every signal transmitted by the beacon and detected at the receiving device provides a TOA, i.e. exact range to the beacon, i.e. a circular (2D) LOP. As skilled persons appreciate, TOA based navigation requires less measurements than TDOA based navigation in order to fix a location or determine a direction, since each measurement provides more information due to the time synchronization. Obviously, this requires a time synchronizing scheme, and in the context of the second embodiment of the invention that scheme is associated with a GPS receiver at the beacon and at the detecting device. Once the beacon transmission is synchronized with the GPS time, for all beacons, then transmissions of all active beacons are synchronized among themselves, what may have further benefits, such as reducing the transmission collision rate among beacons. The latter is disclosed in U.S. Pat. No. 7,440,427 by D. Katz (the present applicant), for: Increasing Channel Capacity of TDMA Transmitters in Satellite based Networks.

(130) Other aspects of using an external source for clock synchronization in communication systems are disclosed in U.S. Pat. No. 7,522,639 by D. Katz (the present applicant), for: Synchronization among Distributed Wireless Devices Beyond Communications Range.

(131) As persons skilled in the art appreciate, TOA or TDOA methods can be similarly applied when an infrastructure of receivers is configured to locate a transmitter, or when a receiver navigates based on signals transmitted by an infrastructure of transmitters. Equally, this symmetry is valid to a moving receiver configured to locate a transmitter, or receiver configured to locate a moving transmitter, since the movement of a transmitter with respect to a receiver is equivalent to the opposite movement of the receiver with respect to the transmitter, in the scope of the present invention.

(132) Then, according to a third embodiment of the invention, the beacon is moving, and a static detecting device determines the direction to and the location of the beacon. In this case the beacon is installed onboard a plane or space vehicle, transmitting periodic signals at a fixed time period (TDOT), known in advance at the detecting station. The detecting device is based on the block diagram presented in FIG. 8, and the direction finding scenario based on FIG. 6.

(133) Interpreted according to the third embodiment of the invention, FIG. 6 illustrates a helicopter assumed to have a beacon onboard, and flying on a line passing at points R.sub.1 and R.sub.2, wherein at point R.sub.2 the angle .sub.2 between its course and a detecting device at point T(x, y) is to be determined. The beacon onboard the helicopter, assumedly transmitting signal 1 and signal 2 at a transmission time difference of TDOT.sub.12, respectively from points R.sub.1 and R.sub.2, and detected at station T at a time difference of TDOA.sub.12. The equation estimating the angle .sub.2 from station T to the helicopter, relatively to the helicopter course, is presented (valid when TR.sub.1, TR.sub.2>>R.sub.1R.sub.2) in this figure and already developed and marked earlier as equation (5): cos(.sub.2)c*(TDOA.sub.12TDOT.sub.12)/R.sub.1R.sub.2.

(134) Knowing TDOT.sub.12 at station T, measuring TDOA.sub.12, and calculating R.sub.1R.sub.2 based on TDOT.sub.12 and the helicopter speed, .sub.2 can be determined at station T.

(135) The angle .sub.2 can be also determined from the Doppler Effect. As persons skilled in the art appreciate, when a signal is transmitted by the beacon and detected at station T, the Doppler shift is proportional to the speed vector between the transmitter and the receiver, hence: cos(.sub.2)=f/f*c/v, wherein f/f is the frequency shift detected at the receiver divided by the transmission frequency, v is the helicopter velocity and c is the speed of light, so alternatively, if f/f is determined at station T, as well as TDOT.sub.12 and TDOA.sub.12, then cos(.sub.2) and the helicopter velocity (v) can be found by solving the two equations: (5) and the Doppler equation, accounting for R.sub.1R.sub.2=TDOT.sub.12*v.

(136) The present invention further discloses a computer non-transitory readable storage medium storing a program for a mobile device to determine the direction to a radio beacon transmitting periodic signals, the computer program comprising a set of instructions for causing the device to perform the steps of: a. providing information enabling determining at least the time difference (TDOT.sub.12) between a transmission time instant of a first signal and a transmission time instant of a second signal, said first and second signals been part of said periodic signals; b. at a first location, determining the location coordinates, and determining a receiving time instant of said first signal; c. at a second location, determining the location coordinates, and determining a receiving time instant of said second signal; d. determining the time difference (TDOA.sub.12) between the receiving time instant of said first signal and the receiving time instant of said second signal, and the distance (baseline.sub.12) between said first and second locations; e. determining a direction to said radio beacon, from said TDOT.sub.12, TDOA.sub.12 and baseline.sub.12.

(137) FIG. 9 illustrates a Flow Chart of Beacon Tracking Process, for a computer program for a mobile device to determine the direction to a radio beacon transmitting periodic signals, referring to the scenario illustrated in FIG. 6; the computer program comprising a set of instructions for causing the device to perform the steps of:

(138) Define min();

(139) Acquire initial coordinates of radio beacon; determine initial distance and initial direction to beacon.

(140) Move in the initial direction to the Radio Beacon, and indicate .sub.0;

(141) Set i=1;

(142) Upon Radio Beacon Transmission i, define point R.sub.i and Measure receiving time & self position.

(143) [Loop]upon Radio Beacon Transmission i+1, define point R.sub.i+1 and Measure receiving time & self position.

(144) Determine TDOA.sub.i(i+1) and TDOT.sub.i(i+1) and R.sub.iR.sub.(i+1).

(145) Determine cos .sub.(i+1)=C*(TDOA.sub.i(i+1)TDOT.sub.i(i+1)]/R.sub.iR.sub.(i+1); Indicate .sub.(i+1);

(146) Check if |.sub.(i+1)|<min().

(147) If the answer is Yes, then indicate: Keep Current Course;

(148) If the answer is No, then indicate: Change Course by .sub.(i+1);

(149) End if initial distance made good; otherwise update: i=i+1 and go to [Loop].

(150) In order to confirm been close enough to the beacon to end this process, equations (19) and (20) can be employed based on the calculated .sub.1 and .sub.(i+1), provided that these angles are not zero.

(151) The provided information enabling determining TDOT.sub.12 is preferable associated with at least one of: a. data configured in advance at said beacon and at said device; b. data communicated from said beacon to said device; c. data specifying TDOT.sub.12; d. minimum time difference (T) between permitted values of TDOT.sub.12; e. time of transmission with respect to the beacon time reference; f. time of transmission with respect to a time reference known to said device; g. time between a predefined phase of said time reference known to said device and time of transmission; h. maximum operating range; i. maximum length of baseline.sub.12.

(152) Preferably, the computer program causing the device to further:

(153) estimate the direction from said second location to said beacon, relatively to the direction from said first location to said second location, as an angle of:

(154) arccos [c*(TDOA.sub.12TDOT.sub.12)/baseline.sub.12]; wherein c is the speed of light.

(155) Preferably, while tracking the beacon, the computer program causing the device to:

(156) determine the direction from said first location to a second location such that [baseline.sub.12c*(TDOA.sub.12TDOT.sub.12)] is substantially small.

(157) The present invention additionally discloses a radio beacon enabling tracking by a moving device, said beacon configured to transmit periodic signals enabling said device to accurately determine a reception time instant of said signals, wherein the time difference between transmissions of at least two of said signals is configured substantially equal to m times T, wherein m is an integer number, and T is greater than at least one of: a. the maximum specified range between said beacon and said device, divided by the speed of light; b. the maximum distance between locations where said two signals are detected, divided by the speed of light.

(158) FIG. 12 illustrates the Radio Beacon Block Diagram, according to said first embodiment of the invention. The beacon comprises a DSSS transmitter configured to transmit short periodic signals enabling a tracking device to accurately determine the reception time instant of said signals, by autocorrelation to the transmitted PRN sequence. By controlling the phase of the PRN Code Generator, as illustrated by the SYNC block coupled to the PRN Generator, the time difference (TDOT) between successive signals is configured, for example in the range of 47.5 s<TDOT<52.5 s. Though that SYNC function is depicted to control only the PRN Generator, it is also possible to apply it to other beacon clocks, for example by alternatively synchronizing the master clock, adding another PLL between the TCXO and the clock generators fed by it, and locking this additional PLL to the SYNC output. As appreciated by skilled persons, the DSSS transmitter depicted in this figure is well known in the present art, for example used by GNSS transmitters or pseudolites; the parameters selected for this embodiment should be considered as example, while other parameters could be configured, such as the transmission frequency, PRN chip rate and the message bit rate, as well as the master clock frequency. A skilled person also understands that such a beacon typically comprises additional building blocks, such as a micro controller or processor, power (DC and RF) circuitry, a battery and so on, that are not depicted since are well known in the art.

(159) According to this first embodiment of the invention, the time difference (TDOT) between successive signals is configured such that TDOT=m*T, m being an integer number and T=1 ms, wherein T is greater than the maximum distance between locations where two successive signals are detected, divided by the speed of light.

(160) Hence, if the detecting device is moving at a speed [v], then: T>v*m*T/c, i.e. c/v>m; and considering m=2500, then [v] is restricted to: v<c/m120 Km/s432,000 Km/h, which is applicable even to MEO satellites.

(161) The requirement that T>[maximum distance between locations where two successive signals are detected/c], requires: 1 ms>baseline.sub.12/cv*50 s/c, limiting: v<c*1 ms/50 s=c/50,000=6 Km/s, still applicable to MEO satellites, as well as airborne, marine and vehicular mounted detecting devices.

(162) According to the first embodiment of the present invention, this beacon is one of:

(163) a Personal Locator Beacon (PLB), to be carried by an individual; or

(164) an Emergency Position Indicating Radio Beacon (EPIRB), to be installed on a vessel; or

(165) an Emergency Locator Beacon (ELT) to be installed onboard an airplane.

(166) Preferably, the radio beacon further comprises a GNSS receiver, and configured to determine the transmission time of said two signals with respect to a predefined phase of a clock synchronized with said GNSS clock.

(167) According to said second embodiment of the invention, the radio beacon further comprises a GNSS receiver, and configured to determine the transmission time of said two signals with respect to the rising edge of a 1 KHz clock synchronized with said GNSS, as illustrated in FIG. 13 (block diagram) and FIG. 11 (timing diagram). FIG. 13 illustrates the Beacon Block Diagram According to a second embodiment of the present invention. This figure comprises all the building blocks depicted in FIG. 12 (the first embodiment), and in addition: a GPS receiver+antenna is depicted at the upper-left corner, from which a 1 Hz (1 PPS) signal is output, coupled to a PLL block generating a 1 KHz (1000 PPS) clock. That 1 KHz clock is routed to the SYNC block that controls the phase of the PRN sequence, consequently controlling the time of transmission and TDOT.

(168) According to this second embodiment, the time period of the 1 KHz clock, i.e. 1 ms, is not shorter than the maximum specified range between the beacon and the tracking device, divided by the speed of light; so that distance should be smaller than c*1 ms=300 Km. Then, with respect to the 1 KHz clock PLL'ed to the 1 Hz GNSS clock, TOA can be determined at 0-300 Km from the beacon, however a detecting device onboard a MEO satellite will better be employed related to a 10 Hz PLL'ed clock, to avoid ambiguous TOA results; still, in either case, no limitations on TDOA measurements.

(169) According to the second embodiment of the present invention, the GNSS receiver comprised in the beacon is at least one of: GPS receiver, or Galileo receiver, or Glonass receiver.

(170) As skilled persons appreciate, a radio beacon is typically an RF transmitter that broadcasts data not necessarily attended by a human user. However, in the context of the present invention, a radio beacon is any kind of RF transmitter that communicates data, even initiated by a human user, such as a mobile phone or mobile satellite terminal.

(171) According to a forth embodiment of the invention, the beacon is a CDMA mobile phone, synchronized to the GPS time, and configured to transmit upon a user command, but align its applied spreading code with a 1 KHz timing signal, as shown in FIG. 11. Hence, the transmission timing in FIG. 11 refers to a specific predefined phase (e.g. rising edge of a specific chip of the modulating code) of said spreading code. At the detecting device, the receiving time is also determined according to the GPS clock, so the TOA is determined as the receiving time instant referring to said predefined phase, minus the time reading of the nearest past 1 KHz rising edge. If the distance to that mobile phone is 300 Km or less, then the TOA can be uniquely determined at the detecting device.

(172) Furthermore, the presently disclosed method for tracking a radio beacon from a moving device can be also applied to a satellite tracking a beacon, either independently or involving a base station.

(173) According to a fifth embodiment of the invention, a radio beacon transmits periodic signals, compatible to a receiver onboard a satellite. The satellite is orbiting around the center of the earth, and from time to time the beacon signals are detected onboard the satellite, and possibly relayed to a base station, and TDOA.sub.12 and baseline.sub.12 are determined according to the present invention, either onboard the satellite or at said base station. Knowing TDOA.sub.12 and baseline.sub.12 and TDOT.sub.12, in addition to a further measurement providing TDOA.sub.34 and baseline.sub.34 and TDOT.sub.34, enable determining the beacon 2D location by a single satellite. As already indicated, further measurements enable determining the 3D position of the beacon.

(174) According to this fifth embodiment, the detecting device is installed onboard a GPS or Galileo satellite, or alternatively a bent pipe relay is installed onboard the satellite enabling a ground station to track the beacon. Such satellite is typically orbiting at about 26,000 Km from the earth center, at 12 h period, so its linear speed is approximately 2**26,000 Km/12 h13,600 Km/h4 Km/s. Considering a radio beacon that transmits every 50 s, our satellite will detect two such consecutive signals at less than 4 Km/s*50 s=200 Km apart (straight line), i.e. may define baseline.sub.12200 Km according to the present invention, i.e. baseline.sub.12/c0.7 ms<1 ms. Accordingly, if the beacon TDOT is configured at a resolution of 1 ms, then it is possible to determine TDOT.sub.12 at the ground station (assuming that the receiving time is measured at the satellite and reported to the ground station, which in turn determines TDOA.sub.12) as the number in form of 1 ms*n (n=integer) nearest to TDOA.sub.12, and along with the measured baseline.sub.12, the direction to the beacon or one hyperbolic LOP on which the beacon is placed can be determined. Based on these and similar additional measurements, the location of the beacon can be determined, by equations (17) and (18), or equations (19) and (20), or a combination thereof.

(175) According to a sixth embodiment of the present invention, the radio beacon is a Marine Survivor Locating Device (MSLD), comprising an RF transmitter configured to broadcast periodic signals, when active, at a constant TDOT, known in advance at a compatible detecting device; said device comprising a GPS receiver and configured to be installed onboard a vessel.

(176) According to this sixth embodiment of the invention, upon detecting, at two different locations, two consecutive signals transmitted by such active MSLD, the detecting device can determine TDOA.sub.12 and baseline.sub.12, and knowing also TDOA.sub.12, can use equation (5) to determine the direction to the MSLD. Preferably, TDOT is configured short enough to provide small estimation error using equation (5). From case (10) an error in direction of less than 6 is expected when the beacon is 5*baseline.sub.12 away from the detecting device, a distance that can be made when sailing for a time of 5*TDOT.

(177) Further measurements, at another pair of locations, enable the detecting device determining the location of this MSLD, based on equations (17) and (18), or equations (19) and (20), or a combination thereof.

(178) The true scope the present invention is not limited to the presently preferred embodiments disclosed herein. For example, the foregoing disclosure uses explanatory terms, such as GPS, DSSS and CDMA, and particularly radio beacon and the Cospas-Sarsat system, which should not be construed so as to limit the scope of protection of the claims, or to otherwise imply that the inventive aspects of the disclosed methods and devices are limited to the particular methods and apparatus disclosed.

(179) In many cases, the place of implementation described herein is merely a designer's preference and not a hard requirement. For example, functions disclosed as implemented at the detecting device may alternatively be partially implemented at cellular base stations or satellite ground stations, as well as on cellular devices or artificially orbiting satellites. Given the rapidly declining cost of digital signal processing and other processing functions, it is easily possible, for example, to transfer the processing or a particular function from one of the functional elements described herein to another functional element without changing the inventive operation of the system.