Method and a sensor for determining a direction-of-arrival of impingent radiation

Abstract

A sensor for determining a direction-of-arrival of radiation impingent on the sensor which has antennas positioned in a particular set-up different from a rectangle, so that information may be derived between two pairs of the antennas, positioned in corners of a rectangular grid and additional information may be derived from an additional antenna, combined with one of the grid antennas forming a third pair of antennas. The additional antenna is positioned away from the corners and other pre-defined lines of the rectangle/grid. In this manner, such as from phase differences between the pairs of antennas, more information may be derived compared to antennas positioned merely at the corners of a rectangle to remove ambiguous angles of direction-of-arrival without compromising accuracy of an angular determination.

Claims

1. A method of determining a three-dimensional direction-of-arrival of radiation impingent on a sensor having a plurality of receiving antennas each being configured to sense the radiation and output a corresponding signal, the method comprising: positioning the antennas so that: at least three of the antennas are first receiving antennas which define corners of a parallelogram having two first and two second parallel sides, one or more of the receiving antennas is/are a second receiving antenna(s), each second antenna forming a pair of antennas with a first antenna, wherein the second antenna of each pair is positioned, in relation to the first antenna with which it is paired, more than 2% of a smallest distance between two first receiving antennas away from all axes extending through any two of the four corners of the parallelogram, any corner of the parallelogram and a centre point of any of the four sides of the parallelogram, and the centre point of any of the sides of the parallelogram and the centre points of any other side of the parallelogram; and determining the three-dimensional direction-of-arrival from at least: a first phase difference between signals received by a first pair of the first receiving antennas positioned on one of the first parallel sides and a distance between the antennas of the first pair of antennas, a second phase difference between signals received by a second pair of the first receiving antennas positioned on one of the second parallel sides and a distance between the antennas of the second pair of antennas, and a third phase difference between signals received by a third pair of antennas, being a pair of antennas comprising a second receiving antenna and a first antenna, and a distance between the antennas of the third pair of antennas.

2. A method according to claim 1, wherein the impingent radiation is at least substantially periodic.

3. A method according to claim 1, further comprising the step of directing radiation toward a target which subsequently generates the impingent radiation by reflecting at least part of the radiation directed toward the target.

4. A method according to claim 1, wherein the determining step comprises: estimating, for each pair of receiving antennas, one or more candidate angles and subsequently, generating a set of candidate angles, each set of candidate angles comprising a candidate angle from each pair of receiving antennas, for each set of candidate angles, determining a direction and a difference angle between the direction and each candidate angle of the set, determining, for each set of candidate angles, a sum of the difference angles between the direction and each candidate angle of the set, determining a first set of candidate angles having the lowest sum and selecting the direction-of-arrival as the direction of the first set of candidate angles.

5. A method according to claim 1 wherein the positioning step comprises positioning the first antennas with a mutual distance of at least 0.6 times a wavelength of the impingent microwave radiation.

6. A method according to claim 5, wherein the determination step is performed on the basis of signals output simultaneously from the first and second receiving antennas.

7. A method according to claim 1, further comprising the step of directing radiation toward a target which subsequently generates the impingent radiation by reflecting at least part of the radiation directed toward the target.

8. A method according to claim 1, wherein the second receiving antenna is positioned within the parallelogram.

9. A method according to claim 1, wherein the sensor has exactly 5 receiving antennas of which three are first receiving antennas.

10. A method according to claim 1, wherein the sensor has exactly four receiving antennas of which three are first receiving antennas.

11. A method for tracking a trajectory of a target in flight, the target reflecting or emitting radiation, the method comprising: at least once, determining the direction-of-arrival of radiation reflected by or emitted from the target using the method of claim 1; tracking the trajectory using a radar; and correcting the trajectory using the direction-of-arrival determined.

12. A sensor for determining a three-dimensional direction-of-arrival of radiation impingent thereon, the sensor comprising no more than six receiving antennas each being configured to sense the radiation and output a corresponding signal, the antennas being positioned so that: at least three of the antennas are first receiving antennas defining corners of a parallelogram having two first and two second parallel sides, one or more of the receiving antennas is/are second receiving antenna(s), each second antenna forming a pair of antennas with another of the plurality of receiving antennas, where the antennas of each pair are positioned, in relation to each other, in the same relationship as an antenna positioned, in relation to one of the first receiving antennas, more than 2% of a smallest distance between two first receiving antennas away from all axes extending through any two of the four corners of the parallelogram, any or the corners of the parallelogram and a centre point of any of the four sides of the parallelogram, and the centre point of any of the sides of the parallelogram and the centre point of any other side of the parallelogram, and the sensor further comprising a determining element configured to receive the output signals from the first receiving antennas and the second receiving antenna(s) and determine the three-dimensional direction-of-arrival from at least: a first phase difference between signals received by a first pair of the first receiving antennas positioned on one of the first parallel sides and a distance between the antennas of the first pair of antennas, a second phase difference between signals received by a second pair of the first receiving antennas positioned on one of the second parallel sides and a distance between the antennas of the second pair of antennas, and a third phase difference between signals received by a third pair of antennas, being a pair of antennas comprising a second antenna, and a distance between the antennas of the third pair of antennas.

13. A sensor according to claim 12, wherein the impingent radiation is at least substantially periodic.

14. A sensor according to claim 12, further comprising a transmitter for directing radiation toward a target which subsequently may generate the impingent radiation by reflecting at least part of the radiation directed toward the target.

15. A sensor according to claim 12, wherein the determining element is configured to: estimate, for each pair of receiving antennas, one or more candidate angles and subsequently generate a plurality of sets of candidate angles, each set of candidate angles comprising a candidate angle from each pair of receiving antennas, for each set of candidate angles, determine a direction and a difference angle between the direction and each candidate angle of the set, determine, for each set of candidate angles, a sum of the difference angles between the direction and each candidate angle of the set, determine a first set of candidate angles having the lowest sum and select the direction-of-arrival as the direction of the determined first set of candidate angles.

16. A device for tracking a trajectory of a target in flight, the target reflecting or emitting radiation, the device comprising: a sensor according to claim 12, wherein the determining element is adapted to: from the output signals from at least part of the antennas, derive a trajectory of the target, and correct the derived trajectory using the determined direction-of-arrival.

17. A sensor according to claim 12, wherein the first antennas are positioned with a mutual distance of at least 0.6 times a wavelength of the impingent microwave radiation.

18. A sensor according to claim 17, wherein the determining element is configured to perform the determination on the basis of signals output simultaneously by the first and second receiving antennas.

19. A sensor according to claim 12, further comprising a transmitter for directing radiation toward a target from which a portion of this radiation is reflected to the sensor.

20. A sensor according to claim 12, wherein the sensor has exactly five receiving antennas of which three are first receiving antennas.

21. A sensor according to claim 12, wherein the sensor has exactly four receiving antennas of which three are first receiving antennas.

22. A sensor according to claim 12, wherein each pair of antennas includes a first receiving antenna.

Description

(1) In the following, preferred embodiments will be described with reference to the drawing, wherein:

(2) FIG. 1 illustrates a prior art monopulse receiving radar,

(3) FIG. 2 illustrates ambiguity in the radar of FIG. 1

(4) FIG. 3 illustrates a radar according to a first embodiment according to the invention,

(5) FIG. 4 illustrates a radar according to a second embodiment according to the invention, and

(6) FIG. 5 illustrates the possible solutions in a parallelogram embodiment.

PHASE-COMPARISON MONOPULSE PRINCIPLE

(7) Consider a standard radar receiver with two separate receiving antennas 1 (RX1) and 2 (RX2) in FIG. 1, the receiving antennas RX1 and RX2 are separated by the distance 3 (D.sub.12). The incoming wave front 5 reflected from a target arrives at an angle 6 (E) relative to a line 4 which is 90 degrees relative to the line 3 going through the two receiving antennas 1 and 2. Due to the angle 6 (E), the signal received by receiving antenna 1 travels an additional distance 7 which equals D.sub.12.Math.sin(E).

(8) Consequently, the phase difference, .sub.12, in radians between the received signal 8 from the receiving antenna RX1 compared to the signal 9 from receiving antenna RX2 will be phase shifted an amount equal to the distance 7 divided by the wavelength multiplied with 2, see equation [1].

(9) $\begin{array}{cc}{}_{12}=2\frac{D_{12}.Math.\sin \left(E\right)}{}& \left[1\right]\end{array}$

(10) Equation [1] has been used by all phase-comparison monopulse tracking radars to determine the physical angle to a target from a measured phase difference .sub.12 between two physically separated antennas, RX1 and RX2.

(11) Since a phase difference between two periodic signals can only be measured unambiguously within radians, the phase difference .sub.12 essentially includes N.sub.12 times 2, where the ambiguity index N.sub.12 is an integer number like 2, 1, 0, 1, 2 etc. Consequently, equation [1] can be rewritten to [2], where .sub.12amb is the phase difference which is directly measured and which always will be within radians.

(12) $\begin{array}{cc}\sin \left(E\right)=\left(\frac{{}_{12\mathrm{amb}}}{2}+N_{12}\right)\frac{}{D_{12}}& \left[2\right]\end{array}$

(13) In the special case of N.sub.12=0, .sub.12amb equals .sub.12 in equation [1]. Since sin(E) always will be absolute less than 1, there is an upper absolute limitation on ambiguity index N.sub.12 which can be used in equation [2], see equation [3].

(14) $\begin{array}{cc}.Math.N_{12}.Math.\mathrm{floor}\left(\frac{D_{12}}{}+0.5\right)& \left[3\right]\end{array}$

(15) In table 1 the number of useable N.sub.12's are listed for a couple of different distances D.sub.12 between the receiving antennas RX1 and RX2.

(16) TABLE-US-00001 TABLE 1 Ambiguity index N.sub.12 versus receiver separation D.sub.12 Receiver separation, D.sub.12 Ambiguity index, N.sub.12 /2 0 3/2 1, 0, 1 5/2 2,1, 0, 1, 2 10 /2 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5

(17) For a target located at position 10 in FIG. 2 relative to the receiving antennas 1 and 2, this means that from only the directly measured phase difference .sub.12amb, there is no way of telling whether the target is located at position 10 or at one of the positions 11 in FIG. 2. The ghost positions 11 in FIG. 2 corresponds to the ambiguity index N.sub.12 being 2, 1, 1, 2 instead of the, in this case, correct ambiguity index N.sub.12=0.

(18) The above described ambiguity problem has always been a challenge for phase-comparison monopulse receiver systems in order to determine the angle to targets relative to the receiver orientation. This has been overcome by either 1) assuming an initial ambiguity index, or by 2) over time observing angular movement of the target and correlating this with predetermined likely movement of the target. For most phase-comparison monopulse radars solution 1) has been used. For the assumption of ambiguity index N.sub.12 equal to 0 to be valid, it is necessary that the receiver beam width is sufficiently narrow to eliminate the likehood of getting ambiguity index'es N.sub.12 that are not 0. For a receiving antenna with a physical width of W in the direction parallel to the direction between receiving antenna RX1 and RX2, the narrowest 3 dB beam width possible in this dimension will be given by [4].

(19) $\begin{array}{cc}{\mathrm{BW}}_{3\mathrm{dB}}=a\sin \left(\frac{}{2.26.Math.W}\right)& \left[4\right]\end{array}$

(20) The angle range corresponding to ambiguity index N.sub.12 is 0 is given by [5].

(21) $\begin{array}{cc}{}_{N_{12}=0}=a\sin \left(\frac{}{2.Math.D_{12}}\right)& \left[5\right]\end{array}$

(22) This means that if the antenna dimension W in one dimension is greater than 1.13 times the distance D.sub.12 between the receiver antennas in the same dimension used for the phase-comparison monopulse, then there will be ambiguity in the direction-of-arrival determination of the incoming wave. Meaning, unless the present invention is used, or additional information is provided, then the direction-of-arrival determination will be ambiguous.

(23) Monopulse Resolving of the Phase Ambiguity

(24) To solve the above ambiguity problem, an additional receiving antenna 12 (RX4) may be provided.

(25) Large-number antenna sensors are known as e.g. Phased array receivers which consist of a number of receivers arranged in a grid, typically linearly spaced. These systems are capable of determining the direction-of-arrival of the reflected/emitted wave from a target, but only if the spacing of at least one of the rows or columns of the receivers is less than /2. The present embodiment is based on only adding one additional receiving antenna RX4 being placed at a different distance than D.sub.12 from either receiving antenna RX1 or RX2.

(26) In FIG. 3, a one-dimensional set-up is described aimed at determining a direction-of-arrival in one dimension, i.e. in relation to a line between the receiving antennas RX1 and RX2. In this embodiment, the receiving antenna (RX4) 12 is positioned at a distance 30 (D.sub.24.sub._.sub.1) from the receiving antenna RX2 and is positioned on the same line that goes through receiving antennas RX1 and RX2. In this manner, the phase shift determined may be used for determining the angle or direction-of-arrival of the beam in the plane of the drawing.

(27) Thus, sin(E) can be determined from the phase difference .sub.24amb in radians between the received signal from the receiving antenna RX2 compared to the signal from receiving antenna RX4, see equation [6].

(28) $\begin{array}{cc}\sin \left(E\right)=\left(\frac{{}_{24\mathrm{amb}}}{2}+N_{24}\right)\frac{}{D_{24\_1}}& \left[6\right]\end{array}$

(29) When the phase differences .sub.12amb and .sub.24amb are determined at the same instance in time, both equations [2] and [6] need to be fulfilled. In FIG. 3, a graphical illustration, with the correct target position 10 corresponding to both N.sub.12 and N.sub.24 equal to 0, is shown as well as the ghost positions 14 corresponding to the ambiguity index N.sub.24 being 1 and 1 and with the ghost positions 11 corresponding to the ambiguity index N.sub.12 being 2, 1, 1 and 2. From FIG. 3 it is easily seen that only the correct position 10 will satisfy both the phase difference .sub.12amb and the phase difference .sub.24amb since none of the ghost positions 11 and 14 coincide. Consequently, the ambiguity has been resolved and the corresponding index N.sub.12 and N.sub.24 has been determined at one given instance in time. There are several ways to determine mathematically which pair of N.sub.12 and N.sub.24 that satisfies both equations [2] and [6]. One way, to do this is to minimize the term err in equation [7] using only values for N.sub.12 that satisfy equation [3]. N.sub.24 can be any integer value in equation [7].

(30) $\begin{array}{cc}\mathrm{err}=.Math.\frac{{}_{24\mathrm{amb}}}{2}+N_{24}-\frac{D_{24\_1}}{D_{12}}\left(\frac{{}_{12\mathrm{amb}}}{2}+N_{12}\right).Math.& \left[7\right]\end{array}$

(31) Another way is to identify the pair of N.sub.12 and N.sub.24 that satisfies both equations [2] and [6] given any measured phase differences .sub.12amb and .sub.24amb and to simply make a two-dimensional look-up table taking .sub.12amb and .sub.24amb as input.

(32) From equation [7] it is clear, that only in the case where the distance D.sub.24.sub._.sub.1 is different from the distance D.sub.12 it will be possible to determine a unique solution for N.sub.12 and N.sub.24.

(33) Full 3 Dimensional Monopulse Resolving of the Phase Ambiguity

(34) Even though real life situations exist in which the ambiguity problem may exist only in one dimension, even though direction-of-arrival or position determination is made in two or three dimensions, in the preferred environment, the ambiguity resolving technique described above is used simultaneously both vertically and horizontally, whereby a three dimensional angle to the target is obtained unambiguously and on the basis of a single received pulse reflected from the target.

(35) Naturally, the set-up of FIG. 3 may be repeated for the two dimensions, but the receiver antenna configuration preferably is made as that of FIG. 4 which is a frontal view of the antenna panel. In FIG. 4, the positions of receiving antenna (RX1) 15 and (RX2) 16 define the vertical direction (Y) 24 of the antenna panel and are separated by the distance (D.sub.12) 19, and the positions of receiving antenna (RX2) 16 and (RX3) 17 define the horizontal direction (X) 23 of the antenna panel and are separated by the distance (D.sub.23) 20. The position of receiving antenna (RX4) 18 is vertically separated from receiving antenna RX2 by the distance (D.sub.24.sub._.sub.1) 21 and horizontally separated by the distance (D.sub.24.sub._.sub.3) 22. Receiving antenna RX4 is separated from RX2 by the distance (D.sub.24):
D.sub.24={square root over (D.sub.24.sub.1.sup.2+D.sub.24.sub.3.sup.2)}

(36) In FIG. 5 the position of receiving antenna (RX1) 15, (RX2) 16 and (RX3) 17 define a parallelogram. Receiving antenna (RX4) 18 needs to be positioned away from axes extending through any pair of: each of the four corners of the parallelogram 15, 16, 17 and 26 and a center point 27 of each of the four sides of the parallelogram.

(37) In FIG. 4, the receiving antennas 15 and 16 are used to determine the vertical angle E to the target from the corresponding phase difference .sub.12amb (e.g., see equation [2]), receiving antennas 16 and 17 are used to determine the horizontal angle A to the target from the corresponding phase difference .sub.23amb (e.g., see equation [8]). Receiving antennas 16 and 18 are used to determine the angle P to the target from the corresponding phase difference .sub.24amb (e.g., see equation [9]). The outputs of the receiving antennas 15, 16, 17, and 18 may be received by a determining element 25 to determine a direction-of-arrival.

(38) $\begin{array}{cc}\sin \left(A\right)=\left(\frac{{}_{23\mathrm{amb}}}{2}+N_{23}\right)\frac{}{D_{23}}& \left[8\right]\\ \sin \left(P\right)=\left(\frac{{}_{24\mathrm{amb}}}{2}+N_{24}\right)\frac{}{D_{24}}& \left[9\right]\end{array}$

(39) From the phase difference .sub.12amb a number of candidate angles E.sub.i is determined using the applicable N.sub.12 in equation [2] from equation [10], in addition from the phase difference .sub.23amb a number of candidate angles A.sub.i is determined using the applicable N.sub.23 in equation [8] from equation [10]. Finally, from the phase difference .sub.24amb a number of candidate angles P.sub.i is determined using the applicable N.sub.24 in equation [9] from equation [10]. From the sets of candidate angles (E.sub.i, A.sub.i, P.sub.i) a direction-of-arrival is determined by minimizing the sum of difference angles between the direction-of-arrival and the set of candidate angles (E.sub.i, A.sub.i, P.sub.i). The direction-of-arrival is represented by the vertical angle E and horizontal angle A with corresponding ambiguity indexes N.sub.12 and N.sub.23.

(40) $\begin{array}{cc}.Math.N_{12}.Math.\mathrm{floor}\left(\frac{D_{12}}{}+0.5\right),.Math.N_{23}.Math.\mathrm{floor}\left(\frac{D_{23}}{}+0.5\right)\mathrm{and}.Math.N_{24}.Math.\mathrm{floor}\left(\frac{D_{24}}{}+0.5\right)& \left[10\right]\end{array}$

(41) The minimization of the three sets of candidate angles (E.sub.i, A.sub.i, P.sub.i) can be done by minimizing the term err in equation [11] using only values for ambiguity index N.sub.12, N.sub.23 and N.sub.24 that satisfy equation [10].

(42) 0$\begin{array}{cc}\mathrm{err}=.Math.\frac{{}_{24\mathrm{amb}}}{2}+N_{24}-\frac{D_{24\_1}}{D_{12}}\left(\frac{{}_{12\mathrm{amb}}}{2}+N_{12}\right)-\frac{D_{24\_3}}{D_{23}}\left(\frac{{}_{23\mathrm{amb}}}{2}+N_{23}\right).Math.& \left[11\right]\end{array}$

(43) In this example, the direction going through antennas RX1 and RX2 is perpendicular to the direction going through antennas RX2 and RX3. It should be noted that this need not be the case.

(44) The resolving of the ambiguity outlined above can be done for every individual measurement point without using knowledge of target location in any previous point(s) in time. For a more robust solution, the ambiguity resolving can be combined with a tracking algorithm aiming at tracking an object and generating a trajectory thereof, whereby the next measurement point on the trajectory for a target is restricted to occur at the vicinity of one or more of previous measurement point, this will typically eliminate the need for solving the ambiguity. In the preferred solution, the ambiguity resolving is carried out independently on all data points belonging to the same target during the acquisition phase of the target tracking. Based on all the resolved ambiguities and the relative movement of the target during the acquisition phase, the final assessment of the starting ambiguity is determined. If a target is lost during tracking for some time making it possible to have shifted in angular ambiguity, then it is recommended to re-acquire the ambiguity indexes.

(45) Thus, the present direction-of-arrival may be used for generating the correct track of e.g. a flying projectile, such as a golf ball or a base ball, which may be tracked by a usual radar, which may otherwise have the ambiguity. Thus, the present invention may be used in addition to the radar, or the radar may be altered to encompass the invention, whereby the present direction-of-arrival data may be used in the determination of the trajectory. In one example, the normal tracking may be used for determining the overall trajectory and the direction-of-arrival is performed only once or a few times in order to ensure that no wrong choices have been made in the radar as to solving ambiguity. If the trajectory determined does not coincide with the direction-of-arrival, the trajectory may be altered. Alternatively, all or most of the points determined of the trajectory may be determined also on the basis of a determined direction-of-arrival.