Amplitude goniometer and associated platform

Abstract

The present invention relates to an amplitude goniometer comprises P receiver channels, P being greater than or equal to 2, each receiver channel being identified by an index p, each receiver channel comprising an antenna coupled to a receiver chain followed by at least two digital receiver modules each comprising an analogue-to-digital conversion module associated with a respective sampling frequency, each sampling frequency not complying with the Shannon criterion and not being a multiple of another frequency, N being the number of frequencies, N being greater than or equal to 2, each frequency being referenced by an index n, the amplitude goniometry estimator working from the amplitudes of the signals originating from at least Q adjacent receiver channels of the P receiver channels, Q being at most equal to P, the sampling frequencies being associated with the analogue-to-digital conversion modules of the Q adjacent receiver channels.

Claims

1. An amplitude goniometer comprising P receiver channels, P being an integer greater than or equal to 2, each receiver channel being identified by an index p corresponding to a given angular order, the index p being an integer between 0 and P−1, each receiver channel including an antenna coupled to a receiver chain, each receiver chain being followed by at least two digital receiver modules each comprising an analog-digital conversion module, each analog-digital conversion module being associated with a respective sampling frequency and having at an input a frequency band, each sampling frequency is such that half the sampling frequency is less than the frequency band, and each sampling frequency not complying with the Shannon theorem and not being a multiple of one of the other sampling frequencies, N being the number of sampling frequencies associated with the analog-digital conversion modules belonging to the P receiver channels, N being greater than or equal to 2, each sampling frequency being referenced by an index n, the index n being between 0 and N−1, an amplitude goniometry estimator working from amplitudes of the signals originating from at least Q adjacent receiver channels among the P receiver channels, Q being an integer at most equal to P, the sampling frequencies being associated with the analog-digital conversion modules of these Q adjacent receiver channels.

2. The amplitude goniometer according to claim 1, wherein the N sampling frequencies are divided into J sampling frequency groups named G.sub.0, . . . , G.sub.J-1, each group comprising at least 2 different sampling frequencies, with J being an integer which is minimal and at most equal to Q.

3. The amplitude goniometer according to claim 2, wherein the analog-digital conversion modules of a receiver channel with index p are associated with the group of sampling frequencies G.sub.p.Math.mod(j), for p ranging from 0 to P−1.

4. The amplitude goniometer according to claim 3, wherein an angular coverage is less than 360° .

5. The amplitude goniometer according to claim 3, wherein an angular coverage is equal to 360° and the number of receiver channels P is greater than or equal to 3.

6. The amplitude goniometer according to claim 5, wherein the number of receiver channels P is a multiple of J or is equal to Q.

7. The amplitude goniometer according to claim 5, wherein the number of receiver channels P is not a multiple of J, or equal to Q, and wherein the sampling frequencies of the groups G.sub.R to G.sub.J-1 are respectively associated with analog-digital conversion modules of complementary digital receiver modules, these complementary digital receiver modules being assigned in any manner to the set of two receiver channels V.sub.0 and V.sub.P-1, and R being the remainder of the Euclidean division of P by J.

8. The amplitude goniometer according to claim 1, wherein the minimum number of adjacent receiver channels required by the amplitude goniometry estimator is equal to 2.

9. The amplitude goniometer according to claim 1, including a computer able to process the signals coming from the digital receiver module.

10. The amplitude goniometer according to claim 1, wherein each analog-digital conversion system is connected to a digital processing module of the signal able to perform a spectral analysis of the sampled signals.

11. The amplitude goniometer according to claim 10, wherein the spectral analysis is done by discrete Fourier transform associated with a weighting of the sampled signals upstream.

12. A platform including an amplitude goniometer according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Features and advantages of the invention will appear more clearly upon reading the following description, provided solely as a non-limiting example, and done in reference to the appended drawings, in which:

(2) FIG. 1 is a schematic view of an interferometer including a computer,

(3) FIG. 2 is a schematic illustration of an exemplary interferometer,

(4) FIG. 3 is a schematic illustration of another exemplary interferometer,

(5) FIG. 4 is a schematic illustration of still another exemplary interferometer,

(6) FIG. 5 is a schematic illustration of another exemplary interferometer,

(7) FIG. 6 is a schematic illustration of an exemplary amplitude goniometer,

(8) FIG. 7 is a schematic illustration of another exemplary amplitude goniometer, and

(9) FIG. 8 is a schematic illustration of another exemplary amplitude goniometer.

DETAILED DESCRIPTION OF THE INVENTION

(10) FIG. 1 illustrates an interferometer 10 using P antennas, P being an integer greater than or equal to 2.

(11) The interferometer 10 is part of a platform, the platform for example being an aircraft.

(12) Each antenna is identified by an index p, corresponding to an integer between 0 and P−1.

(13) Each antenna A.sub.0, . . . , A.sub.P-1 delivers its output signal to the input of a receiver chain CR.sub.0, . . . , CR.sub.P-1, representing the purely analog part.

(14) Each receiver chain CR.sub.0, . . . , CR.sub.P-1 delivers its output signal, filtered and brought to a usable power, to at least two digital receiver modules 20 each including an analog-digital conversion module 22 followed by a digital processing module of the signal 26.

(15) Each analog-digital conversion module 22 is able to perform sampling at a sampling frequency 24.

(16) Hereinafter, an analog-digital conversion module 22 is associated with a sampling frequency 24 when the analog-digital conversion module 22 is able to perform sampling at the sampling frequency 24.

(17) The frequency band at the input of the analog-digital conversion module 22 is not contained in a single Nyquist zone defined by the sampling frequency 24.

(18) The digital processing module of the signal 26 performs a DFT of the digital signal supplied by the analog-digital conversion module 22, very generally after having performed weighting of this signal over the desired analysis duration, this weighting essentially seeking to minimize the secondary spectral lobes for the dynamic of the frequency-separating power.

(19) The interferometer 10 also includes a computer 28 collecting the useful outputs of the DFTs of the various digital processing modules of the signal 26 and able to obtain the direction of arrival of the incident signal illuminating the set of antennas A.sub.1, . . . , A.sub.P.

(20) The antennas A.sub.0, . . . , A.sub.P-1 can be directional. If this is the case, they are generally pointed along a single axis orthogonal to the alignment line of their phase center. The distance distribution of the antennas A.sub.0, . . . , A.sub.P-1 is defined to ensure specified characteristics of angular precision and angular ambiguity rates.

(21) The distribution of the sampling frequencies over the analog-digital conversion modules 22 is chosen to minimize the quantity of digital receiver modules 20 each made up of analog-digital conversion modules 22 and processing modules 26 while fully using the possible performance related to the antenna arrange A.sub.0, . . . , A.sub.P of the interferometer 10.

(22) Several specific cases of interferometers 10 are illustrated in reference to FIGS. 2 to 5.

(23) In these figures, each receiver channel is shown simply in the form of an antenna and each analog-digital conversion module is shown schematically by a rectangle in which the sampling frequency used by said module is shown.

(24) FIG. 2 illustrates a case where the number of receiver channels P is equal to the number of sampling frequencies N, in the case at hand P=N=4.

(25) Each receiver channel has only two analog-digital conversion modules.

(26) The analog-digital conversion modules of the receiver channel indexed 0 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 1 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 2 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3. The analog-digital conversion modules of the receiver channel indexed 3 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3.

(27) Thus, no frequency of the band of interest is located near multiples of the sampling half-frequency, simultaneously for the two sampling frequencies associated with a same receiver chain; or, in the example illustrated above, for f.sub.e,0 and f.sub.e,1 simultaneously, or for f.sub.e,2 and f.sub.e,3 simultaneously.

(28) We have thus taken account of the first element mentioned in the section titled Brief description of the invention, namely that a phase measurement is systematically available on each antenna, even if the frequency of the signal is close to k f.sub.e,n/2 for one of the sampling frequencies f.sub.e,n. Furthermore, in the general case where the measurements done using the two digital receiver modules of a same receiver channel are usable, it is possible to take advantage of this redundant information to improve the measuring precision.

(29) A distribution of the sampling frequencies like that illustrated by FIG. 2 requires using computation to compensate the phase term φ.sub.DFT, or to adapt the number of points of the spectral analysis, with the drawbacks accompanying the description of the second element to be taken into account.

(30) Such an interferometer case (P=N) also makes it possible to compensate for this term by a suitable distribution of the sampling frequencies by noting that P receiver channels only deliver P−1 phase shifts between independent antennas, and that they make it possible to form P different sets of P−1 independent phase shifts. Thus, a suitable distribution of the sampling frequencies is such that each of the P different sets of P−1 independent phase shifts exclusively uses one of the N=P groups of N−1=P−1 possible sampling frequencies. Furthermore, the compensation of the phase term φ.sub.DFT related to a phase shift corresponding to the subtraction of two phases originating from different receiver channels working at the same sampling frequency, it is also possible for a suitable distribution of the sampling frequencies to be such that any phase shift always originates from two phases measured with a same sampling frequency.

(31) To that end, it suffices to build P sampling frequency pairs with indexes n.Math.mod(P) and (n+1).Math.mod(P) for n ranging from 1 to P and to assign each of these P sampling frequency pairs to one of the P receiver channels. This amounts to assigning the sampling frequency pair with indexes p.Math.mod(P) and (p+1).Math.mod(P) to the receiver channel with index p.

(32) FIG. 3 illustrates such a case for which the number of receiver channels P is equal to the number of sampling frequencies N, in the case at hand P=N=4.

(33) Each receiver channel has only two analog-digital conversion modules.

(34) The analog-digital conversion modules of the receiver channel indexed 0 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 1 are respectively associated with the sampling frequency indexed 1, f.sub.e,1, and with the sampling frequency indexed 2, f.sub.e,2. The analog-digital conversion modules of the receiver channel indexed 2 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3. The analog-digital conversion modules of the receiver channel indexed 3 are respectively associated with the sampling frequency indexed 3, f.sub.e,3, and with the sampling frequency indexed 0, f.sub.e,0.

(35) Thus, the phase shift between the antenna indexed 0 and the antenna indexed 1 is related to the sampling frequency indexed 1, f.sub.e,1, the phase shift between the antenna indexed 1 and the antenna indexed 2 is related to the sampling frequency indexed 2, f.sub.e,2, the phase shift between the antenna indexed 2 and the antenna indexed 3 is related to the sampling frequency indexed 3, f.sub.e,3, and the phase shift between the antenna indexed 3 and the antenna indexed 0 is related to the sampling frequency indexed 0, f.sub.e,0. As a result, there are four phase shifts each related to a same sampling frequency, three of which are still independent and based on three sampling frequencies out of the four. Thus, even if the frequency of the signal is equal or close to a multiple of a given sampling half-frequency, there is still a set of three independent phase shifts not related to this sampling frequency.

(36) FIG. 4 illustrates a case where the number of receiver channels P is greater than the number of sampling frequencies N, in the case at hand P=4>N=3.

(37) The analog-digital conversion modules of the receiver channel indexed 0 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 1 are respectively associated with the sampling frequency indexed 1, f.sub.e,1, and with the sampling frequency indexed 2, f.sub.e,2. The analog-digital conversion modules of the receiver channel indexed 2 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 0, f.sub.e,3. The analog-digital conversion modules of the receiver channel indexed 3 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1.

(38) That being said, the analog-digital conversion modules of the receiver channel indexed 3 could also respectively have been associated with the sampling frequency indexed 1, f.sub.e,1, and with the sampling frequency indexed 2, f.sub.e,2, or with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 0, f.sub.e,0.

(39) FIG. 5 illustrates a case where the number of receiver channels P is less than the number of sampling frequencies N, in the case at hand P=3<N=4.

(40) The receiver channels indexed 0 and 1 each include only two analog-digital conversion modules, while the receiver channel indexed 3 includes three analog-digital conversion modules.

(41) The analog-digital conversion modules of the receiver channel indexed 0 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 1 are respectively associated with the sampling frequency indexed 1, f.sub.e,1, and with the sampling frequency indexed 2, f.sub.e,2. The analog-digital conversion modules of the receiver channel indexed 2 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 3, f.sub.e,3.

(42) In each of the cases where the number of receiver channels P is less than the number of sampling frequencies N, each pair of sampling frequencies with index p.Math.mod(P) and (p+1).Math.mod(P) is associated with a pair of analog-digital conversion modules of a same receiver channel with index p. Additionally, the N−P sampling frequencies that are not part of a pair of sampling frequencies with indexes p.Math.mod(P) and (p+1).Math.mod(P), for an index p varying between 0 and P−1, require adding N−P additional analog-digital conversion modules, each being associated with one of these N−P sampling frequencies, and these N P additional analog-digital conversion modules are distributed in any manner over the P receiver channels.

(43) In general, a wideband interferometer with multiple under-sampling has been disclosed minimizing the number of digital receiver modules. Beyond the cost, mass, volume, consumption and reliability aspects directly related to this minimization, this also makes it possible to optimize the computing load of the processing module.

(44) For the case of the amplitude goniometer, the setup is similar to that of FIG. 1, except that the antennas are angularly pointed in an offset manner from one another in the measuring plane of the angle of arrival of an incident signal, such that their directivity causes them to deliver a set of signals whose powers are representative of this angle of arrival.

(45) In general, it is also necessary to have at least 2 different sampling frequencies per receiver channels in order to ensure at least one amplitude measurement and N sampling frequencies on Q adjacent receiver channels to eliminate the frequency ambiguities.

(46) From the N sampling frequencies that are all different and not multiples of one another, J groups of sampling frequencies are built (G.sub.0, . . . , G.sub.J-1), each group comprising at least 2 different sampling frequencies, the set of J groups comprising the set of N sampling frequencies such that J is minimal and at most equal to Q.

(47) For example, let N=3 sampling frequencies f.sub.e,0, f.sub.e,1 and f.sub.e,2, for Q≥2, two groups are obtained: G.sub.0=(f.sub.e,0, f.sub.e,1) and G.sub.1=(f.sub.e,2, f.sub.e,x) with x being able to be 0, 1 or 2.

(48) For example, let N=4 sampling frequencies f.sub.e,0, f.sub.e,1, f.sub.e,2 and f.sub.e,3, for Q≥2, two groups are obtained: G.sub.0=(f.sub.e,0,f.sub.e,1) and G.sub.1=(f.sub.e,2, f.sub.e,3).

(49) For example, let N=5 sampling frequencies f.sub.e,0, f.sub.e,1, f.sub.e,2, f.sub.e,3 and f.sub.e,4, for Q=2, two groups are obtained: G.sub.0=(f.sub.e,0, f.sub.e,1) and G.sub.1=(f.sub.e,2,f.sub.e,3,f.sub.e,4); conversely, for Q≥3, three groups are obtained: G.sub.0=(f.sub.e,0,f.sub.e,1), G.sub.1=(f.sub.e,2, f.sub.e,3) and G.sub.1=(f.sub.e,4, f.sub.e,x) with x being able to be 0, 1, 2 or 3.

(50) The analog-digital conversion modules of a receiver channel with index p are associated with the group of sampling frequencies of the sequence G.sub.p.Math.mod(j), for p ranging from 0 to P−1.

(51) An instantaneous angular coverage of less than 360° creates P−Q+1 sets of Q adjacent receiver channels. The allocation of the groups of sampling frequencies to the receiver channels according to the previously defined rule ensures that it is possible to work with the N sampling frequencies at each of the P−Q+1 sets of Q adjacent receiver channels.

(52) Conversely, an instantaneous angular coverage of 360° creates P sets of Q adjacent receiver channels for circular continuity reasons, the index 0 following the index P−1. In this case, the allocation of the groups of sampling frequencies to the receiver channels according to the previously defined rule does not ensure that it is possible to work with the N sampling frequencies at each of the P sets of Q adjacent receiver channels unless P is a multiple of J or unless Q is equal to P.

(53) Indeed, in this case of an instantaneous angular coverage of 360°, the fact that P is not a multiple of J means that the rule for allocating the groups of sampling frequencies to the receiver channels, previously defined, does not affect all of the sets of Q adjacent receiver channels, comprising the receiver channels with indexes P−1 and 0, all of the defined groups of sampling frequencies (G.sub.0, . . . , G.sub.J-1), unless Q is equal to P.

(54) If Q is less than P, there are still sets of Q adjacent receiver channels, comprising the receiver channels with indexes P−1 and 0, that only have access to the groups of sampling frequencies G.sub.0 to G.sub.R-1, R being the remainder of the Euclidean division of P by J, they therefore do not have access to the groups of sampling frequencies G.sub.R to G.sub.J-1.

(55) As a result, in the case where the instantaneous angular coverage is equal to 360° and P is neither a multiple of J nor equal to Q, in addition to the rule previously defined that assigns, to the receiver channels with indexes P−1 and 0, respectively the groups of sampling frequencies G.sub.R-1 and G.sub.0, one simple optimal solution consists of assigning, to the set of these two receiver channels, the set of sampling frequencies from the groups G.sub.R to G.sub.J-1 not belonging to the set of groups G.sub.R-1 and G.sub.0. This additional allocation of sampling frequencies can be done indifferently over the entire receiver channel with index 0, over the receiver channel with index P−1, or divided in any manner between these two receiver channels.

(56) It must be noted that the angular precision, which goes hand-in-hand with large values of Q, of course requires that amplitude measurements be done for the antennas with extreme indexes of the range of Q indexes. Due to the directivity of the antennas, the gain of the antennas with extreme indexes from the range of the Q indexes on the incident signal is even smaller relative to that on the central antenna of this range when Q is large. This contributes to decreasing the overall sensitivity.

(57) FIG. 6 illustrates a case where the instantaneous angular coverage is 360° with N=4, P=6 and Q=2. N=4 and Q=2 such that J=2 and as a result P is a multiple of J.

(58) There are two groups of sampling frequencies: G.sub.0 comprising the sampling frequency indexed 0, f.sub.e,0, and the sampling frequency indexed 1, f.sub.e,1, and G.sub.1 comprising the sampling frequency indexed 2, f.sub.e,2, and the sampling frequency indexed 3, f.sub.e,3.

(59) The analog-digital conversion modules of the receiver channel indexed 0 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 1 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3. The analog-digital conversion modules of the receiver channel indexed 2 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 3 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3. The analog-digital conversion modules of the receiver channel indexed 4 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 5 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3.

(60) FIG. 7 illustrates a case where the instantaneous angular coverage is 360° with N=4, P=5 and Q=2. N=4 and Q=2 such that J=2 and as a result P is not a multiple of J, and Q is less than P.

(61) There are two groups of sampling frequencies: G.sub.0 comprising the sampling frequency indexed 0, f.sub.e,0, and the sampling frequency indexed 1, f.sub.e,1, and G.sub.1 comprising the sampling frequency indexed 2, f.sub.e,2, and the sampling frequency indexed 3, f.sub.e,3.

(62) The analog-digital conversion modules of the receiver channel indexed 0 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 1 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3. The analog-digital conversion modules of the receiver channel indexed 2 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 3 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3. The receiver channel indexed 4 has four analog-digital conversion modules: two first modules respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1, and two second modules that are in fact complementary, respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 3, f.sub.e,3.

(63) FIG. 8 illustrates a case where the instantaneous angular coverage is 360° with N=3, P=6 and Q=2. N=3 and Q=2 such that J=2 and as a result P is a multiple of J.

(64) There are two groups of sampling frequencies: G.sub.0 comprising the sampling frequency indexed 0, f.sub.e,0, and the sampling frequency indexed 1, f.sub.e,1, and G.sub.1 comprising the sampling frequency indexed 2, f.sub.e,2, and any sampling frequency different from that indexed 2, f.sub.e,2. For the figure, the chosen sample in frequency as that indexed 0, f.sub.e,0, but this could have been that index 1, f.sub.e,1. It must be noted that this option is valid for each receiver channel using G.sub.1.

(65) The analog-digital conversion modules of the receiver channel indexed 0 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 1 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 0, f.sub.e,0. The analog-digital conversion modules of the receiver channel indexed 2 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 3 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 0, f.sub.e,0. The analog-digital conversion modules of the receiver channel indexed 4 are respectively associated with the sampling frequency indexed 0, f.sub.e,0, and with the sampling frequency indexed 1, f.sub.e,1. The analog-digital conversion modules of the receiver channel indexed 5 are respectively associated with the sampling frequency indexed 2, f.sub.e,2, and with the sampling frequency indexed 0, f.sub.e,0.

(66) It should be noted that in the case of an amplitude goniometer, the second element mentioned in the “Brief description of the invention” section is not taken into account. As explained in this section, the amplitude measurement error, due to the different filtering conditions of the signal for the DFTs done by the digital processing modules of the signal (26) when the sampling frequencies are different, is less critical than the phase measurement error for an interferometer. This error is also minimized by the weighting of the signal generally used, which broadens the bandwidth of the DFT filter. The residual error can be corrected if needed with precise knowledge of the frequency of the signal, which is always measured in a radar detector.

(67) Lastly, the invention has been explained for 1D (one-dimensional) goniometers, that is to say, measuring a single angle, the angle in the plane where the antennas are arranged. It must be noted that the generalization to 2D (two-dimensional) goniometers, that is to say, measuring two angles, the angles located in two nonparallel planes, is done using the same basic principles.