WO2021105290A1

WO2021105290A1 - Method and device for estimating an angle of arrival of a radio signal

Info

Publication number: WO2021105290A1
Application number: PCT/EP2020/083520
Authority: WO
Inventors: Daniel Christien; Philippe Laviec
Original assignee: Thales
Priority date: 2019-11-27
Filing date: 2020-11-26
Publication date: 2021-06-03
Also published as: FR3103574B1; EP4066000A1; FR3103574A1

Abstract

The invention concerns a method and a device for estimating an angle of arrival of a radio signal by a plurality of receiver antennas distributed regularly over a circle so as to form a circular network of receiver antennas, and by amplitude goniometry. The method includes the steps of: • - selecting (32) a main antenna and two secondary antennas, • - calculating (34) two phase shifts between the main antenna and the two secondary antennas; • - using (38-48) theoretical phase shift data, associating values of the angle of arrival with first phase shift values, and of the estimated first angle of arrival value in order to determine a final estimated angle of arrival value, obtained either by amplitude goniometry or by phase goniometry.

Description

TITLE: Method and device for estimating an angle of arrival of a radio signal

The present invention relates to a method for estimating an angle of arrival of a radio signal, and a device for estimating an angle of arrival of an associated radio signal.

The invention lies in the field of locating sources of radioelectric emissions, and finds particular application in the field of radar detection.

In this type of application, it is known to use a system for receiving radio signals, comprising one or more receiving antennas. The localization of a radioelectric emission source comprises in particular the detection of the direction of arrival of a transmitted radioelectric signal. The direction of arrival is characterized by an angle, called the angle of arrival of the radio signal, which is the angle between the direction of the axis formed between the emission source and the reception system and a known reference direction .

Several methods of estimating an angle of arrival of a radio signal have been proposed.

In particular, amplitude direction finding is known, which uses the amplitude of the radio signals received on a plurality of directional reception antennas pointing in different reception directions, generally arranged to form a circular network.

Phase direction finding or interferometry generally uses one or more linearly distributed antenna panels, the estimation of an angle of arrival of the radio signal being carried out on the basis of the phase shifts measured between the antennas receiving the radio signal. Interferometry generally makes it possible to obtain more accurate angle of arrival estimates than amplitude direction finding. A drawback of interferometry is the ambiguity of the phase shifts measured to within 2kn, k being a relative integer. To avoid phase shift ambiguities, it is necessary for the distance between two receiving antennas to be less than a value which is calculated theoretically as a function of the minimum wavelength of the radio waves received, and of the maximum angular coverage. In other words, it is necessary for the distance between receiving antennas to be small in order to obtain unambiguous phase shifts, in particular to cover a wide band of frequencies. In addition, to have a blanket angular wide, it is necessary to use several receiving antenna panels, which increases costs.

The object of the invention is to remedy the drawbacks of the prior art, by proposing a method and a device for estimating an angle of arrival of a radio signal with improved precision over a wide frequency band.

To this end, the invention proposes a method for estimating an angle of arrival of a radio signal, implemented by a reception system comprising a plurality of reception antennas distributed regularly over a circle so as to forming a circular array of reception antennas, the reception system being adapted to calculate a first value of angle of arrival estimated by amplitude direction finding. The process comprises steps of:

-selection of a triplet of reception antennas in the circular network of reception antennas, comprising a main antenna and two secondary antennas,

-calculation of a first reception phase shift between the main antenna and a first secondary antenna, and of a second reception phase shift between the main antenna and a second secondary antenna;

use of theoretical phase shift data, associating angle of arrival values with values of first phase shift and second phase shift, and of said first estimated angle of arrival value, to determine an angle of arrival value final estimate, said final angle of arrival value being obtained either by amplitude direction finding or by phase direction finding.

Advantageously, the method of estimating an angle of arrival proposed makes it possible to obtain a final estimated angle of arrival value of improved precision, while using a circular array of reception antennas, suitable for direction finding d. 'amplitude.

The method of estimating an angle of arrival of a radio signal according to the invention may also have one or more of the characteristics below, taken independently or in any technically conceivable combination.

The theoretical phase shift data are calculated beforehand and stored in a data structure.

The theoretical phase shift data is used to obtain zero, one or more second estimated angle of arrival value (s), as a function of the calculated first and second phase shifts. If at least one second estimated angle of arrival value is obtained, for the or each second estimated angle of arrival value, the method comprises a comparison of said second estimated angle of arrival value with said first estimated angle of arrival value, and, depending on the result of the comparisons, obtaining a final estimated angle of arrival value.

The comparison comprises, for the or each second estimated angle of arrival value, a calculation of a difference, in absolute value, between said second estimated angle of arrival value and the first value of angle of arrival estimated, and a comparison of the calculated deviation to a predetermined error threshold.

If the calculated deviation is less than said error threshold for a single second estimated angle of arrival value, said final estimated angle of arrival value is obtained by phase direction finding, using the associated theoretical phase shift data at said second estimated angle of arrival value.

If none of the calculated deviations is less than the predetermined error threshold, or if several calculated deviations are less than the predetermined error threshold, said final estimated angle of arrival value is equal to the first angle value d arrival estimated by amplitude direction finding.

Obtaining at least one second estimated angle of arrival value includes determining at least a local minimum distance, according to a chosen distance measurement, between a first point associated with the first and second measured reception phase shifts. and at least one subset of second points obtained from the theoretical phase shift data.

The determination of at least a local minimum includes:

a distance calculation, according to a chosen distance measurement, between a first point associated with the first and second measured reception phase shifts and at least one subset of second points obtained from the theoretical phase shift data, each second point being associated to a pair of first phase shift and second phase shift of the theoretical phase shift data;

-a determination of at least a local minimum distance among the calculated distances.

The method further comprises a thresholding consisting in comparing the local minimum distance calculated with a distance threshold, and in retaining, among said second points, second candidate points for which the calculated distance is less than the predetermined distance threshold, said second value of estimated angle of arrival being the values of angle of arrival associated in the theoretical phase shift data at the second candidate points.

The distance is a Mahalanobis distance.

The method includes a preliminary step of calculating and storing theoretical phase shift data in the form of a plurality of phase shift structures, each phase shift structure being calculated for a chosen radio signal frequency.

According to another aspect, the invention relates to a device for estimating an angle of arrival of a radioelectric signal, implemented in a reception system comprising a plurality of reception antennas distributed regularly over a circle in such a manner. in forming a circular array of reception antennas, the reception system being adapted to calculate a first value of angle of arrival estimated by amplitude direction finding. The device for estimating an angle of arrival is an electronic calculation device configured to implement:

-a module for selecting a triplet of reception antennas in the circular array of reception antennas, comprising a main antenna and two secondary antennas,

a module for calculating a first reception phase shift between the main antenna and a first secondary antenna, and a second reception phase shift between the main antenna and a second secondary antenna;

a module configured to use theoretical phase shift data, associating angle of arrival values with values of first phase shift and second phase shift, and to use said first estimated angle of arrival value to determine a value of final estimated angle of arrival, said final angle of arrival value being obtained either by amplitude direction finding or by phase direction finding.

According to another aspect, the invention relates to a computer program comprising software instructions which, when they are implemented by a programmable electronic computing device, implement a method for estimating an angle of arrival such as that briefly described above.

According to another aspect, the invention relates to an information medium, on which are recorded software instructions which, when they are implemented by a programmable electronic computing device, implement an angle estimation method. arrival as briefly described above as briefly described above. Other characteristics and advantages of the invention will emerge from the description which is given below, by way of indication and in no way limiting, with reference to the appended figures, among which:

[Fig 1] FIG. 1 schematically illustrates a system for receiving radio signals implementing a device for estimating the angle of arrival of a radio signal according to one embodiment of the invention;

[Fig 2] FIG. 2 is a block diagram of the main steps of a method for estimating the arrival angle of a radio signal according to one embodiment of the invention;

[Fig 3] Figure 3 schematically illustrates curves representing points of a phase shift table associated with a given frequency;

[Fig 4] FIG. 4 schematically illustrates a graph of distances between a first point associated with the measured reception phase shifts and points of the phase shift table illustrated in FIG. 3.

FIG. 1 schematically illustrates a system 1 for receiving radio signals implementing a device for estimating an angle of arrival according to the invention.

The radioelectric signal reception system is for example on board a moving carrier, for example airplane, helicopter, boat.

The radio signals are for example signals emitted by distant radar sources.

The aim of the angle of arrival estimation device according to the invention is to determine the direction of arrival of a radio signal emitted by a remote source. The direction of arrival of the signal is characterized by an angle of arrival of the signal, the angle between the direction of the axis formed between the emission source and the receiving system and a predetermined reference direction.

The radioelectric signal reception system comprises a network 2 of reception antennas Ai, A ₂ ... A _N. In the example of Figure 1, the number of antennas is N = 6.

More generally, the number N of reception antennas is for example between 4 and 32.

Preferably, as illustrated in FIG. 1, the receiving antenna array 2 is a circular array, the receiving antennas A _I ... A _N being regularly distributed over a circle in a plane, called the detection plane. The Ray of the circle and the number N of receiving antennas define the geometry of the network 2.

Reception antennas

to A _N are preferably directional antennas respectively pointed in selected directions of the detection plane, corresponding to angles e _lr ..., e _N with respect to a predetermined reference direction.

The radio signal reception system also comprises a device 4 for estimating the angle of arrival of an RF radio signal received by the antenna network 2.

The angle of arrival estimation device 4 comprises at the input reception channels Vi to V _N associated respectively with each reception antenna

to A _N.

The device 4 is a programmable electronic computing device comprising an analog-digital conversion unit 6, and an electronic computing unit 8, comprising one or more processors, able to execute executable code instructions when the programmable device is powered on. . The device 4 for estimating the angle of arrival of an RF radio signal also comprises an electronic memory 10, suitable for storing data.

According to one variant, the programmable device 4 is produced in the form of a programmed card of the ASIC or FPGA type.

The device 4 for estimating the angle of arrival of an RF radio signal is configured to implement, by the electronic computing unit 8, an amplitude direction-finding module 14, which calculates a first value of estimated angle of arrival e _{is 1} from the signal powers received by the receiving antennas. Any amplitude direction finding method known to those skilled in the art is applicable.

The device 4 for estimating the angle of arrival of an RF radio signal is configured to also implement a module 16 for selecting a triplet of reception antennas forming a base for performing an estimate of angle d. arrival by phase direction finding or interferometry, and a module 18 for calculating phase shifts between radio signals received by the antennas of the selected antenna triplet.

The device 4 for estimating the angle of arrival of an RF radio signal is configured to also implement a module 20 for obtaining one or more second estimated angle of arrival values 0 _{is 2} in data function theoretical phase shifts 12 previously stored, for example in a data structure.

The device 4 for estimating the angle of arrival of an RF radio signal is configured to also implement a module 22 for obtaining a final estimated angle of arrival value 0 _{is final} as a function of the values. of angles of arrival estimated beforehand e _{is l} and e _{is 2} .

The modules 14, 16, 18, 20 and 22 are implemented, in one embodiment, in the form of a computer program comprising software instructions which, when they are implemented by a programmable electronic computing device, implement a method of estimating angle of arrival.

In one embodiment, these software instructions are stored on a computer readable information medium suitable for storing the software instructions and for being coupled to a bus of a computer system. By way of example, this medium is an optical disc, a magneto-optical disc, a ROM memory, a RAM memory, any type of non-volatile memory (for example EPROM, EEPROM, FLASH, NVRAM), a magnetic card or an optical card.

The final estimated angle of arrival value is either obtained by amplitude direction finding or phase direction finding as explained in more detail below.

FIG. 2 is a block diagram of the main steps of a method for estimating an angle of arrival of a radio signal according to one embodiment.

Following the reception by the antenna array of a radioelectric signal, the method comprises a step 30 of obtaining a first estimated angle of arrival value, 0 _{is 1} , calculated by amplitude direction finding. For example, the first estimated angle of arrival value is received from an amplitude direction finding module 14.

The reception phases measured for each antenna of the network are received in step 31 of reception of measured phases. Such a phase measurement for the receiving antennas is carried out by known means.

The method then comprises a step 32 of selecting an antenna base to be used for carrying out the phase direction finding. Preferably, it is a triplet of antennas which is selected, comprising a main antenna A ,, with i ranging between 1 and N, and two secondary antennas, close to the main antenna. The main antenna is selected based on the first estimated angle of arrival value, e _{is l,} and the angle Q, associated with the antenna. Indeed, when the reception network 2 comprises N antennas distributed regularly, two neighboring antennas are separated by an angle of 360 N.

The receiving antenna A is selected as the main antenna if the difference, in absolute value, between e _{is 1} and Q, is less than or equal to 36072N.

Two secondary antennas are adjacent to the selected main antenna and located on either side of the main antenna.

For example, referring to FIG. 1, if the selected main antenna is the antenna Ai, the selected antenna triplet is formed by the antennas (Ai, A ₂ , A ₆ ).

More generally, a selected antenna triplet comprises the selected main antenna A ,, a first secondary antenna A _j , where j = i-1 (modulo N) and a second secondary antenna A _k , where k = i + 1 ( modulo N).

A calculation of phase shifts associated with the selected antenna triplet is performed in the next step 34. If the measured reception phases, received in step 31, are respectively denoted F; for a receiving antenna A, the phase shifts associated with the triplet of antennas are:

a first reception phase shift: DF _{1 ΐh65} = F ₇ - fi;

-a second reception phase shift: AF ₂ , mes = F _fc -

;

The first reception phase shift and the second reception phase shift associated with the selected antenna triplet are stored.

In a known manner, the reception phase shifts measured between antennas are ambiguous to within 2kn. To perform an end value estimate with a phase direction finding method, it is necessary to resolve the ambiguity. In other words, the k value of the number of rotations should be determined for each measured phase shift.

The frequency of the received RF radio signal is also measured during a frequency measurement step 36. For example, the measured frequency of the RF radio signal is equal to 5 GHz.

According to the invention, theoretical phase shift data is used. These theoretical phase shift data are for example calculated for example for several frequency values in a covered frequency band, for example between 2 GHz and 18 GHz are used.

The theoretical phase shift data associate, for a given frequency, values of first phase shift and second phase shift, each pair of first and second phase shifts being associated with a value of angle of arrival of the radiofrequency signal in the detection plane (also called angle of deposit). In addition, values (ki, k ₂ ) of the number of rotations making it possible to resolve the phase shift ambiguity are also theoretically calculable.

For example, in one embodiment, the theoretical phase shift data is stored in a data structure.

For example, such a data structure is a phase shift table.

According to one variant, the theoretical phase shift data are calculated on the fly.

In the embodiment described below, the theoretical phase shift data are calculated beforehand and stored in a data structure, for example a table of phase shifts by frequency considered.

A previously calculated and stored phase shift table is obtained in the next step 38, in particular as a function of the measured frequency of the radiofrequency signal.

In one embodiment, each phase shift table comprises values of first phase shift and second phase shift, each pair of first and second phase shifts being associated with a value of the angle of arrival of the radiofrequency signal in the detection plane (also called the angle of bearing), the angle of arrival values being included in an angular range [-0 _ma x, 0max]. For example, 0 _m ax = 50 °.

In addition, each pair of first and second phase shifts is associated with a pair (ki, k ₂ ) of numbers of rotations making it possible to resolve the ambiguity of the phase shift measured.

For example, a phase shift table is calculated for angle values 0 _P included in the angular range [-0 _ma x, 0max], with an angular sampling step depending on the desired angular precision.

Figure 3 illustrates a graphical representation of a phase shift table obtained for a radio frequency signal frequency of 5 GHz.

The graphic representation 50 comprises points whose coordinates are formed by the first phase shift (represented on the abscissa 54) and the second phase shift (represented on the ordinate 52) corresponding to the values stored in a phase shift table. Each point corresponds to an associated _{0 P angle of arrival value.} The points illustrated in the example of FIG. 3 form branches denoted Ri to R ₇ , some of the branches shown comprising sub-branches corresponding to angular ranges of bearing angle. Each branch corresponds to the same pair (ki, k ₂ ) of numbers of rotations.

For example the branches of figure 3 correspond respectively to: Ri: k _l = -1 / k ₂ = 2 R _2! ki = 0 / k ₂ = 2 R ₃ : k _l = 1 / k ₂ = 2 R ₄ : ki = 1 / k ₂ = 1

R ₅ : kl = 2 / k ₂ = 1 R _{6 '} ki = 2 / k ₂ = 0

R ₇ : k _l = 2 / k ₂ = -1

By way of example, in FIG. 3 a first point 56 has been illustrated corresponding to values of the first reception phase shift DF _{1 ΐh65} and of the second reception phase shift: DF ₂ , mes obtained in step 34 for a radiofrequency signal received.

The point 56 is offset with respect to the branches R ₄ and R ₆ shown, in other words this point is offset with respect to the points of theoretical phase shifts. This point 56 is close, according to a chosen distance measurement, to a point 55 of the branch R ₆ , corresponding to an angle of arrival of 20 ° and to a point 57 of the branch R ₄ , corresponding to an angle arrival of 8 °.

Returning to FIG. 2, the method then comprises a step 40 of calculating distances, according to a chosen distance measurement, between a first point associated with the first and second measured reception phase shifts and at least one subset of second points obtained. on the basis of said phase shift table, each second point being associated with a pair of first phase shift and second phase shift of the phase shift table, as well as with an angle of arrival value q _r .

Preferably, the distance measure used is the Mahalanobis distance, with a predetermined Covariance matrix.

Preferably, the covariance matrix Cov is:

1

Cov 2

1

-2

Advantageously, the covariance matrix thus defined makes it possible to take into account an additive Gaussian noise centered on each phase shift measurement.

Alternatively, other weighted distances than the Mahalanobis distance can be used.

For example, in one embodiment, the distance between the first point and each second point, in the increasing order of the _{associated angle values q r} , obtained from the phase shift table, is calculated. A subset of second points corresponding to local distance minima is determined. Each local minimum of distance corresponds to the distance between the first point and a branch associated with a couple (ki, k2) of numbers of rotations.

According to an implementation variant, for a first point corresponding to values of the first reception phase shift A0 _{l mes} and of the second reception phase shift: AF ₂ , mes obtained in step 34 for a received radiofrequency signal, the local minimums distance from each branch are obtained from a previously stored distance table.

The distance calculation step 40 is followed by a thresholding step 42, consisting in comparing the local distance minima with a distance threshold D _max , and in retaining, among the second points, the second candidate points for which the associated distance, calculated is less than the predetermined _{distance threshold D max.}

For example, the predetermined distance threshold D _max is between 10 ° and 80 °, for example equal to 50 °.

If none of the local distance minima is less than the distance threshold D _max , then step 42 is followed by step 48 described below.

Figure 4 illustrates a curve of distances 60, the distances being calculated in degrees (ordinate 62) as a function of the angle value q _r of the angular range [- 0 _max , 0 _max ], with 0 _max = 5O ° associated at each second point, corresponding to the example in figure 3. It can be seen that several local distance minima (marked by circles in figure 4) are detected, but only the local distance minima 65 and 67, corresponding respectively to the second points 55 and 57 marked on the graph of figure 3, are less than the distance threshold

Dm _a x

Returning to FIG. 2, the thresholding step 42 is followed by a step 44 of testing the selection of a method for estimating the angle of arrival, during which for each second candidate point determined at the step 40, the associated angle value, called the second estimated arrival angle value, is compared with the first estimated arrival angle value 0 _{is 1} , obtained by amplitude direction finding.

In one embodiment, in step 44, for each second candidate point Pk, a difference between the second estimated angle of arrival value 0 _{gSt 2} and the first estimated angle of arrival value 0 _{is l} is calculated: S _k = \ 0 _{gSt 2} - 0 _{is l} |, and the difference S _k is compared with a predetermined error threshold S. For example, the error threshold S is between 10 ° and 30 °, for example equal to 20 °.

The results of each comparison are stored.

If the calculated deviation is less than the error threshold for a single second estimated angle of arrival value

, then step 44 is followed by a step 46 of estimating the value of the angle of arrival by phase direction finding. In fact, in this case, it is possible to obtain an estimated final angle of arrival value by phase direction finding without ambiguity, the ambiguity having been resolved by virtue of the applied method. Preferably, in step 46, values (k1, k2) of the number of rotations, associated with the arrival angle value q ^ _{, 2} in the phase shift table, are obtained from the table phase shifts used, and more generally in the data structure storing the theoretical phase shifts, and the phase direction finding with these values is applied for the selected antenna triplet.

According to a suboptimal variant, the second estimated angle of arrival value q _{ί 2} is retained as the final estimated angle of arrival value.

If the calculated deviation is less than the error threshold for several second estimated angle of arrival values, or if the calculated deviation is greater than the error threshold for all of the second estimated angle of arrival values, then the step

44 is followed by a step 48 of obtaining a final estimated angle of arrival value by amplitude direction finding.

In this case, in one embodiment, in step 48, the first estimated angle of arrival value e _{is l} is retained as the final estimated angle of arrival value.

Claims

1. Method for estimating an angle of arrival of a radio signal, implemented by a reception system (1) comprising a plurality of reception antennas distributed regularly on a circle so as to form a circular network (2) reception antennas, the reception system (1) being suitable for calculating a first value of the angle of arrival estimated by amplitude direction finding, characterized in that it comprises steps of:

- selection (32) of a triplet of receiving antennas in the circular array of receiving antennas, comprising a main antenna and two secondary antennas,

- calculation (34) of a first reception phase shift between the main antenna and a first secondary antenna, and of a second reception phase shift between the main antenna and a second secondary antenna;

- use (38-48) of theoretical phase shift data, associating angle of arrival values with values of first phase shift and second phase shift, and of said first estimated angle of arrival value, to determine a value d 'final estimated angle of arrival, said final angle of arrival value being obtained either by amplitude direction finding or by phase direction finding.

2. Method according to claim 1, wherein said theoretical phase shift data are calculated beforehand and stored in a data structure.

3. Method according to claim 1 or 2, wherein the theoretical phase shift data is used to obtain (38-42) zero, one or more second estimated angle of arrival value (s), as a function of the first and second calculated phase shifts.

4. The method of claim 3, further comprising, in the event that at least one second estimated angle of arrival value is obtained,

- for the or each second estimated angle of arrival value, comparison (44) of said second estimated angle of arrival value with said first estimated angle of arrival value,

- depending on the result of the comparisons, obtaining (46, 48) a final estimated angle of arrival value.

5. The method of claim 4, wherein said comparison (44) comprises, for the or each second estimated angle of arrival value, a calculation of a deviation, in absolute value, between said second angle value d. 'estimated arrival and the first estimated angle of arrival value, and a comparison of the calculated deviation to a predetermined error threshold.

The method of claim 5, wherein, if said calculated deviation is less than said error threshold for a single second estimated angle of arrival value, said final estimated angle of arrival value is obtained (46). by phase direction finding, using the theoretical phase shift data associated with said second estimated angle of arrival value.

7. The method of claim 5, wherein, if none of said calculated deviations is less than the predetermined error threshold, or if several calculated deviations are less than the predetermined error threshold, said estimated angle of arrival value final is equal to the first value of angle of arrival estimated by amplitude goniometry.

8. Method according to any one of claims 3 to 7, wherein obtaining at least one second estimated angle of arrival value comprises a determination (40) of at least a local minimum distance, according to a chosen distance measurement, between a first point associated with the first and second measured reception phase shifts and at least one subset of second points obtained from the theoretical phase shift data.

9. The method of claim 8, wherein said determination of at least a local minimum comprises:

- a distance calculation (40), according to a chosen distance measurement, between a first point associated with the first and second reception phase shifts measured and at least one subset of second points obtained from the theoretical phase shift data, every second point being associated with a pair of first phase shift and second phase shift of the theoretical phase shift data; a determination of at least a local minimum distance among the calculated distances.

10. The method of claim 8 or 9, further comprising a thresholding consisting in comparing (42) the calculated local distance minima with a distance threshold, and in retaining, among said second points, second candidate points for which the calculated distance is less than the predetermined distance threshold, said second estimated angle of arrival value being the angle of arrival values associated in the theoretical phase shift data with the second candidate points.

11. A method according to any one of claims 8 to 10, wherein said distance is a Mahalanobis distance.

12. Method according to any one of claims 1 to 11, comprising a prior step of calculating and storing theoretical phase shift data in the form of a plurality of phase shift structures, each phase shift structure being calculated for a signal frequency. radio station chosen.

13. Device for estimating an angle of arrival of a radio signal, implemented in a reception system comprising a plurality of reception antennas distributed regularly over a circle so as to form a circular array of antennas. reception, the reception system being adapted to calculate a first value of angle of arrival estimated by amplitude direction finding, the device for estimating an angle of arrival being an electronic calculation device characterized in that it is configured to implement:

- a module for selecting a triplet of receiving antennas in the circular array of receiving antennas, comprising a main antenna and two secondary antennas,

- a module for calculating a first reception phase shift between the main antenna and a first secondary antenna, and a second reception phase shift between the main antenna and a second secondary antenna;

14. Apparatus for estimating an angle of arrival of a radioelectric signal according to claim 13, further comprising a suitable electronic memory. in memorizing a data structure comprising theoretical phase shift data are calculated beforehand.

15. A computer program comprising software instructions which, when implemented by a programmable electronic computing device, implement an angle of arrival estimation method according to claims 1 to 12.