Two-dimensional interferometer direction finding method based on multi-frequency sparse area array

Abstract

The invention discloses a two-dimensional interferometer direction finding method based on a multi-frequency sparse area array. The method mainly solves the problems that in the prior art, the array arrangement space size is limited, and the two-dimensional DOA estimation precision is poor in a low signal-to-noise ratio scene. Comprising the following steps: 1) constructing a sparse plane physical array; 2) carrying out channelization processing on the broadband signal received by the antenna; 3) acquiring a vector signal model of the mapped channel by taking the center frequency of the Lth channel signal as a reference; 4) selecting effective channel data from L-1 channels, mapping all the center frequencies of the effective channel data to the center frequency of the Lth channel signal, and combining the signals; 5) calculating the covariance of the signal, and extracting the phase of a triangular element on the matrix; and 6) selecting a phase difference corresponding to the virtual baseline from the extracted phases, and realizing two-dimensional interferometer unambiguous direction finding by using a long and short baseline method. According to the method, two-dimensional DOA high-precision estimation can be effectively realized, and the method can be used for realizing two-dimensional direction finding of a target by a small unmanned aerial vehicle in a low-signal-to-noise-ratio environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, further relates to passive direction finding technology, and in particular to a two-dimensional interferometer direction finding method based on a multi-frequency sparse surface array, which can be used for two-dimensional direction finding of a target in a low signal-to-noise ratio scene where the space size of an antenna array arrangement such as an unmanned aerial vehicle is limited. BACKGROUND

[0002] Two-dimensional DOA estimation is an important branch of array signal processing and is widely used in the fields of wireless communication, radar, and underwater sound. The basic idea is to arrange sensors in a certain plane or space configuration, based on the phase difference of electromagnetic signals collected by different array elements, and to process the phase difference according to the corresponding algorithm to obtain the direction of arrival of the target. Two-dimensional interferometer direction finding is one of the commonly used two-dimensional DOA estimation techniques. The short-baseline interferometer can ensure that the phase difference is unambiguous, but the DOA estimation accuracy is low. The long-baseline interferometer can achieve high-precision DOA estimation, but the long baseline has phase ambiguity and needs to be de-ambiguously. General de-ambiguity methods such as long-short baseline method, remainder theorem method, virtual baseline method, and three-dimensional baseline method all require that the spatial positions of the array elements strictly satisfy certain positional relationships, so the degree of freedom of the array arrangement is low.

[0003] In MOLLAI S, FARZANEH F. Wideband two dimensional interferometric direction finding algorithm using base-triangles and a proposed minimum planar array [J]. AEU-International Journal of Electronics and Communications, 2019, 105: 163-170, Mollai et al. proposed a two-dimensional interferometric direction finding algorithm based on a minimum planar array. This algorithm can achieve two-dimensional DOA unambiguous estimation with fewer array elements by optimizing the antenna arrangement, but it requires a large amount of calculation to obtain the optimal antenna arrangement, and the installation position of the physical array element is required to be very high, which is not conducive to engineering implementation. In addition, the actual incoming wave signal is often a wideband signal, while Mollai et al. consider the incoming wave signal to be a narrowband signal, which will lose most of the signal information. SUMMARY

[0004] The present application aims at the deficiency of the prior art, and provides a two-dimensional interferometer direction finding method based on a multi-frequency sparse array. The present application mainly solves the technical problem of realizing high-precision two-dimensional DOA estimation of a wideband signal by using a sparse array under the condition of low signal-to-noise ratio and limited size of an array platform. Firstly, the received wideband signal is channelized; secondly, different channelized data are selected by a certain rule, and are mapped to the same channel, so as to be equivalent to the same frequency point signal received by a virtual array; then, the covariance of the signal is calculated, and the phase of the first row data is extracted; finally, the long-short baseline interferometer direction finding method is used to realize two-dimensional direction finding of the target. The present application can not only cope with the situation of low signal-to-noise ratio and limited size of an array platform, but also reduce the number of physical array elements, relax the degree of freedom restriction of the physical array arrangement, and is easy to implement in engineering.

[0005] To achieve the above object, the technical scheme of the present application comprises the following:

[0006] (1) arranging three non-collinear antennas in the YOZ plane of a spatial coordinate system to construct a sparse plane physical array, wherein the frequency domain form of the wideband signal received by the antennas is represented as follows:

[0007] x q (f)=a q (f,θ,φ)s(f)+n q (f),

[0008] wherein x q (f) represents the frequency domain form of the signal received by the qth antenna; s(f) represents the discrete Fourier transform of the incident signal complex envelope; n q (f) represents the frequency domain form of the noise component of the signal received by the qth antenna; a q (f,θ,φ) represents the complex exponential of the phase difference between the signals received by the qth antenna and the first antenna, wherein the frequency of the source target signal is f, the azimuth angle is θ, and the elevation angle is φ; q=1,2,3;

[0009] (2) channelizing the wideband signals received by the three antennas to obtain the vector signal model of the lth channel, and the implementation steps are as follows:

[0010] (2.1) assuming that only continuous L channels exist after uniform channelization of the original wideband signal, and the center frequency set of the channels is {f1,f2,...,f L}; then the steering vector of the physical array receiving the lth channel signal is a(f l ,θ,φ):

[0011]

[0012] wherein u=sinθsinφ, v=cosφ, and yq ,z q ) represents the coordinates of the qth antenna in the YOZ plane;

[0013] (2.2) Let the number of sampling points be N, then the source target signal S(f l ) and noise N(f l ) are represented as follows:

[0014]

[0015] wherein s N (f l ) represents the Nth sampling point of the source target continuous signal, represents the combination of the Nth sampling point of the continuous noise received by all antennas;

[0016] (2.3) The vector signal model of the lth channel is obtained according to the following formula:

[0017] X(f l ) = a(f l , θ, φ) S(f l ) + N(f l ),

[0018] wherein l = 1, 2,..., L, and L is the total number of channels;

[0019] (3) Taking the center frequency f L of the Lth channel signal as the reference, the center frequency f l of the lth channel signal is mapped, and the vector signal model of the mapped lth channel is obtained:

[0020] X(f l ) = b(α l , f L , θ, φ) S(f l ) + N(f l ),

[0021] wherein b(α l , f L , θ, φ) represents the mapping result of a(f l , θ, φ) taking the center frequency f L of the Lth channel signal as the reference, and α l represents the frequency point relationship coefficient; X(f l ) is equivalent to the signal received by the 5-element virtual array at the frequency f L ;

[0022] (4)selecting M effective channel data in L-1 channels, mapping the center frequencies of the M effective channel data to the center frequency of the Lth channel signal, and combining to obtain a 2M+3-element virtual array receiving a signal with a frequency of f L

[0023] (5)calculating the covariance R of the virtual array receiving signal v

[0024] (6)extracting the phase of the upper triangular element of the covariance matrix using a phase discriminator

[0025] (7)selecting a frequency point relationship coefficient α to construct a virtual array structure based on the principle of long-short baseline method, selecting a phase difference corresponding to the virtual baseline in the extracted phase according to the virtual array structure, and realizing two-dimensional interferometer unambiguous direction finding by using the long-short baseline method

[0026] Compared with the prior art, the present application has the following advantages:

[0027] Firstly, since the present application maps different channelized data to the same channel after channelizing the antenna receiving signal, it is equivalent to receiving the same frequency point signal by the virtual array, so that two-dimensional DOA estimation can be realized by using two-dimensional interferometer technology in the scene where the size of the array platform is limited.

[0028] Secondly, since the present application directly obtains the phase difference of different antenna receiving signals by extracting the phase of the receiving signal covariance during the processing of the virtual array receiving signal, the characteristics of vector superposition can make it insensitive to noise interference; compared with the traditional method which obtains the phase difference between each other by subtracting each other after extracting the phase of different antenna receiving signals, the present application can realize high-precision two-dimensional DOA estimation in a low SNR situation. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is the flow chart of the method of the present application;

[0030] Figure 2 is a sparse planar array structure diagram provided by the embodiment of the present application, wherein (a) is a four-element sparse planar array structure diagram of the prior art, and (b) is a three-element sparse planar array structure diagram proposed by the present application;

[0031] Figure 3 is a relationship diagram of the two-dimensional DOA estimation unambiguous success rate and SNR using the method of the present application;

[0032] Figure 4 is a relationship diagram of the two-dimensional DOA estimation accuracy and SNR using the method of the present application, (a) is a relationship diagram of the azimuth angle estimation accuracy and SNR, and (b) is a relationship diagram of the elevation angle estimation accuracy and SNR.​​

[0033] Figure 5 Fig. 2 is a diagram showing the relationship between the two-dimensional DOA estimation ambiguity resolution success rate and the sampling point number using the method of the present application;

[0034] Figure 6 Fig. 3 is a diagram showing the relationship between the two-dimensional DOA estimation accuracy and the sampling point number using the method of the present application, (a) is a diagram showing the relationship between the azimuth angle estimation accuracy and the sampling point number, and (b) is a diagram showing the relationship between the elevation angle estimation accuracy and the sampling point number;

[0035] Figure 7 Fig. 4 is a diagram showing the relationship between the two-dimensional DOA estimation ambiguity resolution success rate and the selected frequency point interval using the method of the present application;

[0036] Figure 8 Fig. 5 is a diagram showing the relationship between the two-dimensional DOA estimation accuracy and the selected frequency point interval using the method of the present application, (a) is a diagram showing the relationship between the azimuth angle estimation accuracy and the selected frequency point interval, and (b) is a diagram showing the relationship between the elevation angle estimation accuracy and the selected frequency point interval. DETAILED DESCRIPTION

[0037] The present application will be further described below in conjunction with the accompanying drawings.

[0038] Referring to the accompanying drawings Figure 1 The present application provides a two-dimensional interferometer direction finding technology based on a multi-frequency sparse planar array, which specifically comprises the following steps:

[0039] Step 1) arranging three non-collinear antennas in the YOZ plane of a spatial coordinate system to construct a sparse planar physical array, wherein the antennas receive a wideband signal, and the frequency domain form of the wideband signal is represented as follows:

[0040] x q (f)=a q (f,θ,φ)s(f)+n q (f),

[0041] wherein x q (f) represents the frequency domain form of the signal received by the qth antenna; s(f) represents the discrete Fourier transform of the incident signal complex envelope; n q (f) represents the frequency domain form of the noise component of the signal received by the qth antenna; a q (f,θ,φ) represents the complex exponential of the phase difference between the signal received by the qth antenna and the signal received by the first antenna, wherein the frequency of the source target signal is f, the azimuth angle is θ, and the elevation angle is φ; q=1, 2, 3;

[0042] Step 2) performing channelization processing on the wideband signals received by the three antennas to obtain a vector signal model of the lth channel, and the implementation steps are as follows:

[0043] (2.1) Assuming that the original broadband signal is uniformly channelized and only L continuous channels have signals, the set of center frequencies of the channels is {f1, f2,..., fL}; then the steering vector of the physical array receiving the signal of the lth channel is a(f1, θ, φ): L l

[0044]

[0045] where u = sin θ sin φ, v = cos φ, (y q , z q ) represents the coordinates of the qth antenna in the YOZ plane;

[0046] (2.2) Let the number of sampling points be N; then the source target signal S(f l ) and the noise N(f l ) are represented as follows:

[0047]

[0048] where s N (f l ) represents the Nth sampling point of the continuous signal of the source target, represents the combination of the Nth sampling points of the continuous noise received by all antennas;

[0049] (2.3) The vector signal model of the lth channel is obtained according to the following formula:

[0050] X(f l ) = a(f l , θ, φ) S(f l ) + N(f l ),

[0051] where l = 1, 2,..., L, and L is the total number of channels;

[0052] Step 3) Take the center frequency f L of the Lth channel signal as the reference, map the center frequency f l of the lth channel signal, and obtain the vector signal model of the mapped lth channel:

[0053] X(f l ) = b(α l , f L , θ, φ) S(f l ) + N(f l ),

[0054] where b(α l , f L , θ, φ) represents a(f l ​​,θ,φ) with the center frequency f of the Lth channel signal L As a baseline mapping result, α l Represents the frequency correlation coefficient; X(f) l This is equivalent to a 5-element virtual array receiving a frequency of f. L The signal.

[0055] In this embodiment, the center frequency f of the l-th channel signal mentioned above is... l The specific expression is as follows:

[0056] f l =α l f L ,

[0057] Where, α l Represents the frequency correlation coefficient, 0 < α l ≤1, and when l=L, α l =1.

[0058] The above uses the center frequency f of the Lth channel signal. L The mapping result b(α) serves as the baseline. l ,f L The specific derivation is as follows: ,θ,φ),

[0059]

[0060] Where c represents the speed of light, (y1,z1)=(0,0), i.e. b(α) l ,f L ,θ,φ) and a(f l If the first element of b(α, θ, φ) is equal, then b(α) l ,f L The first element of (α, θ, φ) is removed to avoid duplicate elements in the synthesized virtual array guide vector, resulting in b(α, θ, φ). l ,f L ,θ,φ)=[b2(α l ,f L ,θ,φ),b3(α l ,f L ,θ,φ)] T .

[0061] Step 4) Select M valid channel data from L-1 channels, map their center frequencies to the center frequency of the Lth channel signal, and combine them to obtain a 2M+3 element virtual array receiving frequency f. L signal

[0062] Specifically as follows:

[0063]

[0064] wherein X v (f L ) represents the signal received by the virtual array at the Lth channel, X(f M ) represents the result of mapping the signal of the Mth channel to the Lth channel, b(α M ,f L ,θ,φ) represents the steering vector of X(f M ), n(f M ) represents the noise of the Mth channel, A v (θ,φ) represents the synthesized steering vector, N v (f L ) represents the noise of the synthesized signal.

[0065] Step 5) calculating the covariance R v of the virtual array received signal:

[0066]

[0067] wherein, represents the power of the received signal, represents the noise power, I represents the unit matrix with the dimension of (2M+1)×(2M+1); H represents the conjugate transpose operation.

[0068] Step 6) extracting the phase of the upper triangular elements of the covariance matrix by using a phase discriminator;

[0069] Step 7) based on the principle of long-short baseline method, selecting the frequency point relationship coefficient α to construct the virtual array structure, according to the virtual array structure, selecting the phase difference corresponding to the virtual baseline in the extracted phase, and using the long-short baseline method to realize the unambiguous direction finding of the two-dimensional interferometer.

[0070] The virtual array structure in the embodiment is implemented as follows:

[0071] (7a1) obtaining the frequency point relationship coefficient α by taking half wavelength as the limit:

[0072]

[0073] wherein λ represents the signal wavelength, D=max(D1,D2) represents the larger value in D1 and D2, and D1 and D2 respectively represent the distance between two non-reference antennas and the reference antenna in the sparse plane physical array;

[0074] (7a2) multiplying the non-reference antenna position by α to obtain the virtual array element position, and using the virtual array element and the physical antenna to jointly constitute the virtual array.

[0075] In the embodiment, the phase difference corresponding to the virtual baseline is selected in the extracted phase, and specifically, the indexes M0 of the selected channel data are selected according to α, and the elements in positions (1, 2), (1, 3), (2, 2M0+2) and (3, 2M0+3) in the extracted phase are selected, that is, the phase difference corresponding to the virtual baseline.

[0076] In the embodiment, the long-short baseline method is used to realize the unambiguous direction finding of the two-dimensional interferometer, and the implementation steps are as follows:

[0077] (7b1) According to the linear correlation between the phase difference and the baseline length, the ambiguity degree of the long baseline phase difference, that is, the number k of times of exceeding 2π, is calculated by using the length relationship between the short baseline and the long baseline and combining the unambiguous phase difference of the short baseline.

[0078] (7b2) The unambiguous phase difference of the long baseline is calculated by the following formula:

[0079]

[0080] Wherein, represents the ambiguous phase difference of the long baseline, which is determined according to the phase in the triangular elements of the covariance matrix.

[0081] (7b3) Based on the unambiguous phase differences corresponding to the two long baselines, the two-dimensional DOA estimation result is obtained by the following formula:

[0082]

[0083] Wherein, represents the estimated value of the pitch angle, represents the estimated value of the azimuth angle; represents the unambiguous phase difference of the signals received by the antenna 1 and the antenna 2, represents the unambiguous phase difference of the signals received by the antenna 1 and the antenna 3.

[0084] Embodiment two: The overall implementation steps of the direction finding method proposed in the embodiment are the same as those of embodiment one, and now refer to Figure 2 , wherein (a) is a schematic diagram of a four-element sparse planar array structure, which is an array structure diagram of the most similar implementation scheme of the present application; (b) is a schematic diagram of a three-element sparse planar array structure, which is a physical array structure diagram for illustrating the technical route of the present application, and also contains the spatial position expression of the virtual elements; the implementation process of the present application is further described in detail with specific examples:

[0085] It is assumed that the array surface of the three-element sparse planar array is located in the YOZ plane, as shown in Figure 2 (b) of the present application, wherein the elements 1, 2 and 3 are physical elements, and the elements 4 and 5 are virtual elements.

[0086] At time t, the frequency domain form of the signal received by the qth physical array element is represented as:

[0087] x q (f) = a q (f, θ, φ) s(f) + n q (f), q = 1, 2, 3 <1>

[0088] wherein a q (f, θ, φ) = exp[-j2π(f / c)(dy q sin θ sin φ + dz q cos φ)], s(f) represents the discrete Fourier transform of the incident signal complex envelope, f represents the frequency of the incident signal, n q (f) represents the frequency domain form of the noise component of the signal received by the qth array element, which is independent and identically distributed additive white Gaussian noise with a variance of which is irrelevant to the signal component.

[0089] Assuming that the original wideband signal is uniformly channelized and only L continuous channels have signals, the set of center frequencies of the channels can be represented as {f1, f2,..., f L}. Therefore, the steering vector a(f l , θ, φ) of the physical array receiving the signal of the lth channel is:

[0090]

[0091] u = sin θ sin φ <3>

[0092] v = cos φ <4>wherein (y1, z1) = (0, 0).

[0093] According to formula <1>, the signal model vector of the lth channel is expressed as:

[0094] X(f l ) = a(f l , θ, φ) S(f l ) + N(f l ) <5>

[0095] wherein,

[0096]

[0097]

[0098] N represents the number of sampling points.

[0099] Taking the center frequency f L of the signal of the Lth channel as a reference, the center frequency of the signal of the lth channel is represented as:

[0100] f l = a l f L <8>

[0101] wherein a l represents a frequency point relation coefficient, 0 < a l ≤ 1, when l = L, a l = 1.

[0102] Substituting formula <8> into a(f l , θ, φ), the steering vector of the lth channel signal is obtained as:

[0103]

[0104] wherein (y1, z1) = (0, 0), so b1(a l , f L , θ, φ) = a1(f l , θ, φ). In order to avoid the repetition of the elements of the synthesized virtual array steering vector, b1(a l , f L , θ, φ) is thus eliminated, i.e.:

[0105] b(a l , f L , θ, φ) = [b2(a l , f L , θ, φ), b3(a l , f L , θ, φ)] T <10>

[0106] Therefore, the lth channel signal is represented as:

[0107] X(f l ) = b(a l , f L , θ, φ)S(f l ) + N(f l )<11>

[0108] Suppose the bandwidth of the wideband signal is B, for the selectable frequency set {f1, f2,..., f L-1}, the following can be obtained:

[0109]

[0110] wherein a min and a max are the minimum value and the maximum value of the selectable coefficient. Let the physical array element spacing be D, then the virtual baseline length formed by the virtual array elements (array elements 4, 5) and the reference array elements (array elements 2, 3) ranges from [(1 - a maxD, (1 - α min )D] Thus, there are three relationships between the reference channel signal frequency and the range:

[0111]

[0112] Simplifying equation <14> gives:

[0113]

[0114] Considering the size limitation of the array platform, only the case of D < c / (2f L - 2f L-1 ) is discussed. When the received signal bandwidth B < c / (2D), there is no phase ambiguity for the virtual baseline constructed by all the channel signals; when the received signal bandwidth B > c / (2D), the virtual baseline constructed by the signals with channel center frequency greater than f L -c / (2D) has no phase ambiguity, and the virtual baseline constructed by the signals with channel center frequency less than f L -c / (2D) has phase ambiguity.

[0115] Suppose there are M frequency point signals, M ≤ L, and f L > f1>... > f m >... > f M = (f L -B), i.e., 1 > α1> α2>... > α m >... > α M > 0, combining these signals gives:

[0116]

[0117] where, Expanding A v (θ, φ) gives:

[0118]

[0119] As can be seen from equation <16>, its expression form is equivalent to the received signal model of a sparse planar array. In the case of high signal-to-noise ratio, the phase of each row of X v (f L ) can be directly extracted, and two-dimensional DOA estimation can be realized by using interferometer direction finding. However, when the signal-to-noise ratio is low, the directly extracted phase information is almost overwhelmed by noise, so subsequent processing cannot be realized. By means of signal cross-correlation, this problem can be solved.

[0120] The covariance of X v is:

[0121]

[0122] in, Let represent the power of the Lth channel signal received by the virtual planar array, and I represent the identity matrix with dimensions (2M+3)×(2M+3). According to R... v The structure allows the phase difference of the corresponding baseline to be obtained by extracting the phase of an element at a certain row and column position using a phase detector, and then direction finding is performed using a two-dimensional interferometer.

[0123] by Figure 2 Taking (b) as an example, the m-th frequency signal is combined with the reference channel signal to form a virtual sparse planar array, where the positions of virtual array elements 4 and 5 are respectively (α... m y2,α m z2), (α) m y3,α m z3), the array element formed virtually by array element 1 coincides with the position of array element 1. Therefore, the phase difference of all baselines can be obtained by extracting the phase of the covariance elements, i.e. and Typically, baselines 1-2 and 1-3 are much larger than half a wavelength, therefore and Both are fuzzy phase differences, and and Whether there is ambiguity depends on the frequency signal selected.

[0124] Assumption and Since there is no ambiguity, the long and short baseline method can be used to deambiguate based on the virtual baseline length and the unambiguous phase difference, obtaining the physical baselines 1-2 and 1-3 at the reference frequency f. L Unambiguous phase difference and Since virtual baselines 4-2 and 5-3 are obtained through f m =α m f L Mapped from, virtual baseline length d 4,2 =(1-α) m )d 1,2 d 5,3 =(1-α) m )d 1,3 To ensure that both virtual baselines are simultaneously less than or equal to half the wavelength, we have:

[0125]

[0126] That is, satisfying:

[0127]

[0128] The unambiguous phase difference between baselines 1-2 and 1-3 is obtained using the long and short baseline method. and The two-dimensional DOA estimation can be solved, as shown in the following formula

[0129]

[0130] The two-dimensional DOA estimation can be solved theoretically through formula 21. Of course, due to the existence of noise, and d 1,2 and d 1,3 is much larger than half the wavelength, so selecting only two frequency points to construct a virtual array may also cause the unblurring to fail, therefore, by selecting multiple frequency points, the array combinations required by the long-short baseline step-by-step unblurring method can be constructed, and the success rate of two-dimensional DOA estimation unblurring can be further improved.

[0131] The present application maps the multi-frequency signals of the channelized wideband signal to the same frequency point, and constructs a virtual sparse planar array using the relationship between the reference frequency point and each frequency point to estimate the direction of arrival. Compared with the existing scheme, it uses fewer array elements, and only three array elements are used to realize the two-dimensional direction of arrival estimation of the wideband signal; and there is no requirement for the array configuration, which can relax the degree of freedom restriction of the physical array arrangement; at the same time, the proposed algorithm has good direction finding performance.

[0132] The effect of the present application will be further described below in combination with simulation experiments.

[0133] 1. Simulation conditions:

[0134] The simulation experiment of the present application is carried out in the software environment of MATLAB2024a.

[0135] 2. Simulation content:

[0136] For the working frequency band of 2-8GHz, considering the case that the received signal bandwidth B> c / (2D), three frequency points are selected to construct a virtual array, and the two-dimensional DOA estimation is carried out through the long-short baseline step-by-step unblurring method. Among them, frequency point 1 is the reference frequency point f L , frequency point 2 is (f L -60MHz), and frequency point 3 is alpha m f L =0.95f L . It is worth noting that in order to ensure that all received signals in the working frequency band can virtually form a short baseline, based on the physical array set in table 1, the selection of frequency point 2 must satisfy f L -f m <c / (2D) = 66.7MHz, so the frequency point 2 of all simulation experiments is selected as (f L-60MHz). At the same time, in order to construct a multi-stage long-short baseline, the virtual baseline constructed by the frequency point 3 signal must be greater than the half wavelength of the frequency point 1 signal, therefore, the frequency point 3 of the present application is selected as 0.95f L .

[0137] Table 1 simulation parameter setting table

[0138]

[0139]

[0140] Simulation 1: Influence of signal-to-noise ratio on algorithm performance

[0141] In this simulation experiment, the signal-to-noise ratio is set to (-10:2:0) dB, the sampling point number is 500, the channel phase error is 10°, and the channel amplitude error is 1 dB; the simulation results are shown in Figs. 1 and 2. Figure 3 and 4

[0142] Simulation 2: Relationship between two-dimensional DOA estimation accuracy, de-mangling success rate and sampling point number

[0143] In this simulation experiment, the signal-to-noise ratio is set to 0 dB, the sampling point number is (100:100:1000), the channel phase error is 10°, and the channel amplitude error is 1 dB; the simulation results are shown in Figs. 3 and 4. Figure 5 and 6

[0144] Simulation 3: Relationship between two-dimensional DOA estimation accuracy, de-mangling success rate and selected frequency point interval

[0145] In this simulation experiment, the signal-to-noise ratio is set to 0 dB, the sampling point number is 500, the channel phase error is 10°, and the channel amplitude error is 1 dB. Since frequency point 2 is only used to construct a virtual short baseline smaller than the half wavelength of the signal, the change of frequency point 2 is not considered, and the selection coefficient of frequency point 3 is set to (0.9:0.01:0.97); the simulation results are shown in Figs. 5 and 6. Figure 7 and 8

[0146] 3. Analysis of simulation results:

[0147] Figure 3 Fig. 7 is a graph of the relationship between the two-dimensional DOA estimation de-mangling success rate and SNR, wherein it can be seen that the two-dimensional DOA estimation de-mangling success rate is similar under different reference frequency points, and increases with the increase of the signal-to-noise ratio. When the signal-to-noise ratio is -2 dB, the de-mangling success rate of all signals reaches more than 90%. At a signal-to-noise ratio of 0 dB, the de-mangling success rate of all signals is close to 100%.

[0148] ​​​Figure 4 In the figure, (a) is the relationship diagram of azimuth angle estimation accuracy and SNR, (b) is the relationship diagram of elevation angle estimation accuracy and SNR, wherein it can be seen that the azimuth angle and elevation angle estimation accuracy increase with the increase of the signal-to-noise ratio, but the trend is relatively slow. When the signal-to-noise ratio is 0 dB, the two-dimensional DOA estimation error of all reference frequency signals is less than 0.4°. The reason for the slow curve decline is that the direction finding accuracy statistics only uses the results of unambiguous direction finding, and the phase difference extraction method in the present application makes the unambiguous direction finding results relatively insensitive to noise.

[0149] Figure 5 In the figure, (a) is the relationship diagram of azimuth angle estimation accuracy and SNR, (b) is the relationship diagram of elevation angle estimation accuracy and SNR, wherein it can be seen that the azimuth angle and elevation angle estimation accuracy increase with the increase of the signal-to-noise ratio, but the trend is relatively slow. When the signal-to-noise ratio is 0 dB, the two-dimensional DOA estimation error of all reference frequency signals is less than 0.4°. The reason for the slow curve decline is that the direction finding accuracy statistics only uses the results of unambiguous direction finding, and the phase difference extraction method in the present application makes the unambiguous direction finding results relatively insensitive to noise.

[0150] Figure 6 In the figure, (a) is the relationship diagram of azimuth angle estimation accuracy and SNR, (b) is the relationship diagram of elevation angle estimation accuracy and SNR, wherein it can be seen that the azimuth angle and elevation angle estimation accuracy increase with the increase of the signal-to-noise ratio, but the trend is relatively slow. When the signal-to-noise ratio is 0 dB, the two-dimensional DOA estimation error of all reference frequency signals is less than 0.4°. The reason for the slow curve decline is that the direction finding accuracy statistics only uses the results of unambiguous direction finding, and the phase difference extraction method in the present application makes the unambiguous direction finding results relatively insensitive to noise.

[0151] Figure 7 In the figure, (a) is the relationship diagram of azimuth angle estimation accuracy and SNR, (b) is the relationship diagram of elevation angle estimation accuracy and SNR, wherein it can be seen that the azimuth angle and elevation angle estimation accuracy increase with the increase of the signal-to-noise ratio, but the trend is relatively slow. When the signal-to-noise ratio is 0 dB, the two-dimensional DOA estimation error of all reference frequency signals is less than 0.4°. The reason for the slow curve decline is that the direction finding accuracy statistics only uses the results of unambiguous direction finding, and the phase difference extraction method in the present application makes the unambiguous direction finding results relatively insensitive to noise.

[0152] Figure 8 In the figure, (a) is the relationship diagram of azimuth angle estimation accuracy and SNR, (b) is the relationship diagram of elevation angle estimation accuracy and SNR, wherein it can be seen that the azimuth angle and elevation angle estimation accuracy increase with the increase of the signal-to-noise ratio, but the trend is relatively slow. When the signal-to-noise ratio is 0 dB, the two-dimensional DOA estimation error of all reference frequency signals is less than 0.4°. The reason for the slow curve decline is that the direction finding accuracy statistics only uses the results of unambiguous direction finding, and the phase difference extraction method in the present application makes the unambiguous direction finding results relatively insensitive to noise.

[0153] It should be noted that the user information (including but not limited to user equipment information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present application are information and data authorized by the user or authorized by all parties, and the collection, use and processing of related data need to comply with relevant national and regional laws, regulations and standards, and provide corresponding operation portal for user to choose authorization or refusal.

[0154] The simulation analysis proves the correctness and effectiveness of the method.

[0155] The part not described in detail in the present application belongs to the common knowledge of those skilled in the art.

[0156] The above only describes the preferred embodiments of the present application, and does not limit the present application. Obviously, for those skilled in the art, after understanding the content and principles of the present application, various modifications and changes in form and details can be made without departing from the principles and structures of the present application, but these modifications and changes based on the idea of the present application are still within the protection scope of the claims of the present application.

Claims

1. A method of direction finding based on a multi-frequency sparse planar array two-dimensional interferometer, characterized in that, The method comprises the following steps: (1) arranging three non-collinear antennas in the YOZ plane of a spatial coordinate system to construct a sparse planar physical array, wherein the antennas receive a wideband signal, and the frequency domain form of the wideband signal is represented as follows: x q (f) = a q (f, θ, φ) s(f) + n q (f), where x q (f) represents the frequency domain form of the signal received by the qth antenna; s(f) represents the discrete Fourier transform of the complex envelope of the incident signal; n q (f) represents the frequency domain form of the noise component of the signal received by the qth antenna; a q (f, θ, φ) represents the complex exponential of the phase difference between the signals received by the qth antenna and the first antenna from the source target signal with frequency f, azimuth angle θ, and elevation angle φ; q = 1, 2, 3. (2) performing channelization processing on the wideband signal received by the three antennas to obtain a vector signal model of the lth channel, and the implementation steps are as follows: (2.1) Assume that after the original broadband signal is processed by uniform channelization, only L consecutive channels exist, and the set of center frequencies of the channels is {f1, f2, ..., f...} L }; then the steering vector of the physical array receiving the l-th channel signal is a(f l ,θ,φ): where u = sin 0 sin φ, v = cos φ, (y q ,z q ) denotes the coordinates of the qth antenna in the YOZ plane. (2.2) Let the number of sampling points be N, then the source and target signals S(f l ) and N(f l ) are represented as follows: where s N (f l ) represents the Nth sample point of the source-target continuous signal, represents the combination of the Nth sample point of the continuous noise received by all antennas; (2.3) obtaining the vector signal model of the lth channel according to the following formula: X(f l ) = a(f l , θ, φ)S(f l ) + N(f l ), Wherein, l = 1, 2,..., L, and L is the total number of channels; (3) the center frequency f L As a reference, the center frequency f l is mapped to obtain the vector signal model of the mapped lth channel: X(f l ) = b(α L ,f l ,θ,φ)S(f L )+N(f l ), Wherein, b(a l ,f L ,θ,φ) represents the mapping result of a(f l ,θ,φ) with the center frequency f L of the Lth channel signal as the reference, a l represents a frequency point relationship coefficient; X(f l ) is equivalent to the signal received by the 5-element virtual array at the frequency f L ; (4) Select M valid channel data in L-1 channels, map the center frequencies of all to the center frequency of the Lth channel signal, and after merging, obtain a 2M+3-element virtual array receiving a signal with a frequency of f L ​ (5) compute the covariance R of the virtual array receive signals v ; (6) extracting the phase of the upper triangular element of the covariance matrix by using a phase detector; (7) selecting a frequency point relationship coefficient α to construct a virtual array structure based on the principle of long-short baseline method, selecting a phase difference corresponding to a virtual baseline in the extracted phase according to the virtual array structure, and realizing two-dimensional interferometer unambiguous direction finding by using the long-short baseline method.

2. The method of claim 1, wherein: The center frequency f of the first channel signal in step (3) l The specific expression is as follows: f l = a l f L , wherein α l represents a frequency point relationship coefficient, 0 < α l ≤ 1, and when l = L, α l = 1.

3. The method of claim 1, wherein: Step (3) the center frequency f L of the Lth channel signal is derived from the mapping result b(α l ,f L ,θ,φ) as a reference according to the following equation: Where c represents the speed of light, (y1,z1)=(0,0), i.e. b(α) l ,f L ,θ,φ) and a(f l If the first element of b(α, θ, φ) is equal, then b(α) l ,f L The first element of (α, θ, φ) is removed to avoid duplicate elements in the synthesized virtual array guide vector, resulting in b(α, θ, φ). l ,f L ,θ,φ)=[b2(α l ,f L ,θ,φ),b3(α l ,f L ,θ,φ)] T .

4. The method of claim 1, wherein: The combining in step (4) results in a 2M+3 virtual array receiving a signal with a frequency of f L In detail as follows:​ where X(f v ) (f L ) represents the signal received by the virtual array for the Lth channel, X(f M ) represents the result of mapping the Mth channel signal to the Lth channel, b(a M ,f L , θ, φ) represents the steering vector of X(f M ), n(f M ) represents the noise of the Mth channel, A v (θ, φ) represents the resultant steering vector, and N v (f L ) represents the noise component of the resultant signal.

5. The method of claim 1, wherein: The virtual array receives the signal covariance R according to the following formula: v , according to the following formula: wherein denotes the power of the received signal, denotes the noise power, I denotes the identity matrix of dimension (2M+1) x (2M+1); H denotes the conjugate transpose operation.

6. The method of claim 1, wherein: The virtual array structure in step (7) is implemented as follows: (7a1) obtaining the frequency point relationship coefficient α by taking half wavelength as a limit: Wherein, λ represents the wavelength of the signal, D = max(D1, D2) represents the larger value of D1 and D2, and D1 and D2 respectively represent the distance between two non-reference antennas and a reference antenna in the sparse planar physical array; (7a2) multiplying the position of the non-reference antenna by α to obtain the position of the virtual array element, and using the virtual array element and the physical antenna to jointly constitute a virtual array.

7. The method of claim 6, wherein: The selection of the phase difference corresponding to the virtual baseline in the extracted phase is specifically that the index M0 of the selected channel data is obtained according to α, and the elements at positions (1, 2), (1, 3), (2, 2M0+2) and (3, 2M0+3) in the extracted phase are selected, that is, the phase difference corresponding to the virtual baseline.

8. The method of claim 1, wherein: The long-short baseline method in step (7) is used to realize two-dimensional interferometer unambiguous direction finding, and the implementation steps are as follows: (7b1) according to the linear correlation between the phase difference and the baseline length, using the length relationship between the short baseline and the long baseline, and combining the unambiguous phase difference of the short baseline, the ambiguity degree of the long baseline phase difference, that is, the number k of exceeding 2π, is calculated; (7b2) calculating the unambiguous phase difference of the long baseline by the following formula: wherein represents the ambiguous phase difference of the long baseline; (7b3) obtaining the two-dimensional DOA estimation result based on the unambiguous phase difference corresponding to the two long baselines by the following formula: wherein denotes the pitch angle estimate, denotes the azimuth angle estimate; denotes the unambiguous phase difference of the signals received by antenna 1 and antenna 2, denotes the unambiguous phase difference of the signals received by antenna 1 and antenna 3.

9. The method of claim 7, wherein: The ambiguous phase difference of the long baseline in step (7b2) is determined according to the phase in the upper triangular element of the covariance matrix extracted by the phase detector.

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