Weak target signal direction finding method under strong interference

Abstract

The invention discloses a weak target signal direction finding method under strong interference, and the method comprises the steps: carrying out the signal direction finding through employing a double-circulation nesting mode, updating the signal angle of a current estimation number signal in each internal circulation so as to carry out the direction finding, enabling the estimation number of the signal to add 1 in each external circulation, and carrying out the direction finding. And when direction finding is carried out on the current estimation signal in each inner cycle, separating other newly obtained known signals except the current signal from the received signal data, and estimating the signal angle of the current signal from the received signal data after separation processing through beam forming. And correcting the estimated signal angle by using a preset angle correction closed expression to obtain a signal angle estimated value of the current signal, and calculating the current signal by using a preset complex signal solution expression based on the signal angle estimated value. According to the method provided by the invention, simultaneous accurate direction finding of strong interference signals and weak target signals under the condition of few snapshots or even single snapshots can be realized, and zero padding operation does not need to be carried out.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a method for direction finding of weak target signals under strong interference. Background Art

[0002] In a complex electromagnetic environment, there are various interferences and noises. The signals received by the array are often of unequal power. Strong power interference signals and weak power target signals to be estimated are intertwined and difficult to distinguish. When the radio direction finding system is affected by a complex electromagnetic environment, its anti-interference, accuracy and real-time performance will show a significant downward trend.

[0003] Traditional methods for direction finding of weak target signals under strong interference are generally divided into two categories according to the processing ideas. One is to find the direction of strong interference and weak target signals at the same time, and the other is to find the direction of weak target signals after suppressing strong interference. The more typical methods in the first category are the RELAX algorithm and the CLEAN algorithm. However, in practical applications, this type of method has a large number of iterations and a large amount of calculation, and in order to improve the estimation accuracy, zero padding operations are also required. The more typical methods in the second category are the interference blocking algorithm proposed by Chen Hui et al. and the modified projection blocking method proposed by Dong Hui et al. Under the premise that the direction of the strong interference signal is known or the direction of the strong interference signal has been pre-estimated, the interference blocking algorithm designs an interference blocking matrix to suppress the strong interference signal. At this time, the blocking process will turn the noise term into colored noise, and further pre-whitening will turn the colored noise term into white noise, and then the spatial spectrum algorithm will be combined to find the direction of the weak target signal. The algorithm has low computational complexity and is easy to apply in practice. However, it requires more snapshots to ensure accuracy during signal direction finding. When the number of snapshots in a dynamic environment is small, the direction of the target signal cannot be accurately estimated. In addition, the ability to suppress strong interference is obtained through array element loss. When the number of interferences is large, the more the dimension of the data covariance matrix is ​​reduced, the number of target signals that can be measured will also decrease accordingly. The modified projection blocking method uses the idea of ​​modified projection. It does not require the interference direction to be known in advance, and the algorithm is more robust when the array has a certain phase error. However, when the signal-to-noise ratio is low, the direction finding accuracy is lower than that of the traditional interference blocking method. In addition, the algorithm still requires direction finding under multiple snapshots. When the number of snapshots in a dynamic environment is small, the direction of the target signal cannot be accurately estimated. Summary of the invention

[0004] In order to solve some or all of the technical problems existing in the above-mentioned prior art, the present invention provides a method for direction finding of weak target signals under strong interference.

[0005] The technical solution of the present invention is as follows:

[0006] A method for direction finding of weak target signals under strong interference is provided, the method comprising the following steps:

[0007] Step 1, Setup The signal angle of the first signal is estimated from the received signal data by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the first signal, and the first signal is calculated by using a preset complex signal solution expression based on the signal angle estimation value;

[0008] Step 2, Setup Separate the latest first signal from the received signal data, estimate the signal angle of the second signal from the separated received signal data through beamforming, correct the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the second signal, and calculate the second signal based on the signal angle estimate using a preset complex signal solution expression; Separate the latest second signal from the received signal data, estimate the signal angle of the first signal from the separated received signal data through beamforming, correct the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculate the first signal based on the signal angle estimate using a preset complex signal solution expression;

[0009] Step 3, looping through step 2 until both the signal angle estimation value of the first signal and the signal angle estimation value of the second signal satisfy a preset convergence condition and then proceeding to the next step;

[0010] Step 4: If K=2, output the two latest signals and the signal angle estimation value; if K≥3, proceed to the next step;

[0011] Step 5, let

[0012] Step 6: Send the latest first signal to the The signal is separated from the received signal data, and the first signal is estimated from the separated received signal data by beamforming. The signal angle of the first signal is corrected by using the preset angle correction closed-form expression to obtain the The signal angle estimation value of the signal is calculated based on the signal angle estimation value by using the preset complex signal solution expression. signals; for the first signal to the The following operations are performed on each signal to update the signal: the latest known signals other than the current signal are separated from the received signal data, the signal angle of the current signal is estimated from the received signal data after separation by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the current signal, and based on the signal angle estimation value, the current signal is calculated by using a preset complex signal solution expression;

[0013] Step 7, repeat step 6 until the obtained After the signal angle estimation values ​​of all signals meet the preset convergence conditions, proceed to the next step;

[0014] Step 8, judgement Is it greater than or equal to K? If so, output the latest If not, return to step 5.

[0015] In some optional implementations, the current signal is set as the kth signal, and the received signal data after the latest known signals other than the current signal are separated from the received signal data is expressed as:

[0016]

[0017] Among them, y k represents the received signal data from which other known signals other than the kth signal have been separated, Y represents the original received signal data, Indicates the number of signals contained in the known original received signal data Y, s i represents the ith signal, a(θ i ) represents the steering vector of the i-th signal, θ i Represents the signal angle of the i-th signal.

[0018] In some optional implementations, the angle correction closed-form expression is expressed as:

[0019]

[0020] in, Represents the signal angle estimation value, arcsin represents the inverse sine trigonometric function calculation, Represents the position difference vector of adjacent elements in the antenna array, represents a triangular matrix, g(r) represents a custom vector, π represents pi, the superscript T represents a transpose operation, and the superscript -1 represents an inverse operation;

[0021] Triangle Array It is expressed as:

[0022]

[0023] The vector g(r) is solved using the following formula:

[0024]

[0025] Among them, sin represents the calculation of sine trigonometric function, θ represents the signal angle, and ε represents the colored Gaussian noise vector;

[0026] Here, the signal angle θ used to calculate the vector g(r) uses the signal angle estimated from the received signal data through beamforming.

[0027] In some optional implementations, the complex signal solution expression is expressed as:

[0028]

[0029] Among them, s represents the current signal to be solved, express The conjugate matrix of represents the steering vector of the signal, y represents the received signal data from which other known signals other than the current signal have been separated, and N represents the number of elements in the antenna array.

[0030] In some optional implementations, the convergence condition is set to:

[0031]

[0032] in, represents the signal angle estimate of the kth signal obtained in the h+1th cycle, represents the signal angle estimation value of the kth signal obtained in the hth cycle, and τ represents the preset tolerance.

[0033] In some optional implementations, the tolerance τ is set to the value of the smallest Cramer-Rao bound within the signal-to-noise ratio range.

[0034] The main advantages of the technical solution of the present invention are as follows:

[0035] The method for direction finding of weak target signals under strong interference of the present invention adopts a double loop nesting mode, wherein each inner loop updates the signal angle of the current estimated number of signals, each outer loop increases the estimated number of signals by 1, and when each inner loop performs direction finding on the current estimated signal, other known signals except the current estimated signal are separated from the received signal data, the signal angle is estimated from the separated received signal data through beam forming, and the estimated signal angle is corrected using an angle correction closed-form expression, which can significantly improve the signal direction finding accuracy, realize simultaneous and accurate direction finding of strong interference signals and weak target signals in the case of few snapshots or even single snapshot, and no zero padding operation is required. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings described herein are used to provide a further understanding of the embodiments of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0037] Figure 1 A flowchart of a method for direction finding of weak target signals under strong interference provided by an embodiment of the present invention;

[0038] Figure 2 to Figure 5 The signal spatial spectra are obtained by processing signals with a signal-to-noise ratio of 0 dB, a signal-to-noise ratio of 5 dB, a signal-to-noise ratio of 10 dB, and a signal-to-noise ratio of 20 dB using the direction finding method for weak target signals under strong interference provided in Example 1 of the present invention;

[0039] Figure 6-7 The signal spatial spectra are respectively obtained by processing the signals with a signal-to-noise ratio of 5 dB and a signal-to-noise ratio of 10 dB using the direction finding method for weak target signals under strong interference provided in Example 2 of the present invention;

[0040] Figure 8 This is a schematic diagram of the change in mean square error when signal processing is performed using a weak target signal direction finding method under strong interference under different noise power conditions provided in Example 3 of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0042] The technical solution provided by the embodiments of the present invention is described in detail below with reference to the accompanying drawings.

[0043] See also Figure 1 The embodiment of the present invention provides a method for direction finding of weak target signals under strong interference, the method comprising the following steps:

[0044] Step 1, Setup The signal angle of the first signal is estimated from the received signal data by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the first signal, and the first signal is calculated by using a preset complex signal solution expression based on the signal angle estimation value;

[0045] Step 2, Setup Separating the newly obtained first signal from the received signal data, estimating the signal angle of the second signal from the separated received signal data by beamforming, correcting the estimated signal angle by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the second signal, and calculating the second signal by using a preset complex signal solution expression based on the signal angle estimation value;

[0046] Separating the newly obtained second signal from the received signal data, estimating the signal angle of the first signal from the separated received signal data by beamforming, correcting the estimated signal angle by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the first signal, and calculating the first signal by using a preset complex signal solution expression based on the signal angle estimation value;

[0047] Step 3, looping through step 2 until both the signal angle estimation value of the first signal and the signal angle estimation value of the second signal satisfy a preset convergence condition and then proceeding to the next step;

[0048] Step 4: If K=2, output the two latest signals and the signal angle estimation value; if K≥3, proceed to the next step;

[0049] In the embodiment of the present invention, K represents the number of signals included in the received signal data.

[0050] Step 5, let

[0051] Step 6: Send the latest first signal to the The signal is separated from the received signal data, and the first signal is estimated from the separated received signal data by beamforming. The signal angle of the first signal is corrected by using the preset angle correction closed-form expression to obtain the The signal angle estimation value of the signal is calculated based on the signal angle estimation value by using the preset complex signal solution expression. A signal;

[0052] For the first signal to the The following operations are performed on each signal to update the signal: the latest known signals other than the current signal are separated from the received signal data, the signal angle of the current signal is estimated from the received signal data after separation by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the current signal, and based on the signal angle estimation value, the current signal is calculated by using a preset complex signal solution expression;

[0053] Specifically, in the embodiment of the present invention, For example, for the first signal to the The following operations are performed on each signal to update the signal: the latest known signals other than the current signal are separated from the received signal data, the signal angle of the current signal is estimated from the received signal data after separation by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain the signal angle estimation value of the current signal, and based on the signal angle estimation value, the current signal is calculated by using a preset complex signal solution expression, which is specifically expressed as:

[0054] The most recently obtained second signal and the third signal are separated from the received signal data, the signal angle of the first signal is estimated from the separated received signal data through beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the first signal, and based on the signal angle estimation value, the first signal is calculated using a preset complex signal solution expression; the most recently obtained first signal and the third signal are separated from the received signal data, the signal angle of the second signal is estimated from the separated received signal data through beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the second signal, and based on the signal angle estimation value, the second signal is calculated using a preset complex signal solution expression.

[0055] Specifically, in the embodiment of the present invention, For example, for the first signal to the The following operations are performed on each signal to update the signal: the latest known signals other than the current signal are separated from the received signal data, the signal angle of the current signal is estimated from the received signal data after separation by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain the signal angle estimation value of the current signal, and based on the signal angle estimation value, the current signal is calculated by using a preset complex signal solution expression, which is specifically expressed as:

[0056] Separate the newly obtained second signal, third signal and fourth signal from the received signal data, estimate the signal angle of the first signal from the separated received signal data by beamforming, correct the estimated signal angle by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the first signal, and calculate the first signal by using a preset complex signal solution expression based on the signal angle estimation value;

[0057] Separating the most recently obtained first signal, third signal, and fourth signal from the received signal data, estimating the signal angle of the second signal from the separated received signal data by beamforming, correcting the estimated signal angle by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the second signal, and calculating the second signal by using a preset complex signal solution expression based on the signal angle estimation value;

[0058] The newly obtained first signal, second signal and fourth signal are separated from the received signal data, and the signal angle of the third signal is estimated from the separated received signal data through beamforming. The estimated signal angle is corrected using a preset angle correction closed expression to obtain a signal angle estimation value of the third signal. Based on the signal angle estimation value, the third signal is calculated using a preset complex signal solution expression.

[0059] Step 7, repeat step 6 until the obtained After the signal angle estimation values ​​of all signals meet the preset convergence conditions, proceed to the next step;

[0060] Step 8, judgement Is it greater than or equal to K? If so, output the latest If not, return to step 5.

[0061] The method for direction finding of weak target signals under strong interference provided by an embodiment of the present invention adopts a double-loop nesting method, wherein each inner loop updates the signal angle of the current estimated number of signals, each outer loop increases the estimated number of signals by 1, and when each inner loop performs direction finding on the current estimated signal, other known signals except the current estimated signal are separated from the received signal data, and the signal angle is estimated from the separated received signal data through beamforming, and the estimated signal angle is corrected using an angle correction closed-form expression. This method can significantly improve the accuracy of signal direction finding, realize simultaneous and accurate direction finding of strong interference signals and weak target signals in the case of few snapshots or even a single snapshot, and does not require zero padding.

[0062] Further, in the embodiment of the present invention, taking the current signal as the kth signal as an example, the received signal data after separating the latest known signals other than the current signal from the received signal data can be expressed as:

[0063]

[0064] Among them, y k represents the received signal data from which other known signals other than the kth signal have been separated, Y represents the original received signal data, Indicates the number of signals contained in the known original received signal data Y, si represents the ith signal, a(θ i ) represents the steering vector of the i-th signal, θ i Represents the signal angle of the i-th signal.

[0065] Further, in an embodiment of the present invention, the angle correction closed-form expression is expressed as:

[0066]

[0067] in, Represents the signal angle estimation value, arcsin represents the inverse sine trigonometric function calculation, Represents the position difference vector of adjacent elements in the antenna array, represents a triangular matrix, g(r) represents a custom vector, π represents pi, the superscript T represents a transpose operation, and the superscript -1 represents an inverse operation.

[0068] In the embodiment of the present invention, the triangular array It is expressed as:

[0069]

[0070] In the embodiment of the present invention, the vector g(r) is solved using the following formula:

[0071]

[0072] in, represents the position difference vector of adjacent elements in the antenna array, π represents pi, sin represents the sine trigonometric function calculation, θ represents the signal angle, and ε represents the colored Gaussian noise vector.

[0073] It should be noted that, in the embodiment of the present invention, when the signal angle is corrected using the above angle correction closed-form expression, the signal angle θ used to calculate the vector g(r) uses the signal angle estimated from the received signal data through beamforming.

[0074] Further, in the embodiment of the present invention, the complex signal solution expression is expressed as:

[0075]

[0076] Among them, s represents the current signal to be solved, express The conjugate matrix of represents the steering vector of the signal, represents the signal angle estimation value, y represents the received signal data from which other known signals other than the current signal have been separated, and N represents the number of elements in the antenna array.

[0077] Furthermore, in an embodiment of the present invention, the convergence condition is set as:

[0078]

[0079] in, represents the signal angle estimate of the kth signal obtained in the h+1th cycle, represents the signal angle estimation value of the kth signal obtained in the hth cycle, τ represents the preset tolerance, and the tolerance τ is set according to the actual situation.

[0080] In the embodiment of the present invention, the tolerance τ is set to the smallest Cramer-Rao bound value within the signal-to-noise ratio range.

[0081] Furthermore, in the embodiment of the present invention, taking the kth signal as an example, the derivation process of the angle correction closed-form expression and the complex signal solution expression is described as follows:

[0082] Setting: The original received signal data is Y, and the received signal data Y contains A signal;

[0083] The kth signal can be obtained by separating other known signals except the kth signal from the received signal data, which can be expressed as:

[0084]

[0085] Among them, y k represents the kth signal, that is, the received signal data of other known signals except the kth signal, s i represents the ith signal, a(θ i ) represents the steering vector of the i-th signal, θ i Represents the signal angle of the i-th signal.

[0086] Furthermore, the kth signal can be expressed as:

[0087]

[0088] Among them, |s k | represents the amplitude of the kth signal, e represents a natural constant, j represents an imaginary unit, φ k represents the phase of the kth signal, a(θ k ) represents the steering vector of the kth signal, θ k represents the signal angle of the kth signal, and n0 represents the noise.

[0089] Furthermore, each element of the kth signal can be approximately expressed as:

[0090]

[0091] Among them, y k,n represents the nth element of the kth signal, |s k | represents the amplitude of the kth signal, e represents a natural constant, j represents an imaginary unit, c n represents the position of the nth element in the antenna array, π represents pi, sin represents the calculation of sine trigonometric function, θ k represents the signal angle of the kth signal, φ k represents the phase of the kth signal, N represents the number of elements in the antenna array, ε n represents the noise received by the nth array element, the noise ε n is zero-mean Gaussian white noise, and the variance of zero-mean Gaussian white noise is Represents the noise power.

[0092] Further, a vector r is defined, the vector r contains N-1 elements, and the nth element in the vector r is formed by the product of the nth element and the n+1th element of the kth signal vector;

[0093] Based on the above definition, the nth element in the vector r can be specifically expressed as:

[0094]

[0095] Among them, r n Represents the nth element of vector r, y k,n represents the nth element of the kth signal, y k,n+1 represents the n+1th element of the kth signal, |s k | represents the amplitude of the kth signal, e represents a natural constant, j represents an imaginary unit, c n+1 represents the position of the n+1th element in the antenna array, c n represents the position of the nth element in the antenna array, π represents pi, sin represents the calculation of sine trigonometric function, θ k represents the signal angle of the kth signal, ε n+1 represents the noise received by the n+1th array element, ε n represents the noise received by the nth array element, the noise ε n+1 and noise ε n All are zero-mean Gaussian white noise.

[0096] Based on the above definition, the phase of vector r can be expressed as:

[0097]

[0098] in, represents the phase of vector r, e i represents a (N-1)×1 dimensional column vector in which all elements except the i-th position are 0, i=1,2,...,N-1, the superscript T represents a transpose operation, and ∠(·) represents a phase operation.

[0099] It should be noted that if the array is a non-uniform array, phase ambiguity is inevitable.

[0100] Furthermore, the non-overlapping phase of each element of the vector r can be expressed as:

[0101]

[0102] Among them, g n (r) represents the non-overlapping phase of the nth element of vector r, represents the phase of the nth element of vector r, π represents pi, and κ n is an integer value;

[0103] Integer value κ n Solved by the following formula:

[0104]

[0105] Among them, round(·) represents the rounding function operation.

[0106] Further, define a vector g(r), which contains N-1 elements, and the nth element in the vector g(r) is composed of the non-overlapping phase g of the nth element of the vector r n (r), then the vector g(r) can be expressed as:

[0107]

[0108] in, Represents the position difference vector of adjacent elements in the antenna array, c1 represents the position of the first element in the antenna array, c2 represents the position of the second element in the antenna array, c3 represents the position of the third element in the antenna array, and c N-1 represents the position of the N-1th element in the antenna array, c N represents the position of the Nth element in the antenna array, π represents pi, sin represents the calculation of sine trigonometric function, θ k represents the signal angle of the kth signal, ε represents the colored Gaussian noise vector, ε=[ε2-ε1,ε3-ε2,…,ε N -ε N-1 ] T, ε1 represents the noise received by the first array element, ε2 represents the noise received by the second array element, ε3 represents the noise received by the third array element, and ε N-1 represents the noise received by the N-1th array element, ε N represents the noise received by the Nth array element, and the superscript T represents the transposition operation;

[0109] The covariance matrix Q of the colored Gaussian noise vector can be expressed as:

[0110]

[0111] Where ρ represents the signal-to-noise ratio, represents a triangular matrix;

[0112] Triangle Array It is expressed as:

[0113]

[0114] Furthermore, based on the above definition, πsinθ k The optimal maximum likelihood estimate of can be obtained by minimizing the following objective function:

[0115]

[0116] Among them, T(θ k ) represents the objective function, the superscript T represents the transposition operation, and the superscript -1 represents the inverse operation;

[0117] Therefore, the closed-form solution to the problem of direction finding a signal in colored Gaussian noise can be expressed as:

[0118]

[0119] in, represents the signal angle estimation value of the kth signal, the superscript T represents the transpose operation, and the superscript -1 represents the inverse operation.

[0120] According to the closed-form solution obtained above, the closed-form expression of the angle correction corresponding to the kth signal is expressed as:

[0121]

[0122] Among them, arcsin represents the calculation of the inverse sine trigonometric function.

[0123] After the signal angle of the k-th signal is iteratively corrected by the above angle correction closed-form expression to obtain an accurate signal angle estimate, the complex signal of the k-th signal can be solved by minimizing the following function:

[0124]

[0125] in, express The conjugate matrix of represents the steering vector of the kth signal;

[0126] For fixed Let the above function The derivative of is 0, then the signal s k It can be calculated by the following formula:

[0127]

[0128] in, express The conjugate matrix of , N represents the number of elements in the antenna array.

[0129] The beneficial effects of the method for direction finding of weak target signals under strong interference provided by an embodiment of the present invention are described below with reference to specific examples:

[0130] Example 1

[0131] In Example 1, the array uses a 10-element non-uniform linear array, the element positions are [0 1 4 6 8 9 13 14 1719], the element spacing is half a wavelength, a strong interference signal is set from 60.5°, a weak target signal is set from 20.5°, the signal-to-noise ratio is set to 0dB, 5dB, 10dB, 20dB, and the number of snapshots is a single snapshot. Based on the above settings, signal data is generated, and the signal data is processed using the weak target signal direction finding method under strong interference provided by the embodiment of the present invention, and the following are obtained respectively. Figure 2 -Attached Figure 5 The signal spatial spectrum is shown.

[0132] According to the attached Figure 2 -Attached Figure 5 It can be seen that the method for direction finding of weak target signals under strong interference provided by the embodiment of the present invention can simultaneously estimate the directions of strong interference signals and weak target signals under different signal-to-noise ratios.

[0133] Example 2

[0134] In Example 2, the array uses a 10-element non-uniform linear array, the element positions are [0 1 4 6 8 9 13 14 1719], the element spacing is half a wavelength, a strong interference signal is set to come from 60.5°, two weak target signals are set to come from 20.5° and 40.5° respectively, the signal-to-noise ratio is set to 5dB and 10dB respectively, and the number of snapshots is a single snapshot. Based on the above settings, signal data is generated, and the signal data is processed using the weak target signal direction finding method under strong interference provided by the embodiment of the present invention, and the following are obtained respectively. Figure 6 -Attached Figure 7 The signal spatial spectrum is shown.

[0135] According to the attached Figure 6 -Attached Figure 7 It can be seen that the method for direction finding of weak target signals under strong interference provided by the embodiment of the present invention can simultaneously estimate the directions of strong interference signals and weak target signals under different signal-to-noise ratios and with multiple weak target signals.

[0136] Example 3

[0137] In Example 3, the array uses a 10-element non-uniform linear array with element positions of [0 1 4 6 8 9 13 14 1719] and an element spacing of half a wavelength. A strong interference signal is set from 25.5° and a weak target signal is set from 20.5°. The signal-to-noise ratio is defined as The number of snapshots is a single snapshot, and the noise power range is set to 20dBm to -10dBm. Based on the above settings, signal data is generated, and 200 Monte Carlo experiments are performed using the weak target signal direction finding method under strong interference provided by the embodiment of the present invention. The following is obtained. Figure 8 The change of signal direction finding mean square error under different noise power conditions is shown in the figure. Figure 8 The Cramer-Rao bounds for strong interference signals and weak target signals are also given.

[0138] According to the attached Figure 8 It can be seen that the direction finding method for weak target signals under strong interference provided by an embodiment of the present invention can simultaneously estimate the directions of the strong interference signal and the weak target signal even when the spatial angles of the strong interference signal and the weak target signal are similar, and when the noise power is greater than 5dBm, the direction finding mean square error of the strong interference signal and the weak target signal approaches the Cramer-Rao lower bound.

[0139] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for direction finding of weak target signals under strong interference, characterized in that: The method comprises the following steps: Step 1, Setup The signal angle of the first signal is estimated from the received signal data by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the first signal, and the first signal is calculated by using a preset complex signal solution expression based on the signal angle estimation value; Step 2, Setup Separate the latest first signal from the received signal data, estimate the signal angle of the second signal from the separated received signal data through beamforming, correct the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the second signal, and calculate the second signal based on the signal angle estimate using a preset complex signal solution expression; Separate the latest second signal from the received signal data, estimate the signal angle of the first signal from the separated received signal data through beamforming, correct the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculate the first signal based on the signal angle estimate using a preset complex signal solution expression; Step 3, looping through step 2 until both the signal angle estimation value of the first signal and the signal angle estimation value of the second signal satisfy a preset convergence condition and then proceeding to the next step; Step 4: If K=2, output the two latest signals and the signal angle estimation value; if K≥3, proceed to the next step; Step 5, let Step 6: Send the latest first signal to the The signal is separated from the received signal data, and the first signal is estimated from the separated received signal data by beamforming. The signal angle of the first signal is corrected by using the preset angle correction closed-form expression to obtain the The signal angle estimation value of the signal is calculated based on the signal angle estimation value by using the preset complex signal solution expression. signals; for the first signal to the The following operations are performed on each signal to update the signal: the latest known signals other than the current signal are separated from the received signal data, the signal angle of the current signal is estimated from the received signal data after separation by beamforming, the estimated signal angle is corrected by using a preset angle correction closed-form expression to obtain a signal angle estimation value of the current signal, and based on the signal angle estimation value, the current signal is calculated by using a preset complex signal solution expression; Step 7, repeat step 6 until the obtained After the signal angle estimation values ​​of all signals meet the preset convergence conditions, proceed to the next step; Step 8, judgement Is it greater than or equal to K? If so, output the latest If not, return to step 5.

2. The method for direction finding of weak target signals under strong interference according to claim 1, characterized in that: Assume that the current signal is the kth signal, and the received signal data after separating the latest known signals except the current signal from the received signal data is expressed as: Among them, y k represents the received signal data from which other known signals other than the kth signal have been separated, Y represents the original received signal data, Indicates the number of signals contained in the known original received signal data Y, s i represents the ith signal, a(θ i ) represents the steering vector of the i-th signal, θ i Represents the signal angle of the i-th signal.

3. The method for direction finding of weak target signals under strong interference according to claim 1, characterized in that: The closed-form expression for angle correction is: in, Represents the signal angle estimation value, arcsin represents the inverse sine trigonometric function calculation, Represents the position difference vector of adjacent elements in the antenna array, represents a triangular matrix, g(r) represents a custom vector, π represents pi, the superscript T represents a transpose operation, and the superscript -1 represents an inverse operation; Triangle Array It is expressed as: The vector g(r) is solved using the following formula: Among them, sin represents the calculation of sine trigonometric function, θ represents the signal angle, and ε represents the colored Gaussian noise vector; Here, the signal angle θ used to calculate the vector g(r) uses the signal angle estimated from the received signal data through beamforming.

4. The method for direction finding of weak target signals under strong interference according to claim 3, characterized in that: The complex signal solution expression is expressed as: Among them, s represents the current signal to be solved, express The conjugate matrix of represents the steering vector of the signal, y represents the received signal data from which other known signals other than the current signal have been separated, and N represents the number of elements in the antenna array.

5. The method for direction finding of weak target signals under strong interference according to claim 1, characterized in that: The convergence condition is set as: in, represents the signal angle estimate of the kth signal obtained in the h+1th cycle, represents the signal angle estimation value of the kth signal obtained in the hth cycle, and τ represents the preset tolerance.

6. The method for direction finding of weak target signals under strong interference according to claim 5, characterized in that: The tolerance τ is set to the value of the smallest Cramer-Rao bound within the signal-to-noise ratio range.

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