A method for direction finding of weak target signals under strong interference

Abstract

The present invention discloses a method for direction finding of weak target signals under strong interference, the method comprising: performing signal direction finding in a double-loop nested manner, updating the signal angle of the current estimated number of signals in each inner loop for direction finding, adding 1 to the estimated number of signals in each outer loop, and separating the latest known signals other than the current signal from the received signal data when performing direction finding on the current estimated signal in each inner loop, estimating the signal angle of the current signal from the separated received signal data through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression, obtaining a signal angle estimate of the current signal, and calculating the current signal based on the signal angle estimate using a preset complex signal solution expression. The method of the present invention can achieve simultaneous and precise direction finding of strong interference signals and weak target signals in the case of few snapshots or even a single snapshot, without the need for zero padding.

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 complex electromagnetic environments, plagued by various interference and noise, the signals received by the array are often of unequal power. Strong interference signals and weaker target signals are intertwined, making them difficult to distinguish. When a radio direction-finding system is affected by a complex electromagnetic environment, its anti-interference performance, accuracy, and real-time performance all show a significant decline.

[0003] Traditional methods for direction finding of weak target signals under strong interference generally fall into two categories based on their processing strategies: one involves simultaneous direction finding of both strong and weak interference signals, and the other involves direction finding of weak target signals after suppressing the strong interference. Typical methods in the first category include the RELAX and CLEAN algorithms. However, these methods require a high number of iterations and computational complexity in practical applications, and also require zero-padding to improve estimation accuracy. Typical methods in the second category include the interference blocking algorithm proposed by Chen Hui et al. and the modified projection blocking method proposed by Dong Hui et al. In the interference blocking algorithm, based on the known direction of the strong interference signal or a pre-estimated direction, an interference blocking matrix is ​​designed to suppress the strong interference signal. This blocking process converts the noise term into colored noise, which is then converted to white noise through pre-whitening. A spatial spectrum algorithm is then used to perform direction finding of the weak target signal. This algorithm requires little computation and is easy to apply in practice. However, it requires a large number of snapshots to ensure accuracy during signal direction finding. When the number of snapshots is small in a dynamic environment, the target signal's direction cannot be accurately estimated. Furthermore, the ability to suppress strong interference is achieved at the expense of array element loss. When the number of interferers is large, the greater the reduction in the dimensionality of the data covariance matrix, the smaller the number of target signals that can be directionally determined. The modified projection blocking method utilizes the concept of modified projection, eliminating the need for prior knowledge of the interference direction and being 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 traditional interference blocking methods. Furthermore, this algorithm still requires a large number of snapshots for direction finding. When the number of snapshots is small in a dynamic environment, the target signal's direction 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 solutions of the present invention are 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 estimating a signal angle of a first signal from received signal data by beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculating the first signal using a preset complex signal solution expression based on the signal angle estimate;

[0008] Step 2, Set Separating the most recently obtained first signal from the received signal data, estimating the signal angle of the second signal from the separated received signal data through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the second signal, and calculating the second signal based on the signal angle estimate using a preset complex signal solution expression; separating the most recently obtained second signal from the received signal data, estimating the signal angle of the first signal from the separated received signal data through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculating 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 signal to the The first signal is separated from the received signal data, and the first signal is estimated from the separated received signal data through 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 using the preset complex signal solution expression. signals; for the first signal to the performing the following operations on each signal to update the signal: separating the latest known signals other than the current signal from the received signal data, estimating the signal angle of the current signal from the separated received signal data by beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the current signal, and calculating the current signal based on the signal angle estimate 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, judge 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 separating the latest known signals other than the current signal from the received signal data is expressed as:

[0016]

[0017] Among them, y k represents the received signal data from which other known signals except the k-th signal have been separated, and 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 i-th 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, Indicates the signal angle estimation value, arcsin indicates the calculation of the inverse sine trigonometric function, 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] Triangular array Expressed as:

[0022]

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

[0024]

[0025] Where sin represents the sine trigonometric function calculation, 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 method. Each inner loop updates the signal angle of the current estimated number of signals, and each outer loop increases the estimated number of signals by 1. When performing direction finding on the current estimated signal in each inner loop, 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 beamforming, and the estimated signal angle is corrected using an angle correction closed-form expression. The method 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 a single snapshot, and does not require zero-padding operation. 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] Figures 2 to 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] Figures 6 and 7 The signal spatial spectra are obtained by processing 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, respectively;

[0040] Figure 8 This is a schematic diagram of the change in mean square error when signal processing is performed using the 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] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and 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 efforts are within the scope of protection of the present invention.

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

[0043] See also Figure 1 , an 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 estimating a signal angle of a first signal from received signal data by beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculating the first signal using a preset complex signal solution expression based on the signal angle estimate;

[0045] Step 2, Set Separating the most recently obtained first signal from the received signal data, estimating the signal angle of the second signal from the separated received signal data through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the second signal, and calculating the second signal based on the signal angle estimate using a preset complex signal solution expression;

[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 through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculating the first signal based on the signal angle estimate using a preset complex signal solution expression;

[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 signal to the The first signal is separated from the received signal data, and the first signal is estimated from the separated received signal data through 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 using the preset complex signal solution expression. a signal;

[0052] For the first signal to the performing the following operations on each signal to update the signal: separating the latest known signals other than the current signal from the received signal data, estimating the signal angle of the current signal from the separated received signal data by beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the current signal, and calculating the current signal based on the signal angle estimate using a preset complex signal solution expression;

[0053] Specifically, in the embodiment of the present invention, For example, 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 separated received signal data through beamforming, the estimated signal angle is corrected using a preset angle correction closed-form expression to obtain a signal angle estimate of the current signal, and based on the signal angle estimate, the current signal is calculated using a preset complex signal solution expression, which is specifically expressed as:

[0054] The most recently obtained second signal and 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 using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and based on the signal angle estimate, the first signal is calculated using a preset complex signal solution expression; the most recently obtained first signal and 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 using a preset angle correction closed-form expression to obtain a signal angle estimate of the second signal, and based on the signal angle estimate, the second signal is calculated using a preset complex signal solution expression.

[0055] Specifically, in the embodiment of the present invention, For example, 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 separated received signal data through beamforming, the estimated signal angle is corrected using a preset angle correction closed-form expression to obtain a signal angle estimate of the current signal, and based on the signal angle estimate, the current signal is calculated using a preset complex signal solution expression, which is specifically expressed as:

[0056] Separating the most recently obtained second, third, and fourth signals from the received signal data, estimating the signal angle of the first signal from the separated received signal data through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculating the first signal based on the signal angle estimate using a preset complex signal solution expression;

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

[0058] The most recently 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-form expression to obtain a signal angle estimate of the third signal. Based on the signal angle estimate, 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, judge 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 nested method. Each inner loop updates the signal angle of the current estimated number of signals, and each outer loop increases the estimated number of signals by 1. When performing direction finding on the current estimated signal in each inner loop, 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 beamforming, and the estimated signal angle is corrected using an angle correction closed-form expression. This method can significantly improve the signal direction finding accuracy and 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, without the need for zero-padding operation.

[0062] Furthermore, 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 except the k-th signal have been separated, and Y represents the original received signal data. Indicates the number of signals contained in the known original received signal data Y, si represents the i-th 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] Furthermore, in an embodiment of the present invention, the angle correction closed-form expression is expressed as:

[0066]

[0067] in, Indicates the signal angle estimation value, arcsin indicates the calculation of the inverse sine trigonometric function, 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 Expressed as:

[0069]

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

[0071]

[0072] in, represents the position difference vector between 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] Furthermore, in an 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 value of the smallest Cramer-Rao bound 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 after separating the other known signals except the kth signal, s i represents the i-th 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 k-th 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 Indicates 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] Furthermore, 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 Indicates the position of the n+1th element in the antenna array, c n Indicates 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 are all 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 an (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 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] Furthermore, a vector g(r) is defined, which contains N-1 elements, and the nth element in the vector g(r) is 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 Indicates the position of the N-1th element in the antenna array, c N Indicates 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, 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] Triangular array 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 transpose 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 k-th signal is expressed as:

[0121]

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

[0123] After iteratively correcting the signal angle of the k-th signal using 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 following describes the beneficial effects of the method for direction finding of weak target signals under strong interference provided by an embodiment of the present invention with reference to specific examples:

[0130] Example 1

[0131] In Example 1, 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 60.5° and a weak target signal is set from 20.5°. The signal-to-noise ratios are set to 0dB, 5dB, 10dB, and 20dB, respectively, and the number of snapshots is a single snapshot. Based on the above settings, signal data is generated and processed using the weak target signal direction finding method under strong interference provided by an 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 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 to come from 60.5°, and 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 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 assumed to come from 25.5° and a weak target signal is assumed to come from 20.5°. The signal-to-noise ratio is defined as The number of snapshots is 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 results are as shown in the attached figure. Figure 8 The change of the mean square error of signal direction finding 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 strong interference signals and weak target signals even when the spatial angles of the strong interference signals and weak target signals are similar, and when the noise power is greater than 5 dBm, the direction finding mean square error of the strong interference signals and weak target signals approaches the Cramer-Rao lower bound.

[0139] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes 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 apparatus.

[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 various 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 , estimate the signal angle of the first signal from the 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 using a preset complex signal solution expression based on the signal angle estimate, Represents the known original received signal data The number of signals included; Step 2, Set , separating the most recently obtained first signal from the received signal data, estimating the signal angle of the second signal from the separated received signal data through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the second signal, and calculating the second signal based on the signal angle estimate using a preset complex signal solution expression; separating the most recently obtained second signal from the received signal data, estimating the signal angle of the first signal from the separated received signal data through beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the first signal, and calculating 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 , output the two latest signals and signal angle estimation values, if , proceed to the next step, Indicates the number of signals contained in the received signal data; Step 5, let ; Step 6: Send the latest signal to the The first signal is separated from the received signal data, and the first signal is estimated from the separated received signal data through 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 using the preset complex signal solution expression. signals; for the first signal to the performing the following operations on each signal to update the signal: separating the latest known signals other than the current signal from the received signal data, estimating the signal angle of the current signal from the separated received signal data by beamforming, correcting the estimated signal angle using a preset angle correction closed-form expression to obtain a signal angle estimate of the current signal, and calculating the current signal based on the signal angle estimate 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, judge Is greater than or equal to If so, output the latest If no, return to step 5; The closed-form expression for angle correction is: ； in, represents the signal angle estimate, Indicates the calculation of inverse sine trigonometric functions, Represents the position difference vector of adjacent elements in the antenna array, represents a triangular matrix, represents a custom vector, represents pi, the superscript T represents the transpose operation, and the superscript -1 represents the inverse operation; Triangular array Expressed as: ； vector Solve using the following formula: ； in, Represents the calculation of sine trigonometric functions, Indicates the signal angle, represents a colored Gaussian noise vector; Among them, the calculation vector The signal angle used The signal angle estimated from the received signal data by beamforming is used.

2. The method for direction finding of weak target signals under strong interference according to claim 1, wherein: Set the current signal to The received signal data after separating the latest known signals except the current signal from the received signal data is expressed as: ； in, Indicates that the The received signal data of other known signals besides the signal, Represents the original received signal data, Indicates the A signal, Indicates the The steering vector of the signal, Indicates the The signal angle of a signal.

3. The method for direction finding of weak target signals under strong interference according to claim 1, wherein: The complex signal solution expression is expressed as: ； in, represents the current signal to be solved, express The conjugate matrix of represents the steering vector of the signal, Indicates the received signal data from which other known signals other than the current signal have been separated. Indicates the number of elements in the antenna array.

4. The method for direction finding of weak target signals under strong interference according to claim 1, wherein: The convergence conditions are set as: ， ； in, Indicates the The first The signal angle estimate of the signal, Indicates the The first The signal angle estimate of the signal, Indicates the preset tolerance.

5. The method for direction finding of weak target signals under strong interference according to claim 4, wherein: Tolerance Set to the value of the Cramer-Rao bound that minimizes the signal-to-noise ratio.

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