External Radar Target Detection Method Based on Homogeneous Multi-Frequency and Non-Convex Substitution Function

Abstract

The present invention discloses a method for detecting target using an external radiation radar based on homologous multi-frequency and non-convex substitution functions. The method comprises the following steps: performing a mutual ambiguity operation on a signal from an external radiation source in a homologous multi-frequency scenario, performing phase compensation on the mutual ambiguity functions of different carrier frequencies and then superimposing them to obtain a composite mutual ambiguity function; constructing an observation vector in sections according to the Doppler frequency based on the composite mutual ambiguity function; performing compressed sensing modeling on the mutual ambiguity function of each carrier frequency to obtain a dictionary matrix after superimposing the ambiguity functions corresponding to each carrier frequency, thereby obtaining a total dictionary matrix; constructing a sparse solution model based on the observation vectors and the total dictionary matrix, and iteratively calculating the sparse solution model based on the non-convex substitution function to obtain a target detection result. The method simultaneously improves the signal-to-noise ratio of the mutual ambiguity function and detects small and weak targets.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar target detection, and in particular relates to an external radiation radar target detection method based on homologous multi-frequency and non-convex substitution functions. Background Art

[0002] Exostatic radar, a key type of bistatic radar, does not emit its own detection signal. Instead, it detects and tracks targets using electromagnetic signals transmitted by a third-party source. Traditional exostatic radars using correlation detection receive the direct wave and the target echo. After performing signal processing operations such as direct wave purification and clutter cancellation, they calculate the inter-ambiguity function between the two signals. The time delay and Doppler frequency corresponding to the peak of the inter-ambiguity function reflect the target's position and velocity.

[0003] Currently, commonly used exo-radiation sources are primarily categorized as cooperative and non-cooperative. The latter, encompassing various civilian and commercial signals, are widely used in exo-radiation radars due to their large radiation area and wide coverage. However, while these signals are suitable for exo-radiation radars, data processing limitations limit the receiver's ability to utilize only a portion of the effective bandwidth of the received signal, resulting in low target echo energy. Consequently, in the detection of groups of small targets, the target peak of the mutual ambiguity function is submerged within the noise floor, hindering target detection. Therefore, research is needed on methods to improve the correlation accumulation gain.

[0004] While there are methods that leverage the characteristics of external radiation sources to improve correlation accumulation gain, these methods are specific to a specific signal type, limiting their scope of application. While methods that leverage the characteristics of a specific type of external radiation source structure to improve correlation accumulation gain have broader applicability, there are relatively few research results in this area.

[0005] Compressed sensing is a research field that has developed in recent years and is based on the sparse representation and reconstruction of signals. It has been widely used in fields such as communications, imaging, and radar. Compressed sensing theory states that when a signal is sparse in a certain orthogonal space, it can be sampled at a frequency far lower than the Nyquist sampling rate and reconstructed with high probability. Compressed sensing consists of three main parts: sparse representation of the signal, selection of the measurement matrix, and reconstruction algorithm. The sparse representation of the signal means that the original signal satisfies sparsity or is sparse within a certain transform domain; the measurement matrix compresses the sampling of the signal, which must satisfy certain uncorrelated conditions; and the reconstruction algorithm restores the measured values to the original signal.

[0006] In the detection scenario of a group of small targets, since each target has similar spatial position and velocity, and different scattering cross-sections, the peak broadening of a strong target in the mutual ambiguity function can mask the peaks of its neighboring weaker targets, making detection of weaker targets difficult. However, if the direct wave is used as a set of bases, the target echo can be represented as a linear combination of this set of bases. The coefficients of the linear combination are sparse in the delay-Doppler domain within the detection range. Therefore, a sparse reconstruction algorithm can be used to solve for the non-zero coefficients. The position of the non-zero coefficients in the delay-Doppler domain can be used to obtain the target's range and velocity information, ensuring that the detection of weak targets is not affected by the peak broadening of its neighboring strong targets.

[0007] Existing research on exo-radiator radar target detection using compressed sensing theory has explored methods that exploit the sparsity of target echoes in the delay-Doppler domain to achieve sparse reconstruction of the cross-ambiguity function. However, these computational models rely heavily on the signal-to-noise ratio (SNR) of the target peak in the cross-ambiguity function. In the detection scenario of a group of small targets, the target echo energy is extremely low, and the target peak of the cross-ambiguity function is submerged in the noise floor, which in turn affects the accuracy of the sparse reconstruction of the cross-ambiguity function. Summary of the Invention

[0008] To address the existing problems of low target peak signal-to-noise ratio and strong target peaks covering weak target peaks in group small target detection, the present invention provides a target detection method for external radiation radar based on homologous multi-frequency and non-convex surrogate functions. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0009] In a first aspect, the present invention provides a method for detecting external radiation radar targets based on homologous multi-frequency and non-convex substitution functions, comprising:

[0010] Step 1: Down-convert the signal of an external radiation source in a homologous multi-frequency scenario to separate the useful signals in different frequency bands, and then convert them to baseband to obtain the direct wave baseband signal and target echo baseband signal corresponding to different carrier frequencies;

[0011] Step 2: performing mutual ambiguity calculation on the direct wave baseband signal and the target echo baseband signal, and performing phase compensation on the mutual ambiguity functions of different carrier frequencies and then superimposing them to obtain a synthetic mutual ambiguity function;

[0012] Step 3: constructing an observation vector in segments according to the Doppler frequency based on the synthetic mutual ambiguity function;

[0013] Step 4: Perform compressed sensing modeling on the mutual ambiguity function of each carrier frequency to obtain a dictionary matrix after the ambiguity function corresponding to each carrier frequency is superimposed, thereby obtaining a total dictionary matrix;

[0014] Step 5: Construct a sparse solution model based on the observation vector and the total dictionary matrix, and iteratively calculate the sparse solution model based on a non-convex substitution function to obtain a target detection result.

[0015] In a second aspect, the present invention provides an external radiation radar target detection device based on homologous multi-frequency and non-convex substitution function, comprising:

[0016] The signal preprocessing module is used to down-convert the signal of an external radiation source in a homologous multi-frequency scenario, separate the useful signals in different frequency bands, and then convert them to baseband to obtain the direct wave baseband signal and target echo baseband signal corresponding to different carrier frequencies;

[0017] a mutual ambiguity operation module, configured to perform mutual ambiguity operation on the direct wave baseband signal and the target echo baseband signal, and perform phase compensation on the mutual ambiguity functions of different carrier frequencies and then superimpose them to obtain a synthetic mutual ambiguity function;

[0018] An observation vector construction module, configured to construct an observation vector in sections according to Doppler frequency based on the synthetic mutual ambiguity function;

[0019] A compressed sensing modeling module is used to perform compressed sensing modeling on the mutual ambiguity function of each carrier frequency to obtain a dictionary matrix after the ambiguity function corresponding to each carrier frequency is superimposed, thereby obtaining a total dictionary matrix;

[0020] A sparse solution module is used to construct a sparse solution model according to the observation vector and the total dictionary matrix, and iteratively calculate the sparse solution model based on a non-convex substitution function to obtain a target detection result.

[0021] Beneficial effects of the present invention:

[0022] The present invention first proposes a synthesis algorithm of the mutual ambiguity function based on the homologous multi-frequency model, synthesizes the same type of signals in different frequency bands at the same spatial position, fully utilizes the radiation source with a multi-carrier frequency structure, improves the target peak signal-to-noise ratio, and is not restricted by the signal type. Compared with the current method of relying on the characteristics of a certain signal to improve the target peak signal-to-noise ratio, the present invention has a wider range of applications; then, a compressed sensing model that is applicable to both multi-carrier frequency structures and single-carrier frequency structures is proposed, which eliminates the influence of strong target peaks on adjacent weak target peaks. Finally, a sparse reconstruction algorithm based on a non-convex substitution function is proposed, which effectively overcomes the difficulty of RIP condition verification and makes the theoretical support of the sparse reconstruction process of the mutual ambiguity function clearer and clearer, thereby achieving the improvement of the mutual ambiguity function signal-to-noise ratio and the detection of weak targets at the same time.

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 1 is a flow chart of a method for detecting external radiation radar targets based on homologous multi-frequency and non-convex substitution functions provided by an embodiment of the present invention;

[0025] Figure 2 This is a structural block diagram of an external radiation radar target detection device based on homologous multi-frequency and non-convex substitution function provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0026] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0027] Example 1

[0028] See Figure 1 , Figure 1 : This is a flow chart of a method for detecting external radiation radar targets based on homologous multi-frequency and non-convex substitution functions provided by an embodiment of the present invention. The method includes:

[0029] Step 1: Down-convert the signal of an external radiation source in a homologous multi-frequency scenario to separate the useful signals in different frequency bands, and then convert them to baseband to obtain the direct wave baseband signal and target echo baseband signal corresponding to different carrier frequencies.

[0030] First, the radiation source is selected, the direct wave and the target echo are received and down-converted, and then an FIR bandpass filter is used to separate the useful signals in different frequency bands and convert them to baseband.

[0031] Specifically, the external radiation source signal includes the direct wave signal and the echo signal, and the signal received by the external radiation source radar system is a continuous wave. c1 ,f c2 ,…,f cN is the carrier frequency of the N direct wave signals corresponding to the N transponders of the radiation source at the same physical location. Ignoring the spacing between the transmitting array elements of the N transponders, the delay values corresponding to the N groups of reference signals and the N echo signals of the same target are the same, and the Doppler frequency value is proportional to the carrier frequency f. cn related.

[0032] Therefore, for the external radiation source radar target detection scenario in the same source multi-frequency scenario, let the complex envelope of the signal transmitted by the Nth transponder be u n (t), then the direct wave baseband signal x(t) and the target echo baseband signal y(t) received by the receiving station are in the form of:

[0033]

[0034] Among them, x n(t) is the complex envelope of the signal received by the receiving station for the nth transponder; τ r and τ ep are the time delays of the direct wave signal and the echo signal of the pth target relative to the transmitted signal; β n is the complex gain of the receiving station for the direct wave signal received by the nth transponder; y n (t) is the superposition of the complex envelopes of the P target echoes corresponding to the nth transponder; y np (t) is the complex envelope of the p-th target echo corresponding to the n-th transponder; σ np , f dnp are the complex gain and Doppler frequency of the pth target echo in the echo signal received by the receiving station from the nth transponder; w x and w y are the noise of the direct wave channel and the target echo channel respectively, N is the total number of transponders, and P is the number of targets.

[0035] Step 2: Perform mutual ambiguity calculation on the direct wave baseband signal and the target echo baseband signal, perform phase compensation on the mutual ambiguity functions of different carrier frequencies, and then superimpose them to obtain a synthetic mutual ambiguity function.

[0036] In this embodiment, step 2 specifically includes:

[0037] 21) Calculate the mutual ambiguity function between the baseband signal corresponding to the nth carrier frequency and the target echo baseband signal.

[0038] Specifically, ignoring the noise w x and w y The mutual ambiguity function expression of the direct wave and target echo signal corresponding to the nth carrier frequency is:

[0039]

[0040] Where τ represents the delay, f d represents the Doppler frequency, It represents the direct wave signal of the nth carrier frequency, and T is the accumulation time of the signal.

[0041] 22) The mutual ambiguity function of each carrier frequency is expressed as a linear combination of the mutual ambiguity functions of the direct wave and each target echo at this carrier frequency.

[0042] Specifically, the target echo signal y corresponding to the nth carrier frequency in equation (1) is n Substituting the expression of (t) into formula (2), we get:

[0043]

[0044] Among them, χ np (τ,f d) represents the mutual ambiguity function between the direct wave of the nth carrier frequency and the echo of the nth carrier frequency and the pth target.

[0045] Equation (3) shows that the mutual ambiguity function of each carrier frequency can be expressed as a linear combination of the mutual ambiguity functions of the direct wave and each target echo at that carrier frequency.

[0046] 23) The mutual ambiguity functions corresponding to different carrier frequencies are sampled according to a certain Doppler domain sampling interval, and the mutual ambiguity functions of different carrier frequencies are phase compensated and superimposed to obtain a synthetic mutual ambiguity function after phase compensation and superposition.

[0047] Specifically, from equations (1) and (3), it can be seen that when τ = τ ep -τ r , f d =f dnp When, χ np (τ,f d )for

[0048]

[0049] when When the phase of the target with different carrier frequencies within the received frequency range is negligible, the phase of the mutual ambiguity function of the same target with different carrier frequencies at the peak of the target is only related to the carrier frequency, and the mutual ambiguity function of other targets at the target is approximately zero. Therefore, after phase compensation, the mutual ambiguity function of different carrier frequencies can be used to achieve coherent superposition at the target peak to improve the target peak signal-to-noise ratio. However, for N groups of mutual ambiguity functions of direct waves and target echoes with different carrier frequencies, although the time delay values corresponding to the same target are the same, the Doppler frequency values of the echo signals of the same target with different carrier frequencies are proportional to the carrier frequency, that is, f dnp =v p f cn / c, where v p is the radial velocity of the pth target, and c is the speed of light. Therefore, it is impossible to directly superimpose the mutual ambiguity functions of different carrier frequencies.

[0050] In order to achieve the superposition of the mutual ambiguity functions of different carrier frequencies to improve the detection signal-to-noise ratio, it is necessary to control the sampling interval in the Doppler domain. Assume that the carrier frequency is f cn The Doppler domain sampling interval of the mutual ambiguity function corresponding to the signal is F n , with the first carrier frequency f c1 As a benchmark, if the following relationship is satisfied

[0051]

[0052] Right now

[0053]

[0054] When the target speed and direction are constant, the target's Doppler frequency value is proportional to the signal carrier frequency, so the right half of equation (5) holds. Therefore, when the sampling interval F in the Doppler domain is n When taking values according to formula (6), the number of frequency points of each ambiguity function is made the same, then the same target peak appears at the frequency point at the same position of different ambiguity functions, so that the mutual ambiguity functions of different carrier frequencies can be phase compensated and superimposed.

[0055] Assume that the mutual ambiguity function after phase compensation and superposition is A(τ,f d ), then from formulas (3) to (6) we can get:

[0056]

[0057] Among them, A(τ,f d ) represents the composite mutual ambiguity function, f c1 Indicates the carrier frequency of the direct wave signal corresponding to the first transponder.

[0058] Equation (7) shows that after phase compensation and superposition of the ambiguity functions of multiple transponder signals from the same radiation source, if the radiation power of each transponder is the same, the signal-to-noise ratio can theoretically be improved by 10logNdB. Equation (7) also shows that in the same-source multi-frequency scenario, the superimposed mutual ambiguity function can be expressed as a combination of the mutual ambiguity functions of different targets, which is the basis for the sparse representation of the mutual ambiguity function.

[0059] Step 3: Based on the synthetic mutual ambiguity function, the observation vector is constructed in segments according to the Doppler frequency.

[0060] Specifically, for the mutual ambiguity function, its peak is sparse in the delay-Doppler domain, so the mutual ambiguity function can be sparsely represented.

[0061] Assume that the carrier frequency is f cn In the calculation of the mutual ambiguity function, the time delay τ and the Doppler frequency f d The value ranges are {τ1,τ2,…,τ L} and {f dn1 ,f dn2 ,…,f dnM}, the delay and Doppler frequency sets of interest are Ω τ ={τ p1 ,τ p2 ,…,τ pK} and Ω f,n ={f pn1 ,f pn2 ,…,f pnI}, where L≥K, M≥I. According to the derivation above, we know that

[0062]

[0063] Then the amplitude of the superimposed mutual ambiguity function A(τ,f d ) can be expressed as

[0064]

[0065] In formula (9), Represents the signal x n (t) with The mutual fuzzy function, Indicates that the carrier frequency is f cn , the delay is τ pk , the Doppler frequency is f pni The amplitude gain of the target echo signal at time , its value is

[0066]

[0067] In order to sparsely represent the synthesized mutual ambiguity function in the homologous multi-frequency scenario, let a S is the amplitude of the mutual ambiguity function after superposition A(τ,f d ) is divided along each Doppler frequency unit slice and arranged according to the Doppler frequency to form a column vector, that is, the observation vector, whose dimension is LM×1, then a S The specific expression is

[0068]

[0069] Among them, A(τ l ,f d1m ) represents the time delay τ l , Doppler frequency f d1m The synthetic mutual ambiguity function value under , l∈[1,L], m∈[1,M], L is the number of delay units to be searched, and M is the number of Doppler frequency units to be searched.

[0070] The synthesis algorithm proposed in this embodiment fully utilizes the radiation source with a multi-carrier frequency structure, improves the target peak signal-to-noise ratio, and is not restricted by the signal type. Compared with the current method of improving the target peak signal-to-noise ratio by relying on the characteristics of a certain signal, it has a wider range of applications.

[0071] Step 4: Perform compressed sensing modeling on the mutual ambiguity function of each carrier frequency to obtain a dictionary matrix after the ambiguity function corresponding to each carrier frequency is superimposed, thereby obtaining a total dictionary matrix.

[0072] Specifically, for the direct wave signal of a certain frequency band, within each delay-Doppler unit of interest, the corresponding time delay and frequency delay are applied to the direct wave signal, and a mutual fuzzy operation is performed with the direct wave. The signal is segmented according to the Doppler frequency to form a column vector, and each column vector is arranged in rows to form a dictionary matrix of a certain frequency band signal; the dictionary matrix of each frequency band signal is phase compensated and superimposed to form a total dictionary matrix.

[0073] In this embodiment, step 4 specifically includes:

[0074] 41) The mutual ambiguity function of the nth carrier frequency is sparsely represented.

[0075] Specifically, for the ambiguity function χ of the nth carrier frequency n , whose dimension is LM×1, has:

[0076]

[0077] In formula (12), B n is the measurement matrix of the nth carrier frequency, with a dimension of LM×KI, and each column is a copy of the mutual ambiguity function of the delay-Doppler frequency of the direct wave under the carrier frequency. n The expression is

[0078]

[0079] Among them, the composition B n Column vector of The expression is

[0080]

[0081] σ n is the sparse vector of the nth carrier frequency, with dimension KI×1.

[0082] From formula (10), we can see that the position of its non-zero value corresponds to the delay-Doppler information of the n-th reference signal and the echo signal. n The expression is

[0083]

[0084] 42) The ambiguity functions corresponding to each carrier frequency are superimposed to obtain the superimposed dictionary matrix, and the observation vector a is calculated based on this. S Perform sparse representation.

[0085] Specifically, in order to vector a S Sparse representation is performed. From formula (9), we can see that vector a S The element A(τ l ,f d1m ) can be expressed as

[0086]

[0087] Therefore, the vector a S It can be expressed as

[0088]

[0089] In formula (17), B S It is the measurement matrix after the ambiguity functions corresponding to n carrier frequencies are superimposed, with a dimension of LM×KI, and each column is a copy of the mutual ambiguity function of the delay-Doppler frequency after superposition.

[0090] B S It can be expressed as

[0091]

[0092] Among them, n is the phase compensation matrix, which can be expressed as

[0093]

[0094] in,

[0095] It can be expressed as

[0096]

[0097] 43) The observation vector is sparsely represented and converted into real number form.

[0098] Specifically, since Equation (17) is in complex form, it is necessary to convert Equation (17) into real form in order to facilitate sparse recovery calculation.

[0099]

[0100]

[0101]

[0102] In summary, according to formula (17) and formula (21) to (23), we have

[0103]

[0104] Therefore, for Equation (24), as long as the sparse vector can be obtained Will Restore to Afterwards, according to The position of the non-zero value in the delay-Doppler unit where the echo exists can be determined.

[0105] This embodiment uses compressed sensing technology to eliminate the influence of a strong target peak on an adjacent weak target peak. The proposed compressed sensing model is applicable to both a multi-carrier frequency structure and a single-carrier frequency structure. Compared with the existing compressed sensing model that is only applicable to a single-carrier frequency structure, it has a wider range of applications.

[0106] Step 5: Construct a sparse solution model based on the observation vector and the total dictionary matrix, and iteratively calculate the sparse solution model based on the non-convex substitution function to obtain the target detection result.

[0107] In this embodiment, step 5 specifically includes:

[0108] 51) Construct a pseudo-norm to replace the l0-norm.

[0109] Specifically, in order to overcome the difficulty of RIP condition verification, the following pseudo-norm is used to replace the l0 norm:

[0110]

[0111] In formula (25), len(x) is the number of elements in the column vector x, x i is the i-th element of x. r (x) is

[0112]

[0113] 52) Based on the observation vector and the total dictionary matrix, a sparse solution model for the mutual ambiguity function after homologous multi-frequency synthesis is established, and its expression is:

[0114]

[0115] 53) Based on the Lagrangian function of the pseudo-norm and sparse solution model, design the optimal solution fixed point iterative algorithm to solve the sparse vector

[0116] Specifically, according to the Lagrangian function of formula (27), when the number of targets P≥1, for Its satisfaction

[0117]

[0118] in, is a diagonal matrix whose elements in row i and column i are for

[0119]

[0120] for The i-th element of .

[0121] 54) The current vector is brought into the optimal solution fixed point expression, and an iterative cycle is performed until σ reaches convergence to obtain the final solution vector of the sparse recovery model to achieve target detection.

[0122] Specifically, by bringing the current vector into the optimal solution fixed point expression (28), a new vector σ can be obtained, which is then brought into the iterative loop of formula (28) and iterated repeatedly until σ reaches convergence. The final solution at this time is That is the solution vector of the sparse recovery model, thus obtaining the target detection result.

[0123] The sparse reconstruction algorithm based on non-convex substitution function proposed in the embodiment of the present invention effectively overcomes the difficulty of RIP condition verification and makes the theoretical support of the sparse reconstruction process of mutual fuzzy functions clearer and more specific.

[0124] The present invention first proposes a synthesis algorithm of the mutual ambiguity function based on the homologous multi-frequency model, synthesizes the same type of signals in different frequency bands at the same spatial position, fully utilizes the radiation source with a multi-carrier frequency structure, improves the target peak signal-to-noise ratio, and is not restricted by the signal type. Compared with the current method of relying on the characteristics of a certain signal to improve the target peak signal-to-noise ratio, the present invention has a wider range of applications; then, a compressed sensing model that is applicable to both multi-carrier frequency structures and single-carrier frequency structures is proposed, which eliminates the influence of strong target peaks on adjacent weak target peaks. Finally, a sparse reconstruction algorithm based on a non-convex substitution function is proposed, which effectively overcomes the difficulty of RIP condition verification and makes the theoretical support of the sparse reconstruction process of the mutual ambiguity function clearer and clearer, thereby achieving the improvement of the mutual ambiguity function signal-to-noise ratio and the detection of weak targets at the same time.

[0125] Example 2

[0126] Based on the above embodiment 1, this embodiment provides an external radiation radar target detection device based on homologous multi-frequency and non-convex substitution function. Figure 2 , Figure 2 This is a structural block diagram of an external radiation radar target detection device based on homologous multi-frequency and non-convex substitution function provided by an embodiment of the present invention, the device comprising:

[0127] The signal preprocessing module is used to down-convert the signal of an external radiation source in a homologous multi-frequency scenario, separate the useful signals in different frequency bands, and then convert them to baseband to obtain the direct wave baseband signal and target echo baseband signal corresponding to different carrier frequencies;

[0128] a mutual ambiguity operation module, configured to perform mutual ambiguity operation on the direct wave baseband signal and the target echo baseband signal, and perform phase compensation on the mutual ambiguity functions of different carrier frequencies and then superimpose them to obtain a synthetic mutual ambiguity function;

[0129] An observation vector construction module, configured to construct an observation vector in sections according to Doppler frequency based on the synthetic mutual ambiguity function;

[0130] A compressed sensing modeling module is used to perform compressed sensing modeling on the mutual ambiguity function of each carrier frequency to obtain a dictionary matrix after the ambiguity function corresponding to each carrier frequency is superimposed, thereby obtaining a total dictionary matrix;

[0131] A sparse solution module is used to construct a sparse solution model according to the observation vector and the total dictionary matrix, and iteratively calculate the sparse solution model based on a non-convex substitution function to obtain a target detection result.

[0132] The device provided in this embodiment can implement the method provided in the above embodiment 1. Therefore, the detailed process can be found in the above embodiment 1 and will not be repeated again.

[0133] Therefore, the device provided in this embodiment can also achieve the improvement of the signal-to-noise ratio of the mutual ambiguity function and the detection of weak targets at the same time.

[0134] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for detecting external radiation radar targets based on homologous multi-frequency and non-convex substitution function, characterized in that: include: Step 1: Down-convert the signal of an external radiation source in a homologous multi-frequency scenario to separate the useful signals in different frequency bands, and then convert them to baseband to obtain the direct wave baseband signal and target echo baseband signal corresponding to different carrier frequencies; Step 2: performing mutual ambiguity calculation on the direct wave baseband signal and the target echo baseband signal, and performing phase compensation on the mutual ambiguity functions of different carrier frequencies and then superimposing them to obtain a synthetic mutual ambiguity function; Step 3: constructing an observation vector in segments according to the Doppler frequency based on the synthetic mutual ambiguity function; Step 4: Perform compressed sensing modeling on the mutual ambiguity function of each carrier frequency to obtain a dictionary matrix after the ambiguity function corresponding to each carrier frequency is superimposed, thereby obtaining a total dictionary matrix; include: 41) The mutual ambiguity function of the nth carrier frequency is sparsely represented, and its expression is: Among them, χ n represents the cross-ambiguity function of the nth carrier frequency, χ n (τ l ,f dnm ) represents the nth carrier frequency, delay τ l , Doppler frequency f dnm The mutual fuzzy function value under B n is the dictionary matrix of the nth carrier frequency, with a dimension of LM×KI, and each column is a copy of the mutual ambiguity function of the delay-Doppler frequency of the direct wave under the carrier frequency, σ n is the sparse vector of the nth carrier frequency, with dimension KI×1; 42) The ambiguity functions corresponding to each carrier frequency are superimposed to obtain a superimposed dictionary matrix, and the observation vector a is obtained accordingly. S Perform sparse representation; the superimposed dictionary matrix is expressed as: Among them, B S is the dictionary matrix after superposition, Ψ n is the phase compensation matrix, N is the total number of transponders; Then the observation vector a S The sparse expression is: represents a sparse vector; 43) The observation vector is sparsely represented and converted into a real number form, which is expressed as follows: in, Represents a sparse vector The real number form of B represents the total dictionary matrix B S The real number form of a represents the observation vector a S The real form of ; Step 5: Constructing a sparse solution model based on the observation vector and the total dictionary matrix, and iteratively calculating the sparse solution model based on a non-convex substitution function to obtain a target detection result, including: 51) Construct the following pseudo-norm: Among them, len(x) is the number of elements in the column vector x, x i is the i-th element of x; 52) Based on the observation vector and the total dictionary matrix, a sparse solution model of the mutual ambiguity function after homologous multi-frequency synthesis is established, and its expression is: 53) Based on the pseudo-norm and the Lagrangian function of the sparse solution model, design an optimal solution fixed point iterative algorithm to solve the sparse vector Among them, the optimal solution fixed point expression is: in, is a diagonal matrix whose elements in row i and column i are for: for The i-th element of ; 54) The current vector is brought into the optimal solution fixed point expression, and an iterative loop is performed until σ reaches convergence to obtain the final solution vector of the sparse recovery model to achieve target detection.

2. The external radiation radar target detection method based on homologous multi-frequency and non-convex substitution function according to claim 1 is characterized in that: In step 1, the direct wave baseband signal and the target echo baseband signal corresponding to the different carrier frequency signals are expressed as: Among them, x(t) is the direct wave baseband signal corresponding to different carrier frequency signals, x n (t) is the complex envelope of the signal received by the receiving station from the nth transponder, τ r and τ ep are the time delays of the direct wave signal and the echo signal of the pth target relative to the transmitted signal; β n is the complex gain of the receiving station for the direct wave signal received by the nth transponder, u n is the complex envelope of the signal transmitted by the nth transponder, f cn is the carrier frequency of the direct wave signal corresponding to the nth transponder; y(t) is the target echo baseband signal corresponding to different carrier frequency signals, y n (t) is the superposition of the complex envelopes of the P target echoes corresponding to the nth transponder; y np (t) is the complex envelope of the p-th target echo corresponding to the n-th transponder, σ np 、f dnp are the complex gain and Doppler frequency of the pth target echo in the echo signal received by the nth transponder at the receiving station, respectively, and w x (t) and w y (t) are the noise of the direct wave channel and the target echo channel, N is the total number of transponders, and P is the number of targets.

3. The external radiation radar target detection method based on homologous multi-frequency and non-convex substitution function according to claim 2 is characterized in that: Step 2 includes: 21) Calculate the mutual ambiguity function between the baseband signal corresponding to the nth carrier frequency and the target echo baseband signal. The calculation formula is: Where τ represents the delay, f d represents the Doppler frequency, represents the direct wave signal of the nth carrier frequency, and T represents the accumulation time of the signal; 22) The mutual ambiguity function of each carrier frequency is expressed as a linear combination of the mutual ambiguity functions of the direct wave and each target echo at this carrier frequency, and its expression is: Among them, χ np (τ,f d ) represents the mutual ambiguity function between the direct wave of the nth carrier frequency and the echo of the nth carrier frequency and the pth target; 23) The mutual ambiguity functions corresponding to different carrier frequencies are sampled according to a certain Doppler domain sampling interval, and the mutual ambiguity functions of different carrier frequencies are phase compensated and superimposed to obtain a synthetic mutual ambiguity function after phase compensation and superposition, whose expression is: Among them, A(τ,f d ) represents the composite mutual ambiguity function, f c1 Indicates the carrier frequency of the direct wave signal corresponding to the first transponder.

4. The external radiation radar target detection method based on homologous multi-frequency and non-convex substitution function according to claim 3 is characterized in that: In step 23), the Doppler domain sampling interval is expressed as: Wherein, F1 represents the Doppler domain sampling interval of the mutual ambiguity function corresponding to the first carrier frequency.

5. The external radiation radar target detection method based on homologous multi-frequency and non-convex substitution function according to claim 3 is characterized in that: In step 3, the expression of the observation vector is: Among them, A(τ l ,f d1m ) represents the time delay τ l , Doppler frequency f d1m The synthetic mutual ambiguity function value under , l∈[1,L], m∈[1,M], L is the number of delay units to be searched, and M is the number of Doppler frequency units to be searched.

6. An external radiation radar target detection device based on homologous multi-frequency and non-convex substitution function, characterized in that: include: The signal preprocessing module is used to down-convert the signal of an external radiation source in a homologous multi-frequency scenario, separate the useful signals in different frequency bands, and then convert them to baseband to obtain the direct wave baseband signal and target echo baseband signal corresponding to different carrier frequencies; a mutual ambiguity operation module, configured to perform mutual ambiguity operation on the direct wave baseband signal and the target echo baseband signal, and perform phase compensation on the mutual ambiguity functions of different carrier frequencies and then superimpose them to obtain a synthetic mutual ambiguity function; An observation vector construction module, configured to construct an observation vector in sections according to Doppler frequency based on the synthetic mutual ambiguity function; A compressed sensing modeling module is used to perform compressed sensing modeling on the mutual ambiguity function of each carrier frequency to obtain a dictionary matrix after the ambiguity function corresponding to each carrier frequency is superimposed, thereby obtaining a total dictionary matrix; Specifically include: The mutual ambiguity function of the nth carrier frequency is sparsely represented and its expression is: Among them, χ n represents the cross-ambiguity function of the nth carrier frequency, χ n (τ l ,f dnm ) represents the nth carrier frequency, delay τ l , Doppler frequency f dnm The mutual fuzzy function value under B n is the dictionary matrix of the nth carrier frequency, with a dimension of LM×KI, and each column is a copy of the mutual ambiguity function of the delay-Doppler frequency of the direct wave under the carrier frequency, σ n is the sparse vector of the nth carrier frequency, with dimension KI×1; The ambiguity functions corresponding to each carrier frequency are superimposed to obtain the superimposed dictionary matrix, and the observation vector a is obtained accordingly. S Perform sparse representation; the superimposed dictionary matrix is expressed as: Among them, B S is the dictionary matrix after superposition, Ψ n is the phase compensation matrix, N is the total number of transponders; Then the observation vector a S The sparse expression is: represents a sparse vector; The observation vector is sparsely represented and converted into a real number form, and its expression is: in, Represents a sparse vector The real number form of B represents the total dictionary matrix B S The real number form of a represents the observation vector a S The real form of ; A sparse solution module is used to construct a sparse solution model based on the observation vector and the total dictionary matrix, and iteratively calculate the sparse solution model based on a non-convex substitution function to obtain a target detection result; specifically comprising: Construct the following pseudo-norm: Among them, len(x) is the number of elements in the column vector x, x i is the i-th element of x; Based on the observation vector and the total dictionary matrix, a sparse solution model of the mutual ambiguity function after homologous multi-frequency synthesis is established, and its expression is: Based on the pseudo-norm and the Lagrangian function of the sparse solution model, an optimal solution fixed point iterative algorithm is designed to solve the sparse vector Among them, the optimal solution fixed point expression is: in, is a diagonal matrix whose elements in row i and column i are for: for The i-th element of ; The current vector is brought into the optimal solution fixed point expression, and an iterative loop is performed until σ reaches convergence to obtain the final solution vector of the sparse recovery model to achieve target detection.

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