A subspace unitary transformation-based dual basis radar range-dependent clutter compensation method

Abstract

The application discloses a double-base radar distance-dependent clutter compensation method based on a subspace unitary transformation, and comprises the following steps: constructing a space-time steering matrix of a to-be-detected distance unit and a training sample set respectively; constructing a transformation matrix according to the space-time steering matrix, so that the clutter subspace of each training sample in the training sample set and the to-be-detected distance unit are consistent; in the fitting process, taking the transformation error of each training sample in the training sample set and the to-be-detected distance unit as a target optimization function; compensating the echo data corresponding to each training sample in the training sample set by using the transformation matrix to obtain corresponding compensated echo data; calculating a covariance matrix corresponding to the to-be-detected distance unit by using all the compensated echo data; solving a STAP weight vector according to the covariance matrix; and suppressing the clutter of the echo data corresponding to the to-be-detected distance unit by using the STAP weight vector. The application improves the clutter suppression performance and has strong scene use versatility.

Description

Technical Field

[0001] This invention belongs to the field of radar communication technology, specifically relating to a bistatic radar range-dependent clutter compensation method based on subspace unitary transform. Background Technology

[0002] Space-Time Adaptive Processing (STAP) is based on the coupling relationship between clutter spatial frequency and Doppler frequency. It uses two-dimensional space-time degrees of freedom to suppress clutter, which can improve the radar's ability to detect moving targets in clutter backgrounds.

[0003] The prerequisite for the STAP algorithm to achieve good clutter suppression performance is that the number of independent and identically distributed training samples used to estimate the clutter covariance matrix needs to be more than twice the system's degrees of freedom. However, when bistatic radar systems operate in down-looking mode, the clutter they face exhibits severe range dependence, making it difficult to obtain sufficient independent and identically distributed training samples. Consequently, the accuracy of covariance matrix estimation decreases, leading to a decline in STAP clutter suppression performance. Therefore, to mitigate the impact of range dependence on STAP performance, it is necessary to study effective range-dependent clutter compensation methods to eliminate the non-stationarity of range-dependent clutter and improve clutter suppression performance. Currently, existing range-dependent clutter compensation methods can be mainly divided into two types: the first type is main lobe clutter compensation methods, such as Doppler Warping (DW), Adaptive Doppler Warping (ADW), Angle Doppler Compensation (ADC), and Adaptive Angle Doppler Compensation (A). 2 DC). Among them, DW and ADW belong to one-dimensional Doppler compensation algorithms, which do not consider the spread of clutter in the spatial domain; ADC and A 2 DC is a two-dimensional compensation algorithm that aligns the clutter spectrum center simultaneously along both the spatial and temporal domains. All the methods mentioned above only align some clutter cells along the main lobe of the clutter spectrum and are only applicable to clutter spectra with strong beam directionality. The second type is a full-spectrum clutter compensation method, such as derivative-based updating (DBU) and registration-based compensation (RBC). These methods can compensate for both main lobe clutter and side lobe clutter simultaneously, exhibiting better clutter compensation performance.

[0004] However, the first method mentioned above only compensates for main lobe clutter; although the second method can compensate for both main lobe clutter and side lobe clutter, it is only applicable to single-base or some dual-base radar configurations and is not universal. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a bistatic radar range-dependent clutter compensation method based on subspace unitary transform. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a bistatic radar range-dependent clutter compensation method based on subspace unitary transform, comprising:

[0007] Construct the spatiotemporal steering matrix for the distance unit to be detected and for each training sample in the training sample set, respectively;

[0008] A transformation matrix is ​​constructed based on the spatiotemporal steering matrix to fit the clutter subspace of each training sample in the training sample set to be consistent with that of the range cell to be detected. The fitting process uses the transformation error between the spatiotemporal steering matrix of each training sample in the training sample set and the spatiotemporal steering matrix of the range cell to be detected as the objective optimization function, and transforms the objective optimization function into an optimization problem with unitary constraints. Solving the optimization problem yields the transformation matrix corresponding to each training sample in the training sample set.

[0009] The echo data corresponding to each training sample in the training sample set is compensated using the transformation matrix to obtain the corresponding compensated echo data.

[0010] Calculate the covariance matrix corresponding to the range cell to be detected using all the compensated echo data;

[0011] The STAP weight vector is calculated based on the covariance matrix, and then the STAP weight vector is used to suppress clutter in the echo data corresponding to the range cell to be detected.

[0012] In one embodiment of the present invention, the spatiotemporal guidance matrix formula of the constructed range cell to be detected is expressed as:

[0013]

[0014] in, This represents the spatiotemporal steering matrix of the range cell l0 to be detected. This represents the spatiotemporal steering vector corresponding to the i-th clutter cell on the range cell l0 to be detected, where i = 1 to N. c N c This indicates the number of clutter cells on the range cell l0 to be detected. This represents the spatial steering vector corresponding to the i-th clutter cell on the range cell l0 to be detected. This represents the time-domain steering vector corresponding to the i-th clutter cell on the range cell l0 to be detected.

[0015] In one embodiment of the present invention, the spatiotemporal guidance matrix formula for each training sample in the constructed training sample set is expressed as:

[0016]

[0017] Among them, S l This represents the spatiotemporal steering matrix of training sample l in the training sample set. This represents the spatiotemporal steering vector corresponding to the i-th clutter cell on training sample l in the training sample set, where i = 1 to N. c s s (f s,l,i ) represents the spatial steering vector corresponding to the i-th clutter cell on training sample l in the training sample set, s t (f d,l,i ) represents the time-domain steering vector corresponding to the i-th clutter unit on training sample l in the training sample set.

[0018] In one embodiment of the present invention, the objective optimization function is transformed into an optimization problem with unitary constraints, expressed as follows:

[0019]

[0020] Among them, T l Let ||·|| represent the transformation matrix corresponding to training sample l in the training sample set. F The spacetime orientation matrix represents the Frobenius norm, (·). H This indicates the conjugate transpose operation, where I represents the identity matrix.

[0021] In one embodiment of the present invention, the process of solving the optimization problem is expressed by the following formula:

[0022]

[0023] Where tr(·) represents the trace operation. U and V represent the unitary matrices formed by the left and right singular vectors of Q, respectively, and Λ represents the diagonal matrix formed by the singular values ​​of Q. Z = V H T l H U; The transformation matrix T is calculated using the property that Z is a unitary matrix. l =UV H .

[0024] In one embodiment of the present invention, the formula for compensating the echo data corresponding to each training sample in the training sample set using the transformation matrix is ​​expressed as follows:

[0025] x′ l =T l x l ;

[0026] Where, x′ l x represents the compensated echo data corresponding to training sample l in the training sample set. l This indicates that training sample l in the training sample set corresponds to the echo data before compensation.

[0027] In one embodiment of the present invention, the formula for calculating the covariance matrix corresponding to the range cell to be detected using all compensated echo data is expressed as follows:

[0028]

[0029] in, Let L represent the covariance matrix corresponding to the distance unit l0 to be detected, and let L represent the number of training samples in the training sample set.

[0030] In one embodiment of the present invention, the formula for solving the STAP weight vector based on the covariance matrix is ​​expressed as:

[0031]

[0032] Where w represents the STAP weight vector, μ represents a scalar constant, and (·) -1 represents the inverse operation, and s represents the target guidance vector.

[0033] In one embodiment of the present invention, the clutter suppression formula for the range cell to be detected using the STAP weight vector is expressed as follows:

[0034]

[0035] in, This represents the clutter suppression result corresponding to the range cell l0 to be detected. This represents the echo data corresponding to the distance unit l0 to be detected.

[0036] The beneficial effects of this invention are:

[0037] The present invention proposes a bistatic radar range-dependent clutter compensation method based on subspace unitary transformation, comprising: constructing the spatiotemporal steering matrix of the range cell to be detected and each training sample in the training sample set; constructing a transformation matrix based on the spatiotemporal steering matrix to fit the clutter subspace of each training sample in the training sample set to maintain consistency with that of the range cell to be detected; wherein, the fitting process uses the transformation error between the spatiotemporal steering matrix of each training sample in the training sample set and the spatiotemporal steering matrix of the range cell to be detected as the objective optimization function, and transforms the objective optimization function into an optimization problem with unitary matrix constraints, and solves the optimization problem to obtain the transformation matrix corresponding to each training sample in the training sample set; using the transformation matrix to compensate the echo data corresponding to each training sample in the training sample set to obtain the corresponding compensated echo data; calculating the covariance matrix corresponding to the range cell to be detected using all compensated echo data; solving the STAP weight vector based on the covariance matrix, and using the STAP weight vector to suppress clutter in the echo data corresponding to the range cell to be detected. As can be seen, this invention rotates the clutter subspace of each training sample in the training sample set into the clutter subspace of the range cell to be detected by a transformation matrix, so that the clutter statistical characteristics of each training sample in the training sample set are approximately consistent with the clutter statistical characteristics of the range cell to be detected, thereby eliminating the non-stationarity of range-dependent clutter and constructing an accurate covariance matrix to improve clutter suppression performance. The method proposed in this invention can compensate for both main lobe clutter and side lobe clutter, and has no requirements on the geometric configuration of the radar system. It is not only applicable to single-base configuration radar systems, but also to any dual-base configuration, such as high-orbit satellite launch and low-orbit satellite reception configurations, satellite launch and UAV reception configurations, and satellite launch and ground reception configurations, etc., making it highly versatile in various scenarios.

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating a bistatic radar range-dependent clutter compensation method based on subspace unitary transform provided in an embodiment of the present invention.

[0040] Figure 2 This is a schematic diagram of the geometric configuration of the sky bistatic radar used in the simulation experiment provided in the embodiment of the present invention;

[0041] Figure 3 The embodiments of the present invention are based on Figure 2 The diagram shows a simulated two-dimensional power spectrum of clutter obtained under the geometric configuration of a bistatic sky radar.

[0042] Figure 4 This is the embodiment of the present invention that provides the following: Figure 3A schematic diagram of the two-dimensional space-time power spectrum of clutter after range-dependent compensation;

[0043] Figure 5 This is a schematic diagram comparing the improvement factors before and after compensation using the method proposed in this invention. Detailed Implementation

[0044] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0045] Please see Figure 1 This invention provides a bistatic radar range-dependent clutter compensation method based on subspace unitary transform, specifically including the following steps:

[0046] S10. Construct the spatiotemporal steering matrix of the distance unit to be detected and each training sample in the training sample set.

[0047] like Figure 2 In the bistatic radar system scenario shown, T and R represent the transmitting platform and the receiving platform, respectively, and H... T and H R These represent the heights of the transmitting platform T and the receiving platform R, respectively; C represents the clutter element; and R... T and R R V represents the distance from the transmitting platform T and the receiving platform R to the clutter element, respectively. T and V R Let represent the velocities of the radar transmitting platform and the radar receiving platform, respectively; Re represent the Earth's radius; O represent the Earth's center; and α represent the angles between the radar transmitting platform and the radar receiving platform and the Earth's center.

[0048] based on Figure 2 The spatiotemporal steering matrix formula for the range cell to be detected, constructed in the embodiment of the present invention, is expressed as follows:

[0049]

[0050] in, The spatiotemporal guidance matrix representing the range cell l0 to be detected. This represents the spatiotemporal steering vector corresponding to the i-th clutter cell on the range cell l0 to be detected, where i = 1 to N. c N c This indicates the number of clutter units on the range cell l0 to be detected or on each training sample l in the training sample set, meaning the number of clutter units on the range cells of the radar system is the same. This represents the spatial steering vector corresponding to the i-th clutter cell on the range cell l0 to be detected. This represents the time-domain steering vector corresponding to the i-th clutter cell on the range cell l0 to be detected. Wherein,

[0051] Spatial guidance vector The formula is expressed as:

[0052]

[0053] Where N represents the number of spatial receiving channels, This represents the spatial frequency corresponding to the i-th clutter unit on the detection range unit l0.

[0054] Correspondingly, time-domain steering vector The formula is expressed as:

[0055]

[0056] Where K represents the number of coherent pulses, This represents the Doppler frequency corresponding to the i-th clutter unit on the detection range unit l0.

[0057] Similarly, the spatiotemporal guidance matrix formula for each training sample in the training sample set constructed in this embodiment of the invention is expressed as:

[0058]

[0059] Among them, S l This represents the spatiotemporal steering matrix of training sample l in the training sample set. This represents the spatiotemporal steering vector corresponding to the i-th clutter cell on training sample l in the training sample set, where i = 1 to N. c s s (f s,l,i ) represents the spatial steering vector corresponding to the i-th clutter cell on training sample l in the training sample set, s t (f d,l,i ) represents the time-domain steering vector corresponding to the i-th clutter cell on training sample l in the training sample set. Wherein,

[0060] Spatial guidance vector s s (f s,l,i The formula is expressed as:

[0061] s s (f s，l，i )=[1,exp(j2πf s，l，i ), …, exp(j2π(N-1)f s，l，i )] T (5)

[0062] Among them, f s,l,i This represents the spatial frequency corresponding to the i-th clutter unit on training sample l in the training sample set.

[0063] Correspondingly, the time-domain steering vector s t(f d,l,i The formula is expressed as:

[0064] s t (f d,l,i )=[1,exp(j2πf d,l,i ),…,exp(j2π(K-1)f d,l,i )] T (6)

[0065] Among them, f d,l,i This represents the Doppler frequency corresponding to the i-th clutter unit on training sample l in the training sample set.

[0066] S20. Construct a transformation matrix based on the spatiotemporal steering matrix to fit the clutter subspace of each training sample in the training sample set to be consistent with that of the distance cell to be detected. In the fitting process, the transformation error between the spatiotemporal steering matrix of each training sample in the training sample set and the spatiotemporal steering matrix of the distance cell to be detected is used as the objective optimization function. The objective optimization function is transformed into an optimization problem with unitary matrix constraints. Solving the optimization problem yields the transformation matrix corresponding to each training sample in the training sample set.

[0067] The design of the transformation matrix is ​​particularly important in the method proposed in this invention. According to the inventor's analysis, by introducing the transformation matrix, ideally, the clutter subspace of the training samples and the distance cell to be detected in the fitting training sample set can be expressed by the following formula:

[0068]

[0069] After transformation matrix T l After performing a linear transformation on the training sample l, the clutter subspace of the unit to be detected l0 can be made consistent with that of the training sample l.

[0070] However, in practical applications, it is difficult to meet the assumptions of formula (7). This embodiment of the invention proposes to use the transformation error between the spatiotemporal steering matrix of each training sample in the training sample set and the spatiotemporal steering matrix of the distance unit to be detected as the objective optimization function. At the same time, in order to ensure that the echo data passes through the transformation matrix T l After the linear transformation, the noise characteristics remain unchanged, and the constraints during the solution process guarantee that the transformation matrix T l It is a unitary matrix. From the perspective of the subspace, through the transformation matrix T... l The clutter subspace of the training samples is rotated into the clutter subspace of the range cell to be detected, making the clutter statistical characteristics of the training samples approximately consistent with those of the range cell to be detected, thereby eliminating the range dependency of the clutter. Finally, in this embodiment of the invention, the objective optimization function is transformed into an optimization problem with unitary constraints, expressed as follows:

[0071]

[0072] Among them, ||·|| F The spacetime orientation matrix represents the Frobenius norm, (·). H This indicates the conjugate transpose operation, where I represents the identity matrix.

[0073] Furthermore, the detailed solution process for formula (8) is as follows:

[0074]

[0075] Where tr(·) represents the trace operation. It can be seen from formula (9) that minimizing... Equivalent to maximizing

[0076] make Furthermore, singular value decomposition is performed on matrix Q to obtain Q = UΛV H Let U and V represent the unitary matrix formed by the left and right singular vectors of Q, respectively, and Λ represent the diagonal matrix formed by the singular values ​​of Q. Then:

[0077]

[0078] Let Z = V H T l H Given that Z is a unitary matrix, all its diagonal elements are less than or equal to 1. When Z is the identity matrix, i.e., all its diagonal elements are 1, formula (10) reaches its maximum value, thus determining the transformation matrix T at this time. l One solution is:

[0079] T l =UV H (11)

[0080] S30. Use the transformation matrix to compensate the echo data corresponding to each training sample in the training sample set to obtain the corresponding compensated echo data.

[0081] As is well known, the echo signal corresponding to training sample l in the training sample set can be expressed as:

[0082] x l =c l +n l (12)

[0083] Where, n l c represents zero-mean Gaussian white noise on the training sample l. l Let represent the clutter signal on training sample l, which is the superposition of echo signals from multiple clutter units on training sample l, and can be expressed as:

[0084]

[0085] Where, ξ l,i ξ represents the amplitude of the i-th clutter cell on training sample l in the training sample set. l,i s is obtained through existing technical calculation methods. l,i s represents the spatiotemporal steering vector of the i-th clutter cell in the training sample set l. l,i N is calculated using formula (4). c This represents the number of clutter units on training sample l in the training sample set. Therefore, in this embodiment of the invention, the compensation formula for the echo data corresponding to each training sample in the training sample set using the transformation matrix is ​​expressed as:

[0086] x′ l =T l x l (14)

[0087] Where, x′ l T represents the compensated echo data corresponding to training sample l in the training sample set. l Let x represent the transformation matrix corresponding to training sample l in the training sample set. l This represents the echo data before compensation corresponding to training sample l in the training sample set. After transformation matrix T... l After compensation processing, the compensated echo data x′ corresponding to the training sample l l The clutter statistical characteristics are close to the echo data corresponding to the unit l0 to be detected. The clutter statistical characteristics.

[0088] S40. Calculate the covariance matrix corresponding to the range cell to be detected using all the compensated echo data.

[0089] In this embodiment of the invention, the formula for calculating the covariance matrix corresponding to the range cell to be detected using all compensated echo data is expressed as follows:

[0090]

[0091] in, Let x′ represent the covariance matrix corresponding to the distance unit l0 to be detected, where L represents the number of training samples in the training sample set. l This represents the compensated echo data corresponding to training sample l in the training sample set, (·). H This indicates the operation of finding the conjugate transpose.

[0092] S50. Solve for the STAP weight vector based on the covariance matrix, and use the STAP weight vector to suppress clutter in the echo data corresponding to the range cell to be detected.

[0093] In this embodiment of the invention, the formula for solving the STAP weight vector based on the covariance matrix is ​​expressed as follows:

[0094]

[0095] Where w represents the STAP weight vector, and μ represents a scalar constant. Let represent the covariance matrix corresponding to the distance cell l0 to be detected, (·). -1 denoted as the inverse operation, and s represents the target guidance vector. Here, s is calculated in a similar way to the calculation of the spatiotemporal guidance matrix of the distance cell to be detected in S10 and each training sample in the training sample set. The difference is that the distance cell includes the target when s is calculated.

[0096] In this embodiment of the invention, the formula for clutter suppression using the STAP weight vector on the range cell to be detected is expressed as follows:

[0097]

[0098] in, This represents the clutter suppression result corresponding to the range cell l0 to be detected, where w represents the STAP weight vector, (·). H This indicates the operation of finding the conjugate transpose. This represents the echo data corresponding to the range cell l0 to be detected. The covariance matrix is ​​estimated from the training samples after compensation. It asymptotically converges to the true covariance matrix of the unit being detected. At this point, the STAP algorithm can achieve better clutter suppression performance. The calculation method is shown in formulas (12) and (13), that is:

[0099]

[0100] in, This represents zero-mean Gaussian white noise on the detection range cell l0. The clutter signal on the range cell l0 to be detected is the superposition of echo signals from multiple clutter cells on the range cell l0 to be detected, and can be expressed as:

[0101]

[0102] in, This represents the amplitude of the i-th clutter cell on the range cell l0 to be detected. Obtained through existing technical calculation methods This represents the spatiotemporal steering vector of the i-th clutter cell on the range cell l0 to be detected. N is calculated using formula (1). c This indicates the number of clutter cells on the distance cell l0 to be detected.

[0103] To verify the effectiveness of the bistatic radar range-dependent clutter compensation method based on subspace unitary transform provided in this embodiment of the invention, the following experiments were conducted.

[0104] 1. Experimental simulation parameters

[0105] The hardware platform for the simulation experiment in this embodiment of the invention is: an Intel(R) Core(TM) i7-9700 CPU with a clock speed of 3.00 GHz and 16 GB of memory. The software platform for the simulation experiment in this embodiment of the invention is: Windows 10 operating system and MATLAB R2020b.

[0106] The parameters for the simulation experiment in this embodiment of the invention are set as follows: launch platform T, height H T Approximately 828 km, speed V T The speed is approximately 7.4 km / s, the longitude and latitude are (93°E, 45°N), and the altitude of the receiving platform is H. R Approximately 25km, speed V R The speed is 120 m / s, and the longitude and latitude are (110°E, 34°N). The number of space receiving channels N = 8, the radar operating wavelength λ = 0.3 m, the array element spacing d = 0.16 m, the number of coherent pulses per pulse repetition period K = 32, the pulse repetition frequency PRF = 2 kHz, and the clutter noise ratio CNR = 30 dB.

[0107] 2. Simulation content and result analysis

[0108] Figure 3 and Figure 4 The figures show the clutter space-time two-dimensional power spectra before and after compensation using the method proposed in this invention. Figure 3 and Figure 4 The horizontal axis in the diagram represents spatial frequency. Figure 3 and Figure 4 The vertical axis in the figure represents the normalized Doppler frequency, compared to Figure 3 and Figure 4 It can be seen that after compensation by the method proposed in this invention, the clutter power spectrum is significantly narrowed, indicating that this invention can compensate for distance-dependent clutter and eliminate the non-stationarity of clutter.

[0109] Figure 5 This diagram shows a comparison of the improvement factors before and after compensation using the method proposed in this invention. Figure 5 The horizontal axis in the figure represents the normalized Doppler frequency. Figure 5The vertical axis represents the improvement factor in decibels. The pink solid line represents the improvement factor curve after direct STAP processing without clutter compensation, while the green dashed line represents the improvement factor curve after clutter compensation using the method proposed in this invention, followed by clutter suppression using STAP. Figure 5 It can be seen that the notch of the improvement factor is significantly narrowed, indicating that the method proposed in this invention improves the performance of slow target detection.

[0110] The simulation results above verify the correctness, effectiveness and reliability of the method proposed in this invention.

[0111] As can be seen from the above, the method proposed in this invention does not require any geometric configuration of the radar system. It is applicable to any bistatic configuration, such as bistatic radar systems with high-orbit satellite launch and low-orbit satellite reception, satellite launch and UAV reception, and satellite launch and ground reception. It is also applicable to single-static radar systems.

[0112] In summary, the bistatic radar range-dependent clutter compensation method based on subspace unitary transformation proposed in this invention includes: constructing the spatiotemporal steering matrix of the range cell to be detected and each training sample in the training sample set; constructing a transformation matrix based on the spatiotemporal steering matrix to fit the clutter subspace of each training sample in the training sample set to maintain consistency with the range cell to be detected; wherein, the fitting process uses the transformation error between the spatiotemporal steering matrix of each training sample in the training sample set and the spatiotemporal steering matrix of the range cell to be detected as the objective optimization function, and transforms the objective optimization function into an optimization problem with unitary matrix constraints, and solves the optimization problem to obtain the transformation matrix corresponding to each training sample in the training sample set; using the transformation matrix to compensate the echo data corresponding to each training sample in the training sample set to obtain the corresponding compensated echo data; calculating the covariance matrix corresponding to the range cell to be detected using all compensated echo data; solving the STAP weight vector based on the covariance matrix, and using the STAP weight vector to suppress clutter in the echo data corresponding to the range cell to be detected. As can be seen, the embodiments of the present invention rotate the clutter subspace of each training sample in the training sample set into the clutter subspace of the range cell to be detected by transforming the matrix, so that the clutter statistical characteristics of each training sample in the training sample set are approximately consistent with the clutter statistical characteristics of the range cell to be detected, thereby eliminating the non-stationarity of range-dependent clutter and constructing an accurate covariance matrix, thus improving clutter suppression performance. The method proposed in this invention can compensate for both main lobe clutter and side lobe clutter, and has no requirements on the geometric configuration of the radar system. It is not only applicable to single-base configuration radar systems, but also to any dual-base configuration, such as high-orbit satellite launch and low-orbit satellite reception configurations, satellite launch and UAV reception configurations, and satellite launch and ground reception configurations, etc., making it highly versatile in various scenarios.

[0113] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0114] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the specification and accompanying drawings, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0115] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A bistatic radar range-dependent clutter compensation method based on subspace unitary transform, characterized in that, include: Construct the spatiotemporal steering matrix for the distance unit to be detected and for each training sample in the training sample set, respectively; A transformation matrix is ​​constructed based on the spatiotemporal steering matrix to fit the clutter subspace of each training sample in the training sample set to be consistent with that of the range cell to be detected. The fitting process uses the transformation error between the spatiotemporal steering matrix of each training sample in the training sample set and the spatiotemporal steering matrix of the range cell to be detected as the objective optimization function, and transforms the objective optimization function into an optimization problem with unitary constraints. Solving the optimization problem yields the transformation matrix corresponding to each training sample in the training sample set. The echo data corresponding to each training sample in the training sample set is compensated using the transformation matrix to obtain the corresponding compensated echo data. Calculate the covariance matrix corresponding to the range cell to be detected using all the compensated echo data; The STAP weight vector is calculated based on the covariance matrix, and the STAP weight vector is used to suppress clutter in the echo data corresponding to the range cell to be detected. The objective function is transformed into an optimization problem with unitary constraints, expressed as follows: ； in, Indicates the distance unit to be detected The spatiotemporal guidance matrix, The training sample set represents the training samples. The spatiotemporal guidance matrix, The training sample set represents the training samples. The corresponding transformation matrix, This indicates the search for the Frobenius norm. This indicates the operation of finding the conjugate transpose. Represents the identity matrix; The process of solving optimization problems can be expressed by the following formula: ； in, This indicates the trace operation. , U , V They represent Q The unitary matrix composed of the left and right singular vectors. Λ express Q A diagonal matrix composed of the singular values ​​of . ;use The transformation matrix is ​​obtained by calculating the properties of the unitary matrix. .

2. The bistatic radar range-dependent clutter compensation method based on subspace unitary transform according to claim 1, characterized in that, The spatiotemporal steering matrix of the constructed range cell to be detected is expressed as follows: ； in, Indicates the distance unit to be detected The spatiotemporal guidance matrix, Indicates the distance unit to be detected Upper The spatiotemporal steering vector corresponding to each clutter unit , Indicates the distance unit to be detected Or each training sample in the training sample set Number of upper clutter cells Indicates the distance unit to be detected Upper The spatial steering vector corresponding to each clutter unit Indicates the distance unit to be detected Upper The time-domain steering vector corresponding to each clutter unit.

3. The bistatic radar range-dependent clutter compensation method based on subspace unitary transform according to claim 2, characterized in that, The spatiotemporal steering matrix of each training sample in the constructed training sample set is expressed by the following formula: ； in, The training sample set represents the training samples. The spatiotemporal guidance matrix, The training sample set represents the training samples. Upper The spatiotemporal steering vector corresponding to each clutter unit , The training sample set represents the training samples. Upper The spatial steering vector corresponding to each clutter unit The training sample set represents the training samples. Upper The time-domain steering vector corresponding to each clutter unit.

4. The bistatic radar range-dependent clutter compensation method based on subspace unitary transform according to claim 1, characterized in that, The formula for compensating the echo data corresponding to each training sample in the training sample set using the transformation matrix is ​​expressed as follows: ； in, The training sample set represents the training samples. The corresponding compensated echo data, The training sample set represents the training samples. The echo data before compensation.

5. The bistatic radar range-dependent clutter compensation method based on subspace unitary transform according to claim 4, characterized in that, The formula for calculating the covariance matrix of the range cell to be detected using all compensated echo data is as follows: ； in, Indicates the distance unit to be detected The corresponding covariance matrix, This indicates the number of training samples in the training sample set.

6. The bistatic radar range-dependent clutter compensation method based on subspace unitary transform according to claim 5, characterized in that, The formula for solving the STAP weight vector based on the covariance matrix is ​​expressed as follows: ； in, Represents the STAP weight vector. Represents a scalar constant. This indicates the inverse operation. This represents the target guidance vector.

7. The bistatic radar range-dependent clutter compensation method based on subspace unitary transform according to claim 6, characterized in that, The formula for clutter suppression using the STAP weight vector to the range cell to be detected is expressed as follows: ； in, Indicates the distance unit to be detected The corresponding clutter suppression results, Indicates the distance unit to be detected The corresponding echo data.

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