Radar waveform power spectrum processing method and device based on Cauchy Schwarz divergence

Abstract

The invention discloses a radar waveform power spectrum processing method and device based on Cauchy Schwarz divergence, and the method comprises the steps: setting the initial parameters of a radar, and completing the initialization setting of the parameters of the radar; according to the radar echo data of the clutter signal, estimating to obtain an N * N-dimensional clutter power spectrum and clutter frequency domain covariance; according to the radar echo data of the target signal, estimating to obtain an N * N-dimensional target power spectrum and a target frequency domain covariance; determining a first matrix and a second matrix according to the power spectrum of the set noise and the noise frequency domain covariance; and performing iterative optimization on the initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix, and determining a radar waveform power spectrum under the Cauchy Schwarz divergence criterion. According to the method, a complex non-convex optimization problem can be converted into a convex optimization problem which is easy to iteratively solve, and the target detection performance of a radar system is further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of radar waveform power spectrum processing, and in particular to a radar waveform power spectrum processing method and device based on Cauchy-Schwarz divergence. Background Art

[0002] As the electromagnetic environment becomes increasingly complex, the adaptive processing technology that relies solely on the receiving end of the radar system has gradually approached its performance bottleneck. Therefore, how to make full use of the capabilities of the radar system transmitter to design the transmission waveform to improve the system's adaptability to the external environment has become an important topic in the research of modern intelligent radar. In the traditional working mode, the radar system's transmission waveform and transceiver mode usually remain in a fixed mode, the system is in an open-loop working state, lacks the ability to recognize the environment, and cannot effectively use the degrees of freedom of the transmitter to optimize its working performance. Compared with traditional radars, cognitive radars have closed-loop processing capabilities and can adaptively design matching transmission waveforms based on target information, environmental conditions, etc. to adapt to different working environments, thereby reducing the negative impact of the environment on radar performance and achieving radar system performance improvement. Reasonable transmission waveform design can enable the radar system to maintain stable performance in complex environments, thereby improving detection capabilities and overall work efficiency.

[0003] At present, for the design of radar transmission waveform energy spectrum under clutter background, the waveform of the transmitter is usually adjusted by adopting the corresponding waveform optimization design criteria based on the acquisition of target and environment information. How to design a transmission waveform that matches the environment to improve the radar's detection performance of the target has become a core issue in the detection waveform design of cognitive radar systems. Among the traditional waveform optimization criteria, there are mainly two categories: one is the maximum signal-to-noise ratio criterion, which improves the target detection performance by improving the signal-to-noise ratio of the system output; the other is the maximum relative entropy criterion, which aims to improve the target detection capability in clutter environment by maximizing the relative entropy between probability density functions in binary hypothesis testing. However, these methods usually focus on improving target detection performance, but fail to fully consider the suppression of system false alarm performance. From the perspective of the robustness of the radar system warning work, in order to prevent false warnings, the system must ensure low false alarm performance while improving the probability of target detection. In other words, when optimizing the radar waveform, it is necessary not only to enhance the detectability of the target signal, but also to control the false alarm rate to avoid too many false alarms in the system.

[0004] Therefore, in waveform design, how to balance the relationship between detection performance and false alarm suppression has become an important issue that needs to be urgently solved in cognitive radar waveform design. Summary of the invention

[0005] To this end, the present invention provides a radar waveform power spectrum processing method and device based on Cauchy-Schwarz divergence, uses the Cauchy-Schwarz divergence between the probability density functions of two hypotheses to be tested as a criterion, constructs a waveform optimization method that can weigh the missed detection probability and the false alarm probability under energy constraints, solves the problem that the traditional single-criterion optimization method is difficult to achieve the above-mentioned two probability trade-offs, and can simplify the solution process by constructing a proxy function of the optimization criterion, transforming a complex non-convex optimization problem into a convex optimization problem that is easy to iteratively solve, and further realizing the improvement of the target detection performance of the radar system.

[0006] In order to achieve the above object, the present invention provides the following technical solution: a radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, comprising:

[0007] Set the initial parameters of the radar and complete the initialization of the radar parameters;

[0008] According to the radar echo data of the clutter signal, the N×N dimensional clutter power spectrum and the clutter frequency domain covariance are estimated; according to the radar echo data of the target signal, the N×N dimensional target power spectrum and the target frequency domain covariance are estimated;

[0009] Determine a first matrix and a second matrix according to a power spectrum of set noise and a noise frequency domain covariance;

[0010] The initial reference waveform power spectrum is iteratively optimized according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0011] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, in the process of setting the initial parameters of the radar, the initial parameters include: the total energy of the radar transmission waveform, the initial reference waveform power spectrum and the number of frequency points in the working frequency band.

[0012] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, the expression of the first matrix is:

[0013] C1=R X +2R C

[0014] In the formula, C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0015] The expression of the second matrix is:

[0016] C2=R X +RC

[0017] Where C2 is the second matrix.

[0018] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, in the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is:

[0019]

[0020] In the formula, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0021] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, the steps of iteratively optimizing the initial reference waveform power spectrum are:

[0022] Set the initial number of iterations and the maximum number of iterations;

[0023] Calculate a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0024] Obtaining a second gradient auxiliary matrix by calculation according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0025] Calculate and obtain a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0026] Obtaining a third matrix and a first auxiliary vector of a k-th iteration by calculation according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix and the noise frequency domain covariance;

[0027] According to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform, the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration are calculated;

[0028] Calculate the residual value of the objective function according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration;

[0029] The residual value of the objective function is judged. If the residual value of the objective function is less than a set threshold, the radar waveform power spectrum after the kth iteration is output, and the process ends. If the residual value of the objective function is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated.

[0030] According to the radar transmission waveform power spectrum after the kth iteration, a final radar waveform power spectrum is calculated and obtained.

[0031] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, in the process of calculating the residual value of the objective function, the second optimization objective function expression is:

[0032]

[0033] in,

[0034]

[0035] In the formula, represents the real part operator of a complex number; Λ (k) is the third matrix; (k) is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H Find the inverse operator for the conjugate transpose; is the Kronecker product; vec(·) is the matrix vectorization operator; are all block sub-matrices of the first gradient auxiliary matrix;

[0036] The present invention also provides a radar waveform power spectrum processing device based on Cauchy-Schwartz divergence, based on the above radar waveform power spectrum processing method based on Cauchy-Schwartz divergence, comprising:

[0037] The radar parameter initialization module is used to set the initial parameters of the radar and complete the initialization setting of the radar parameters;

[0038] The power spectrum and frequency domain covariance acquisition module is used to estimate and obtain the N×N dimensional clutter power spectrum and clutter frequency domain covariance according to the radar echo data of the clutter signal; and estimate and obtain the N×N dimensional target power spectrum and target frequency domain covariance according to the radar echo data of the target signal;

[0039] A first matrix and a second matrix acquisition module, used to determine the first matrix and the second matrix according to the power spectrum of the set noise and the noise frequency domain covariance;

[0040] The waveform power spectrum iterative optimization module is used to iteratively optimize the initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix, so as to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0041] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the radar parameter initialization module, in the process of setting the initial parameters of the radar, the initial parameters include: the total energy of the radar transmission waveform, the initial reference waveform power spectrum and the number of frequency points in the working frequency band.

[0042] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the first matrix and second matrix acquisition module, the expression of the first matrix is:

[0043] C1=R X +2R C

[0044] In the formula, C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0045] The expression of the second matrix is:

[0046] C2=R X +R C

[0047] Where C2 is the second matrix.

[0048] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the waveform power spectrum iterative optimization module, in the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is:

[0049]

[0050] In the formula, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0051] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the waveform power spectrum iterative optimization module, the submodule for iteratively optimizing the initial reference waveform power spectrum includes:

[0052] The iteration number setting submodule is used to set the initial iteration number and the maximum iteration number;

[0053] A first gradient auxiliary matrix calculation submodule, configured to calculate a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0054] A second gradient auxiliary matrix calculation submodule, configured to calculate a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0055] A third gradient auxiliary matrix calculation submodule, configured to calculate a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0056] A third matrix and first auxiliary vector calculation submodule, configured to calculate a third matrix and a first auxiliary vector of a k-th iteration according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix and the noise frequency domain covariance;

[0057] A Lagrange multiplier and radar transmission waveform power spectrum calculation module, used for calculating the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform;

[0058] The objective function residual value calculation submodule is used to calculate the objective function residual value according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration;

[0059] The objective function residual value judgment processing submodule is used to judge the objective function residual value. If the objective function residual value is less than a set threshold, the radar waveform power spectrum after the kth iteration is output and the process ends; if the objective function residual value is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated;

[0060] The final radar waveform power spectrum calculation submodule is used to calculate and obtain the final radar waveform power spectrum according to the radar transmission waveform power spectrum after the kth iteration.

[0061] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the objective function residual value calculation submodule of the waveform power spectrum iterative optimization module, in the process of calculating the objective function residual value, the second optimization objective function expression is:

[0062]

[0063] in,

[0064]

[0065] In the formula, represents the real part operator of a complex number; Λ (k) is the third matrix; (k) is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H Find the inverse operator for the conjugate transpose; is the Kronecker product; vec(·) is the matrix vectorization operator; They are all block sub-matrices of the first gradient auxiliary matrix.

[0066] The invention has the following advantages: the invention completes the initialization setting of radar parameters by setting initial parameters of radar settings; estimates and obtains N×N-dimensional clutter power spectrum and clutter frequency domain covariance according to radar echo data of clutter signals; estimates and obtains N×N-dimensional target power spectrum and target frequency domain covariance according to radar echo data of target signals; determines a first matrix and a second matrix according to the power spectrum of set noise and the noise frequency domain covariance; iteratively optimizes an initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix, and determines the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion. Among them, the steps of iteratively optimizing the power spectrum of the initial reference waveform are: setting the initial number of iterations and the maximum number of iterations; calculating a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and dividing the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; calculating a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; calculating a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; calculating a third gradient auxiliary matrix according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise The method comprises the following steps: calculating the covariance in the acoustic frequency domain, obtaining the third matrix and the first auxiliary vector of the kth iteration; calculating the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform; calculating the residual value of the objective function according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration; judging the residual value of the objective function, if the residual value of the objective function is less than the set threshold, outputting the radar waveform power spectrum after the kth iteration, and ending; if the residual value of the objective function is not less than the set threshold, recalculating the first gradient auxiliary matrix; calculating the final radar waveform power spectrum according to the radar transmission waveform power spectrum after the kth iteration. The present invention uses the Cauchy-Schwarz divergence between the probability density functions of two hypotheses to be tested as a criterion, constructs a waveform optimization method that can weigh the missed detection probability and the false alarm probability under energy constraints, solves the problem that the traditional single-criterion optimization method is difficult to achieve the above-mentioned two probability trade-offs, and can simplify the solution process by constructing a proxy function of the optimization criterion, transforming a complex non-convex optimization problem into a convex optimization problem that is easy to iteratively solve, thereby further improving the target detection performance of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0068] The structures, proportions, sizes, etc. illustrated in this specification are only used to match the contents disclosed in the specification so as to facilitate understanding and reading by persons familiar with the technology. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantial technical significance. Any structural modification, change in proportion or adjustment of size shall still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0069] Figure 1 This is a schematic flow chart of a radar waveform power spectrum processing method based on Cauchy-Schwarz divergence provided in Example 1 of the present invention;

[0070] Figure 2 A schematic diagram of radar transmission-reception of an extended target model in a possible embodiment provided in Embodiment 1 of the present invention under the condition that signal-related clutter and signal-independent noise are considered;

[0071] Figure 3 A schematic diagram of energy spectrum comparison between the present invention and the traditional signal-to-noise ratio criterion, relative entropy criterion and mutual information criterion in a possible embodiment provided in Embodiment 1 of the present invention;

[0072] Figure 4 A schematic diagram of a receiver operating characteristic curve of an energy spectrum of the present invention in a possible embodiment provided in Embodiment 1 of the present invention;

[0073] Figure 5 A schematic diagram of a change in target detection probability with transmit power in a possible embodiment provided in Embodiment 1 of the present invention;

[0074] Figure 6 This is a schematic diagram of the architecture of a radar waveform power spectrum processing device based on Cauchy-Schwarz divergence provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0075] The following is a description of the implementation of the present invention by specific embodiments. People familiar with the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are 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 creative work are within the scope of protection of the present invention.

[0076] Example 1

[0077] See also Figure 1 Embodiment 1 of the present invention provides a radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, comprising the following steps:

[0078] S1. Set the initial parameters of the radar to complete the initialization of the radar parameters;

[0079] S2. According to the radar echo data of the clutter signal, an N×N-dimensional clutter power spectrum and a clutter frequency domain covariance are estimated; according to the radar echo data of the target signal, an N×N-dimensional target power spectrum and a target frequency domain covariance are estimated;

[0080] S3, determining a first matrix and a second matrix according to a power spectrum of set noise and a noise frequency domain covariance;

[0081] S4. Iteratively optimize the initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0082] In this embodiment, in step S1, the initial parameters of the radar are set to complete the initialization setting of the radar parameters;

[0083] Specifically, the total energy of the radar transmitting waveform, the initial reference waveform power spectrum, and the number of frequency points in the working frequency band are set; among which, the total energy of the radar transmitting waveform is E s , should be set according to hardware conditions; the initial reference waveform power spectrum S0 can be set to a commonly used waveform power spectrum, which can be but not limited to a linear frequency modulation signal; the number of frequency points in the working frequency band is N.

[0084] In this embodiment, in step S2, based on the radar echo data of the clutter signal, an N×N-dimensional clutter power spectrum and a clutter frequency domain covariance are estimated; based on the radar echo data of the target signal, an N×N-dimensional target power spectrum and a target frequency domain covariance are estimated;

[0085] Specifically, according to the radar echo data of the clutter signal, the N×N dimensional clutter power spectrum and the clutter frequency domain covariance R are estimated. C; According to the radar echo data of the target signal, the N×N-dimensional target power spectrum and the target frequency domain covariance R are estimated X ;

[0086] The radar echo data can be obtained by using previously collected observation data or by accessing the environment database. The corresponding frequency domain covariance matrix is ​​calculated by the power spectrum estimation method.

[0087] In this embodiment, in step S3, the first matrix and the second matrix are determined according to the power spectrum of the set noise and the noise frequency domain covariance;

[0088] Specifically, the expression of the first matrix is:

[0089] C1=R X +2R C

[0090] In the formula, C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0091] The expression of the second matrix is:

[0092] C2=R X +R C

[0093] Where C2 is the second matrix.

[0094] In this embodiment, in step S4, the initial reference waveform power spectrum is iteratively optimized according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0095] Specifically, in the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is:

[0096]

[0097] In the formula, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0098] The step of iteratively optimizing the initial reference waveform power spectrum is as follows:

[0099] S41, setting the initial number of iterations and the maximum number of iterations;

[0100] Specifically, set the number of iterations k = 1, and the maximum number of iterations K max ;

[0101] S42, calculating a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and dividing the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0102] Specifically, the first gradient auxiliary matrix is ​​calculated based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix.

[0103]

[0104] In the formula, E=[I N ,O N ], and Π k for:

[0105]

[0106] The first gradient auxiliary matrix is ​​divided into four N×N dimensional block sub-matrices Right now:

[0107]

[0108] In the formula,

[0109] S43, calculating and obtaining a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0110] Among them, the second gradient auxiliary matrix The calculation formula is:

[0111]

[0112] S44, calculating and obtaining a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0113] Among them, the third gradient auxiliary matrix The calculation formula is:

[0114]

[0115] S45, calculating and obtaining a third matrix and a first auxiliary vector of the kth iteration according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix and the noise frequency domain covariance;

[0116] Among them, the third matrix Λ (k) The calculation formula is:

[0117]

[0118] In the formula, is the Kronecker product;

[0119] The first auxiliary vector ξ (k) The calculation formula is:

[0120]

[0121] Where vec(·) is the matrix vectorization operator.

[0122] S46. Calculate and obtain the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform;

[0123] Specifically, according to the third matrix Λ (k) , the first auxiliary vector ξ (k) and the total energy E of the radar transmitting waveform s , calculate the Lagrange multiplier λ after the kth iteration ( k ) and radar emission waveform power spectrum s( k ).

[0124] Among them, the second optimization objective function expression is:

[0125]

[0126] In the formula, Represents the complex real part operator.

[0127] The Lagrange multiplier method is used to obtain the k-th iteration radar waveform power spectrum s( k ):

[0128]

[0129] In the formula, λ (k) It is the equation The solution of , and satisfies λ (k) >0.

[0130] S47, calculating and obtaining a residual value of an objective function according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration;

[0131] Specifically, according to the radar transmission waveform power spectrum s after the kth iteration (k) and the radar transmission waveform power spectrum s after the k-1th iteration (k-1) , calculate and obtain the residual value of the objective function;

[0132] S48, judging the residual value of the objective function, if the residual value of the objective function is less than a set threshold, outputting the radar waveform power spectrum after the kth iteration, and ending; if the residual value of the objective function is not less than the set threshold, recalculating the first gradient auxiliary matrix;

[0133] Specifically, the residual value of the objective function is judged, and if the residual value of the objective function is less than a set threshold, the radar waveform power spectrum s after the kth iteration is output. (k) , end; if the residual value of the objective function is not less than the set threshold, proceed to step S42;

[0134] S49. Calculate and obtain a final radar waveform power spectrum according to the radar transmission waveform power spectrum after the kth iteration.

[0135] Specifically, according to the radar transmission waveform power spectrum s after the kth iteration (k) , calculate and obtain the final radar waveform power spectrum s opt .

[0136] In a possible embodiment, an example of radar waveform power spectrum processing for providing an extended target model is as follows:

[0137] The schematic diagram of radar transmission and reception under the extended target model considering signal-related clutter and signal-independent noise is as follows Figure 2 As shown;

[0138] The comparison results of radar waveform power spectrum obtained by the present invention and the radar waveform power spectrum design method based on signal-to-noise ratio, mutual information and relative entropy under the same energy constraint conditions are as follows: Figure 3 Compared with the method based on the signal-to-noise ratio, the waveform power spectrum obtained based on the relative entropy and the design of the present invention can distribute the waveform energy to the frequency where the target response is stronger than the clutter.

[0139] The receiver operating characteristic curves obtained by the present invention and the radar waveform power spectrum design methods based on signal-to-noise ratio, mutual information, and relative entropy under the same energy constraint conditions are as follows: Figure 4 As shown. Figure 4It can be seen that under the same false alarm probability condition, the waveform designed by the present invention has a higher detection probability than the waveforms obtained based on the signal-to-noise ratio and the relative entropy method, and can better detect the target.

[0140] The relationship curve between the total energy of the transmitted waveform and the target detection probability obtained by the present invention and the radar waveform power spectrum design method based on signal-to-noise ratio, mutual information and relative entropy under the same false alarm probability constraint condition is as follows: Figure 5 As shown. Figure 5 It can be seen that the waveform designed by the present invention has a higher detection probability than the waveforms obtained based on the signal-to-noise ratio and the relative entropy method under the same transmission energy condition, that is, to achieve the same detection probability, the demand for transmission energy can be reduced.

[0141] In summary, the present invention completes the initialization setting of radar parameters by setting initial parameters of radar settings; estimates and obtains N×N-dimensional clutter power spectrum and clutter frequency domain covariance according to radar echo data of clutter signals; estimates and obtains N×N-dimensional target power spectrum and target frequency domain covariance according to radar echo data of target signals; determines a first matrix and a second matrix according to the power spectrum of set noise and the noise frequency domain covariance; iteratively optimizes the initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix, and determines the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion. Among them, the steps of iteratively optimizing the power spectrum of the initial reference waveform are: setting the initial number of iterations and the maximum number of iterations; calculating a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and dividing the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; calculating a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; calculating a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; calculating a third gradient auxiliary matrix according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise The method comprises the following steps: calculating the covariance in the acoustic frequency domain, obtaining the third matrix and the first auxiliary vector of the kth iteration; calculating the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform; calculating the residual value of the objective function according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration; judging the residual value of the objective function, if the residual value of the objective function is less than the set threshold, outputting the radar waveform power spectrum after the kth iteration, and ending; if the residual value of the objective function is not less than the set threshold, recalculating the first gradient auxiliary matrix; calculating the final radar waveform power spectrum according to the radar transmission waveform power spectrum after the kth iteration. The present invention uses the Cauchy-Schwarz divergence between the probability density functions of two hypotheses to be tested as a criterion, constructs a waveform optimization method that can weigh the missed detection probability and the false alarm probability under energy constraints, solves the problem that the traditional single-criterion optimization method is difficult to achieve the above-mentioned two probability trade-offs, and can simplify the solution process by constructing a proxy function of the optimization criterion, transforming a complex non-convex optimization problem into a convex optimization problem that is easy to iteratively solve, thereby further improving the target detection performance of the radar system.

[0142] It should be noted that the method of the embodiment of the present disclosure can be performed by a single device, such as a computer or a server. The method of the present embodiment can also be applied in a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present disclosure, and the multiple devices will interact with each other to complete the described method.

[0143] It should be noted that the above describes some embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0144] Example 2

[0145] See also Figure 6 Embodiment 2 of the present invention also provides a radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, including:

[0146] Radar parameter initialization module 001 is used to set the initial parameters of the radar and complete the initialization setting of the radar parameters;

[0147] The power spectrum and frequency domain covariance acquisition module 002 is used to estimate and obtain N×N dimensional clutter power spectrum and clutter frequency domain covariance according to the radar echo data of the clutter signal; and estimate and obtain N×N dimensional target power spectrum and target frequency domain covariance according to the radar echo data of the target signal;

[0148] A first matrix and a second matrix acquisition module 003, used to determine the first matrix and the second matrix according to the power spectrum of the set noise and the noise frequency domain covariance;

[0149] The waveform power spectrum iterative optimization module 004 is used to iteratively optimize the initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix, and determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0150] In this embodiment, in the radar parameter initialization module 001, in the process of setting the initial parameters of the radar, the initial parameters include: total energy of the radar transmission waveform, power spectrum of the initial reference waveform and number of frequency points in the working frequency band.

[0151] In this embodiment, in the first matrix and second matrix acquisition module 003, the expression of the first matrix is:

[0152] C1=R X +2R C

[0153] In the formula, C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0154] The expression of the second matrix is:

[0155] C2=R X +R C

[0156] Where C2 is the second matrix.

[0157] In this embodiment, in the waveform power spectrum iterative optimization module 004, in the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is:

[0158]

[0159] In the formula, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0160] In this embodiment, in the waveform power spectrum iterative optimization module 004, the submodule for iteratively optimizing the initial reference waveform power spectrum includes:

[0161] Iteration number setting submodule 041 is used to set the initial iteration number and the maximum iteration number;

[0162] A first gradient auxiliary matrix calculation submodule 042 is used to calculate a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0163] A second gradient auxiliary matrix calculation submodule 043 is used to calculate a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0164] A third gradient auxiliary matrix calculation submodule 044 is used to calculate and obtain a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0165] A third matrix and first auxiliary vector calculation submodule 045 is used to calculate the third matrix and the first auxiliary vector of the kth iteration according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix and the noise frequency domain covariance;

[0166] A Lagrange multiplier and radar transmission waveform power spectrum calculation module 046 is used to calculate the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform;

[0167] The objective function residual value calculation submodule 047 is used to calculate the objective function residual value according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration;

[0168] The objective function residual value judgment processing submodule 048 is used to judge the objective function residual value. If the objective function residual value is less than a set threshold, the radar waveform power spectrum after the kth iteration is output and the process ends; if the objective function residual value is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated.

[0169] The final radar waveform power spectrum calculation submodule 049 is used to calculate and obtain the final radar waveform power spectrum according to the radar transmission waveform power spectrum after the kth iteration.

[0170] In this embodiment, in the objective function residual value calculation submodule 047 of the waveform power spectrum iterative optimization module 004, in the process of calculating the objective function residual value, the second optimization objective function expression is:

[0171]

[0172] in,

[0173]

[0174] In the formula, represents the real part operator of a complex number; Λ (k) is the third matrix; (k)is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H Find the inverse operator for the conjugate transpose; is the Kronecker product; vec(·) is the matrix vectorization operator; are all block sub-matrices of the first gradient auxiliary matrix;

[0175] It should be noted that the information interaction, execution process and other contents between the modules of the above-mentioned system are based on the same concept as the method embodiment in Example 1 of the present application, and the technical effects they bring are the same as those of the method embodiment of the present application. For specific contents, please refer to the description in the method embodiment shown above in the present application, and will not be repeated here.

[0176] Example 3

[0177] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which a program code of a radar waveform power spectrum processing method based on Cauchy-Schwartz divergence is stored. The program code includes instructions for executing the radar waveform power spectrum processing method based on Cauchy-Schwartz divergence of Embodiment 1 or any possible implementation thereof.

[0178] The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more available media. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0179] Example 4

[0180] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0181] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence of embodiment 1 or any possible implementation thereof.

[0182] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor implemented by reading software codes stored in a memory. The memory can be integrated in the processor or can be located outside the processor and exist independently.

[0183] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable systems. The computer instructions can be stored in a computer-readable storage medium, or transmitted from a computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center.

[0184] Obviously, those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computing system, they can be concentrated on a single computing system, or distributed on a network composed of multiple computing systems, and optionally, they can be implemented by a program code executable by a computing system, so that they can be stored in a storage system and executed by the computing system, and in some cases, the steps shown or described can be executed in a different order than here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present invention is not limited to any specific combination of hardware and software.

[0185] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, characterized in that: include: Set the initial parameters of the radar and complete the initialization of the radar parameters; According to the radar echo data of the clutter signal, the N×N dimensional clutter power spectrum and the clutter frequency domain covariance are estimated; according to the radar echo data of the target signal, the N×N dimensional target power spectrum and the target frequency domain covariance are estimated; Determine a first matrix and a second matrix according to a power spectrum of set noise and a noise frequency domain covariance; The initial reference waveform power spectrum is iteratively optimized according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

2. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 1, characterized in that: In the process of setting the initial parameters of the radar, the initial parameters include: total energy of the radar transmission waveform, power spectrum of the initial reference waveform and the number of frequency points in the working frequency band.

3. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 2, characterized in that: The expression of the first matrix is: C1=R X +2R C Where C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance; The expression of the second matrix is: C2=R X +R C Where C2 is the second matrix.

4. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 3 is characterized in that: In the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is: In the formula, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

5. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 4, characterized in that: The steps of iteratively optimizing the initial reference waveform power spectrum are: Set the initial number of iterations and the maximum number of iterations; Calculate a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; Obtaining a second gradient auxiliary matrix by calculation according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; Calculate and obtain a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; Obtaining a third matrix and a first auxiliary vector of a k-th iteration by calculation according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix and the noise frequency domain covariance; According to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform, the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration are calculated; Calculate the residual value of the objective function according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration; The residual value of the objective function is judged. If the residual value of the objective function is less than a set threshold, the radar waveform power spectrum after the kth iteration is output, and the process ends. If the residual value of the objective function is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated. According to the radar transmission waveform power spectrum after the kth iteration, a final radar waveform power spectrum is calculated and obtained.

6. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 5, characterized in that: In the process of calculating the residual value of the objective function, the second optimization objective function expression is: in, In the formula, represents the real part operator of a complex number; Λ (k) is the third matrix; ξ (k) is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H Find the inverse operator for the conjugate transpose; is the Kronecker product; vec(·) is the matrix vectorization operator; They are all block sub-matrices of the first gradient auxiliary matrix.

7. A radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, adopting the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to any one of claims 1 to 6, characterized in that: include: The radar parameter initialization module is used to set the initial parameters of the radar and complete the initialization setting of the radar parameters; The power spectrum and frequency domain covariance acquisition module is used to estimate and obtain the N×N dimensional clutter power spectrum and clutter frequency domain covariance according to the radar echo data of the clutter signal; and estimate and obtain the N×N dimensional target power spectrum and target frequency domain covariance according to the radar echo data of the target signal; A first matrix and a second matrix acquisition module, used to determine the first matrix and the second matrix according to the power spectrum of the set noise and the noise frequency domain covariance; The waveform power spectrum iterative optimization module is used to iteratively optimize the initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix, so as to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

8. The radar waveform power spectrum processing device based on Cauchy-Schwarz divergence according to claim 7, characterized in that: In the radar parameter initialization module, in the process of setting the initial parameters of the radar, the initial parameters include: total energy of the radar transmission waveform, power spectrum of the initial reference waveform and number of frequency points in the working frequency band.

9. A multi-fidelity modeling device for improving material formulation performance prediction according to claim 8, characterized in that: In the first matrix and second matrix acquisition module, the expression of the first matrix is: C1=R X +2R C In the formula, C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance; The expression of the second matrix is: C2=R X +R C Where C2 is the second matrix.

10. A multi-fidelity modeling device for improving material formulation performance prediction according to claim 9, characterized in that: In the waveform power spectrum iterative optimization module, the submodule for iteratively optimizing the initial reference waveform power spectrum includes: The iteration number setting submodule is used to set the initial iteration number and the maximum iteration number; A first gradient auxiliary matrix calculation submodule, configured to calculate a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; A second gradient auxiliary matrix calculation submodule, configured to calculate a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; A third gradient auxiliary matrix calculation submodule, configured to calculate a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; A third matrix and first auxiliary vector calculation submodule, configured to calculate a third matrix and a first auxiliary vector of a k-th iteration according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix and the noise frequency domain covariance; A Lagrange multiplier and radar transmission waveform power spectrum calculation module, used for calculating the Lagrange multiplier and the radar transmission waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmission waveform; The objective function residual value calculation submodule is used to calculate the objective function residual value according to the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration; The objective function residual value judgment processing submodule is used to judge the objective function residual value. If the objective function residual value is less than a set threshold, the radar waveform power spectrum after the kth iteration is output and the process ends; if the objective function residual value is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated; The final radar waveform power spectrum calculation submodule is used to calculate and obtain the final radar waveform power spectrum according to the radar transmission waveform power spectrum after the kth iteration.

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