A robust waveform design method for inter-pulse fluctuation uncertainty set of spherical target

Abstract

This invention discloses a robust waveform design method for uncertain sets of inter-pulse fluctuations of spherical targets. The steps include: selecting the radar waveform to be optimized and the filter size; modeling the target inter-pulse fluctuations and the transmitted waveform constraints to form an optimization problem; transforming the optimization problem into an equivalent problem and solving the equivalent problem to obtain the covariance matrix of the radar transmitted waveform; synthesizing the radar transmitted waveform using the obtained waveform covariance matrix, and solving the receiving filter based on the synthesized waveform. This invention provides a radar waveform design method that is robust to target inter-pulse fluctuations. This waveform, while ensuring magnitude constraints, fully utilizes prior information about target inter-pulse fluctuations, providing robust target detection performance under uncertain sets of spherical target fluctuations.

Description

Technical Field

[0001] This invention belongs to the field of radar waveform design technology, and in particular relates to a robust waveform design method for the uncertainty set of inter-pulse fluctuations of spherical targets. Background Technology

[0002] Waveform optimization theory has been extensively studied and advanced in recent years. Unlike traditional radar systems that only transmit fixed waveforms, more advanced radar systems should adaptively adjust the transmitted waveform according to their operating environment and mission objectives to achieve better target detection, identification, and tracking performance.

[0003] In traditional slow-time radar waveform design, the target's complex amplitude is assumed to be a fixed constant, remaining unchanged between pulses. Current research primarily focuses on improving radar performance when the target's Doppler frequency is not accurately known. In 2010, De Maio et al. published a robust waveform algorithm for the target's Doppler frequency under Gaussian noise in IEEE Transactions on Signal Processing. This work was further extended by Naghsh et al. in 2014 by considering the influence of waveform-related clutter. In 2015, Aubry et al. proposed a robust waveform design scheme using filter banks in the IEEE Journal of Selected Topics on Signal Processing. Later, in 2020, Du et al. proved in IEEE Signal Processing Letters that a globally optimal waveform solution can be obtained without range-ambiguous clutter. In reality, in Doppler processing scenarios, the target's attitude relative to the radar may change between pulses, causing variations in the target's complex amplitude. This phenomenon essentially introduces additional modulation into the target echo, leading to signal model mismatch and severely impacting the performance of traditional waveform design methods.

[0004] Based on the above reasons and facts, researching robust transmit waveform and receive filter design methods for interpulse fluctuations of moving targets has significant practical implications. It can effectively compensate for the shortcomings of existing waveform design methods in handling interpulse fluctuations of targets, improving the radar's ability to detect moving targets in complex scenarios. In 2022, Xie et al. published a robust waveform design method based on relaxed duality (Robust JointCode-Filter Design under Uncertain Target Interpulse Fluctuation) in Signal Processing. This method describes the interpulse fluctuations of the target using an arched uncertainty set and considers waveform similarity and energy constraints. However, there is currently no research on radar waveform design methods that consider magnitude constraints for the uncertainty set of interpulse fluctuations of spherical targets. Summary of the Invention

[0005] To address the problem that traditional waveform design methods neglect inter-pulse fluctuations in moving target detection, resulting in a loss of detection performance, this invention provides a radar waveform design method that is robust to inter-pulse fluctuations. This waveform can fully utilize prior information about inter-pulse fluctuations while ensuring modulus constraints, providing robust target detection capability even with an uncertain set of spherical target fluctuations.

[0006] This invention discloses a robust waveform design method for inter-pulse fluctuation uncertainty sets of spherical targets, comprising the following steps:

[0007] Select the waveform and filter size to be optimized for the radar;

[0008] The target inter-pulse fluctuation model and the transmitted waveform constraint model are performed to form an optimization problem;

[0009] The optimization problem is transformed into an equivalent problem, and the covariance matrix of the radar transmission waveform is obtained by solving the equivalent problem.

[0010] The radar transmitted waveform is synthesized using the obtained waveform covariance matrix, and the receiving filter is solved based on the synthesized waveform.

[0011] Furthermore, a single-station radar transmits a series of waveform vectors. Encoded pulses are used to detect moving targets, and the nth pulse emitted is used... Encoding is performed, where N is the number of radar pulses transmitted, and the target's Doppler steering vector is used. express, The covariance matrix is ​​used to represent Gaussian white noise; at the radar receiver, it is used... This represents the receiving filter vector; the parameter N is determined based on the actual hardware capabilities and desired performance. The larger the value of N, the higher the system's degrees of freedom.

[0012] Furthermore, the target inter-pulse fluctuation model and the transmitted waveform constraint model are performed to form an optimization problem, including:

[0013] First, the uncertainty set of the target magnitude vector is modeled based on existing prior knowledge: using... The complex amplitude of the nth pulse target is defined as follows: The true magnitude vector of the target is given by a priori target magnitude vector. spherical uncertain set centered In this context, the set is represented as:

[0014] ;

[0015] in By controlling the degree of uncertainty, the parameters are determined based on the accuracy of prior information regarding the actual fluctuations of the target. ;

[0016] In the process of optimizing the radar waveform, in addition to energy constraints, the magnitude fluctuation of the waveform to be optimized is also constrained to ensure that the radar transmitter operates in the linear region. Therefore, the feasible region of the radar waveform is represented as follows:

[0017] ;

[0018] The parameters a and b control the lower and upper bounds of the optimized waveform magnitude, respectively. The smaller a is and the larger b is, the greater the jitter of the optimized waveform; the larger a is and the smaller b is, the smaller the jitter of the optimized waveform.

[0019] The radar waveform and filter design are modeled as the following optimization problem:

[0020] ;

[0021] in This represents the conjugate transpose symbol.

[0022] Furthermore, the optimization problem can be made equivalent, and the equivalent problem is represented as follows:

[0023] ;

[0024] Equivalence problem The internal optimization problem is equivalently transformed into the following problem based on Lagrangian duality theory:

[0025] ;

[0026] I N It is an N-dimensional identity matrix, and λ is the dual variable. , ;

[0027] Therefore, the radar transmission waveform to be optimized is obtained by solving the following positive semidefinite problem:

[0028] ;

[0029] Where rank represents the rank of the matrix, and tr represents the trace of the matrix.

[0030] Furthermore, the semidefinite programming problem is solved using the interior-point method:

[0031] Let the problem obtained be recorded. The solution is Next, we will start from The final transmitted waveform is synthesized in the middle. ;

[0032] if If it is rank one, then Through the Matrix decomposition yields the result; if If the rank is greater than 1, then it will be synthesized through randomization. Specifically, it includes:

[0033] First, based on the matrix Generate H random vectors that satisfy the modulus constraint. And calculate the worst SNR sequence corresponding to these vectors respectively. ,in The value is obtained by solving the optimal value of the following convex problem.

[0034] ;

[0035] in ;make The index corresponding to the largest value in the middle is ,Right now The final synthesized waveform is represented as follows: ;remember for The solution is then obtained by solving the receiver filter:

[0036] .

[0037] Compared with the prior art, the present invention has the following beneficial effects;

[0038] In practical Doppler processing for moving target detection, the target's attitude relative to the radar may change between pulses due to motion. This causes variations in the complex amplitude of the target echo, resulting in a significant performance degradation of existing waveform design methods due to model mismatch. This invention provides a robust radar waveform design method for target inter-pulse fluctuations. This method, while maintaining magnitude constraints, designs robust waveforms and filters to target inter-pulse fluctuations, significantly enhancing the worst-case output signal-to-noise ratio performance under the uncertainty set of spherical target amplitude fluctuations. Attached Figure Description

[0039] Figure 1 This invention presents a robust radar waveform design method for uncertain sets of inter-pulse fluctuations of spherical targets.

[0040] Figure 2 The target fluctuation scenario considered by the robust radar waveform design method proposed in this invention;

[0041] Figure 3 A modulus diagram of the optimized waveform provided for an example of the present invention;

[0042] Figure 4 The output signal-to-noise ratio of the optimized waveform provided in this invention varies with randomly generated target amplitude vector samples;

[0043] Figure 5 The worst-case output signal-to-interference-plus-noise ratio of the optimized waveform provided in this invention example varies with the size of the uncertain set. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings, but this is not intended to limit the present invention in any way. Any modifications or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0045] This invention discloses a robust waveform design method for inter-pulse fluctuation uncertainty sets of spherical targets, comprising the following steps:

[0046] 1. Select the waveform and filter size to be optimized for the radar;

[0047] The waveform and filter size are determined based on actual hardware limitations and desired performance; a single-station radar transmits a series of waveform vectors. Encoded pulses are used to detect moving targets, and the nth pulse emitted is used... Encoding is performed, where N is the number of radar pulses transmitted, and the target's Doppler steering vector is used. express, The covariance matrix is ​​used to represent Gaussian white noise; at the radar receiver, it is used... This represents the receiving filter vector; the parameter N is determined based on the actual hardware capabilities and desired performance. The larger the value of N, the higher the system's degrees of freedom, but the higher the hardware requirements.

[0048] 2. Model the target pulse fluctuations and waveform constraints, and formulate an optimization problem;

[0049] First, the uncertainty set of the target magnitude vector is modeled based on existing prior knowledge. Using... The complex amplitude of the nth pulse target is defined as follows: The true magnitude vector of the target is given by a priori target magnitude vector. spherical uncertain set centered In this context, the set can be represented as

[0050] ;

[0051] in The degree of uncertainty was controlled. The larger the value, the more prior information the target's true magnitude vector contains. The lower the credibility, the more reliable it is. When, it represents the prior information vector at this time. It is invalid when When, it represents the prior information vector at this time. It is accurate; here, the parameters are determined based on the accuracy of the prior information on the actual fluctuations of the target. ;

[0052] Furthermore, since radar transmitters are typically expected to operate in a linear region in practice, the optimization of the radar waveform, in addition to energy constraints, also constrains the magnitude fluctuation of the waveform to be optimized. Therefore, the feasible region of the radar waveform can be expressed as follows:

[0053] ;

[0054] The two parameters, a and b, control the lower and upper bounds of the optimized waveform magnitude, respectively. They should be determined according to actual needs. The smaller a is and the larger b is, the greater the jitter of the optimized waveform; the larger a is and the smaller b is, the smaller the jitter of the optimized waveform.

[0055] Based on the foregoing analysis, the radar waveform and filter design can be modeled as the following optimization problem.

[0056] ;

[0057] in This represents the conjugate transpose symbol.

[0058] 3. Optimize the radar transmit waveform and receive filter; including the following steps:

[0059] 3.1 The covariance matrix of the radar transmitted waveform is obtained by solving the equivalent problem;

[0060] analyze The structure is such that, and by using the strong maxima-minima theorem, it can be found that the solution... Equivalent to solving the following problem

[0061]

[0062] and The internal optimization problem can be equivalently transformed into the following problem based on Lagrangian duality theory:

[0063] ;

[0064] Therefore, the radar transmission waveform to be optimized can be obtained by solving the following positive semidefinite problem.

[0065] ;

[0066] The above semidefinite programming problem can be solved using the interior-point method. Let be the solution obtained from the problem. The solution is Next, we will start from The final transmitted waveform is synthesized in the middle. Furthermore, if If it is rank one, then By means of Matrix decomposition yields the result; if If the rank is greater than 1, then it will be synthesized through randomization. First, based on the matrix Generate H random vectors that satisfy the modulus constraint. And calculate the worst SNR sequence corresponding to these vectors respectively. ,in The value can be obtained by solving the optimal value of the following convex problem.

[0067] ;

[0068] in .make The index corresponding to the largest value in the middle is ,Right now The final synthesized waveform can be represented as ;remember for The solution is then obtained by solving the receiver filter:

[0069] ;

[0070] 3.2 The radar transmitted waveform is synthesized using the obtained waveform covariance matrix, and the receiving filter is solved based on the synthesized waveform.

[0071] Compared with the prior art, the present invention has the following beneficial effects;

[0072] In practical Doppler processing for moving target detection, the target's attitude relative to the radar may change between pulses due to motion. This causes variations in the complex amplitude of the target echo, resulting in a significant performance degradation of existing waveform design methods due to model mismatch. This invention provides a robust radar waveform design method for target inter-pulse fluctuations. This method, while maintaining magnitude constraints, designs robust waveforms and filters to target inter-pulse fluctuations, significantly enhancing the worst-case output signal-to-noise ratio performance under the uncertainty set of spherical target amplitude fluctuations.

[0073] As used herein, the term "preferred" is meant as an example, illustration, or illustration. Any aspect or design described herein as "preferred" need not be construed as being more advantageous than other aspects or designs. Rather, the use of the term "preferred" is intended to present the concept in a specific manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusionary "or." That is, unless otherwise specified or clear from the context, "X uses A or B" naturally includes either of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0074] Furthermore, although this disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the accompanying drawings. This disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the aforementioned components (e.g., elements, etc.), the terminology used to describe such components is intended to correspond to any component (unless otherwise indicated) that performs the specified function of said component (e.g., is functionally equivalent to it), even if structurally not equivalent to the disclosed structure performing the functions in the exemplary implementations of this disclosure shown herein. Moreover, although specific features of this disclosure have been disclosed with respect to only one of several implementations, such features may be combined with one or more features of other implementations that may be desirable and advantageous for a given or particular application. Furthermore, with regard to the use of the terms “comprising,” “having,” “containing,” or variations thereof in the Detailed Description or claims, such terms are intended to be included in a manner similar to the term “including.”

[0075] The functional units in this invention embodiment can be integrated into a processing module, or each unit can exist physically separately, or multiple units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. The aforementioned devices or systems can execute the storage methods in the corresponding method embodiments.

[0076] In summary, the above embodiments are one implementation of the present invention, but the implementation of the present invention is not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made that deviate from the spirit and principle of the present invention should be considered equivalent substitutions and are included within the protection scope of the present invention.

Claims

1. A robust waveform design method for a set of inter-pulse fluctuations uncertainty of a spherical target, characterized in that, Includes the following steps: Select the waveform and filter size to be optimized for the radar; The target inter-pulse fluctuation model and the transmitted waveform constraint model are performed to form an optimization problem; The optimization problem is transformed into an equivalent problem, and the covariance matrix of the radar transmission waveform is obtained by solving the equivalent problem. The radar transmitted waveform is synthesized using the obtained waveform covariance matrix, and the receiving filter is solved based on the synthesized waveform. A single-station radar transmits a series of waveform vectors Encoded pulses are used to detect moving targets, and the nth pulse emitted is used... Encoding is performed, where N is the number of radar pulses transmitted, and the target's Doppler steering vector is used. express, The covariance matrix is ​​used to represent Gaussian white noise; at the radar receiver, it is used... This represents the receiving filter vector; the parameter N is determined based on the actual hardware capabilities and desired performance. The larger the value of N, the higher the system's degrees of freedom. The target inter-pulse fluctuation model and transmitted waveform constraint model are performed to form an optimization problem, including: First, the uncertainty set of the target magnitude vector is modeled based on existing prior knowledge: using... The complex amplitude of the nth pulse target is defined as follows: The true magnitude vector of the target is given by a priori target magnitude vector. spherical uncertain set centered In this context, the set is represented as: ； in This is an uncertain set control parameter, which controls the size of the uncertain set. Here, the parameter is determined based on the accuracy of the prior information on the target fluctuations that is actually available. The value; In the process of optimizing the radar waveform, in addition to energy constraints, the magnitude fluctuation of the waveform to be optimized is also constrained to ensure that the radar transmitter operates in the linear region. Therefore, the feasible region of the radar waveform is represented as follows: ； The parameters a and b control the lower and upper bounds of the optimized waveform magnitude, respectively. The smaller a is and the larger b is, the greater the jitter of the optimized waveform; the larger a is and the smaller b is, the smaller the jitter of the optimized waveform. The radar waveform and filter design are modeled as the following optimization problem: ； in Indicates the conjugate transpose symbol; The optimization problem is equivalent, and the equivalent problem is represented as follows: ； Equivalence problem The internal optimization problem is equivalently transformed into the following problem based on Lagrangian duality theory: ； Among them, I N It is an N-dimensional identity matrix, and λ is the dual variable. , ; Therefore, the radar transmission waveform to be optimized is obtained by solving the following positive semidefinite problem: ； Where rank represents the rank of the matrix, and tr represents the trace of the matrix.

2. The robust waveform design method for inter-pulse fluctuation uncertainty sets of spherical targets according to claim 1, characterized in that, The semidefinite programming problem is solved using the interior point method: Let the problem obtained be recorded. The solution is Next, we will start from The final transmitted waveform is synthesized in the middle. ; if If it is rank one, then Through the Matrix decomposition yields the result; if If the rank is greater than 1, then it will be synthesized through randomization. Specifically, this includes: First, based on the matrix Generate H random vectors that satisfy the modulus constraint. And calculate the worst SNR sequence corresponding to these vectors respectively. ,in The value is obtained by solving the optimal value of the following convex problem. ； in ;make The index corresponding to the largest value in the middle is ,Right now The final synthesized waveform is represented as follows: ; remember for The solution is then obtained by solving the receiver filter: 。

Images