Micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition

Abstract

The invention discloses a micro Doppler frequency suppression method based on adaptive successive variational mode decomposition (SVMD). According to the method, spectrum entropy minimization is taken as an optimization target, a particle swarm optimization (PSO) algorithm is utilized to adaptively search and determine an optimal cost parameter of SVMD, and adaptive determination of the number of decomposition mode functions is realized at the same time. Under the optimal parameter condition, modal decomposition is carried out on radar echo signals, a modal component with the maximum energy is used as a main body signal according to an energy judgment criterion, other modal components are used as micro-motion signals to be suppressed, and therefore effective separation of micro-Doppler components and the main body signal is achieved. By processing and analyzing simulation data and actually measured radar data, the result shows that the method can effectively suppress the micro-Doppler frequency and improve the definition and the distinguishability of main body signals, and has high practical value.

Description

Technical Field

[0002] This invention belongs to the field of radar signal processing technology, and in particular relates to a micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition. Background Technology

[0003] In inverse synthetic aperture radar (ISAR) imaging, complex targets often contain locally moving parts. Their echo signals not only reflect the rigid motion of the target as a whole, but also contain disturbance components caused by local non-rigid motion. Examples include the rotor rotation of a UAV, the rotation of vehicle tires, and the limb swinging of a human body during walking or running. These local motions are collectively referred to as "micro-motions," which introduce additional Doppler frequency components into the echo signal. This phenomenon is defined as the "micro-Doppler effect."

[0004] In typical ISAR imaging, if the target's rotation angle is small during the coherent accumulation time, it can be considered a rigid body. In this case, its azimuth information can be obtained through Doppler modulation, thus achieving high-resolution imaging. However, for targets with significant micro-motion, the rigid body assumption is no longer satisfied. If traditional ISAR imaging algorithms are still used, the frequency changes introduced by the micro-motion components will form interference stripes extending along the azimuth in the imaging results, severely affecting the imaging quality of the target body. Therefore, it is urgent to effectively separate the main body component and the micro-motion component in the radar echo to eliminate micro-motion interference and improve imaging quality.

[0005] However, existing methods still have limitations. Their decomposition performance is highly dependent on two key parameters: the number of mode decompositions and the cost parameter. These parameters are usually set manually based on experience or obtained through trial and error, lacking global optimization capabilities and adaptive mechanisms. Inappropriate parameter selection can easily lead to problems such as mode leakage, over-decomposition, or under-decomposition, thereby affecting the accurate extraction of micro-Doppler components and the overall signal separation quality. Therefore, an adaptive method for suppressing micro-Doppler frequencies is urgently needed. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition (SVMD). This method uses spectral entropy as the objective function, introduces the PSO algorithm to adaptively search and optimize the cost parameters in SVMD, and adaptively determines the number of decomposed mode functions based on this. Ultimately, it achieves effective separation of the micro-motion signal from the main signal without requiring manual parameter setting. The technical solution of this invention is as follows: Micro-Doppler frequency suppression methods based on adaptive successive variational mode decomposition include: S1: For the received radar echo signal The signal needs to be converted to a real number for processing first. Set the initial projection parameter M (i.e., the number of projections), and let the value of m range from 1 to M. Project the signal onto the m-th direction to obtain the real-valued signal: (1) in, It is a signal In direction The projection onto the surface is used as the input signal for subsequent decomposition.

[0007] S2: For projection signals The optimal cost parameters are determined by performing the PSO optimization algorithm.

[0008] (1) Set the basic parameters of PSO, including the cost parameter search range [ [ ], maximum number of iterations T, particle swarm size N, etc.

[0009] (2) For the i-th particle ( The corresponding cost parameters Perform the SVMD decomposition process to obtain K eigenmode components. .

[0010] (2) Take the mode component with the highest energy Spectrum As the main signal spectrum, the entropy value H is calculated using equation (3) and used as the fitness value of the i-th particle.

[0011] (3) The position with the minimum fitness value is found as the global optimal position, which is the current optimal cost parameter.

[0012] (3) By updating the position of the particle, i.e. the value of the cost parameter, repeat step (2), compare the changes in fitness value, and continuously adjust the global optimal position and the particle update direction. (4) in, Let represent the cost parameter of particle i in the t-th iteration. Indicates its speed, Its historically optimal position; This represents the globally optimal position in the t-th iteration. , It is a random number between [0,1]. , It is a learning factor used to regulate the degree to which particles depend on individual and group experiences; This is the inertia weight, used to balance global and local search capabilities. A larger one... It facilitates global search, escaping local optima and avoiding getting trapped in local optima; while smaller... This approach facilitates local search, allowing the algorithm to quickly converge to the optimal solution. In solving practical optimization problems, it is often desirable to first employ a global search to quickly converge the search space to a certain region, and then use a local fine-grained search to obtain a high-precision solution. Therefore, an adaptive adjustment strategy is proposed, which linearly reduces the [value / size] as iterations proceed. The value of . Its iterative formula is equation (5): (5) in, and These represent the maximum inertia weight and the minimum inertia weight, respectively. Indicates the current iteration number. This indicates the maximum number of iterations.

[0013] (4) When the number of iterations reaches the set upper limit T, stop the iteration. At this time, output the cost parameter corresponding to the global optimal particle position. This parameter is the optimal cost parameter of SVMD decomposition.

[0014] S3: Under the optimal parameter conditions described in S2, the SVMD algorithm is used to extract the mode component with the highest energy as the main signal. The specific process of the SVMD algorithm is described in detail below.

[0015] (1) Take the real-valued signal obtained by projecting it onto the m-th direction from S1. The optimal particle position obtained in S2 is used as the cost parameter, representing the signal to be decomposed. Initialization parameters include the number of decomposed modes L=1, the number of iterations n=0, and the initial center frequency. Preset threshold , and Lagrange multiplier wait.

[0016] (2) Update the Lth mode function of the decomposed function using equation (6). .

[0017] (6) in, The modal function is obtained in the (n+1)th iteration. for The frequency domain expression, The center frequency of the Lth modal function in the nth iteration is... It is the Lagrange multiplier after the nth iteration.

[0018] After modal update, the new center frequency is calculated by weighting its spectral energy distribution. : (7) And update the Lagrange multipliers accordingly. : (8) in, n is the step size factor. Step (2) is continuously increased and repeated until the difference between adjacent iteration modes satisfies equation (9), at which point the process terminates. (9) (3) After each mode extraction is completed, determine whether the total reconstruction error of the current mode decomposition meets the set accuracy threshold. If it meets equation (10): (10) in, This represents the total length of the signal. If this condition is met, the overall decomposition process terminates; otherwise, the extraction of the next mode continues until the termination criterion is met.

[0019] The above is about real-valued signals. The process of SVMD decomposition yields a set of L modal components. .

[0020] (11) S4: Finally, restore the multi-directional results to complex form and then calculate the average to obtain the set of decomposition results of the complex signal. : (12) In the collection The mode component with the highest energy is the main signal that is needed, thus realizing the separation of micro-Doppler frequencies.

[0021] Beneficial effects: 1. It overcomes the limitations of traditional BVMD algorithms in setting the number of modes; 2. It effectively solves the problem that the cost parameter in the SVMD algorithm relies on human experience and is difficult to adapt to complex signal characteristics; 3. An adaptive suppression algorithm for micro-Doppler frequency was implemented. Attached Figure Description

[0022] Figure 1 This is a flowchart of the algorithm used in this invention; Figure 2 This is the time-frequency diagram of the simulated signal; Figure 3 This is the time-frequency diagram of the main signal after decomposition of the simulated signal; Figure 4 This is a time-frequency diagram of the measured signal from the UAV. Figure 5 The time-frequency plot of the measured signal is obtained by separating the SVMD_PSO. Figure 6 The time-frequency diagram of the measured signal after SVMD separation; Figure 7 The time-frequency diagram of the measured signal after separation using VMD; Figure 8 The time-frequency diagram is the result of EMD separation of the measured signal. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition includes the following steps: S1: Acquire radar echo data in complex form, perform projection operations on it along multiple preset projection directions, and extract the real part of the signal in each projection direction as the input signal for subsequent decomposition. S2: Set the initial number of decomposition modes to 1, and process each real part signal of the projection obtained in S1. Specifically, for each projection signal, use the PSO algorithm with the objective function of minimizing spectral entropy to search for and determine the optimal cost parameters; S3: Under the optimal parameter conditions described in S2, the SVMD algorithm is used to extract the mode component with the highest energy as the main signal; according to the preset threshold judgment condition, it is determined whether the currently obtained mode component meets the requirements of signal separation: if it meets the requirements, proceed to step S4; if it does not meet the requirements, the number of modes is incremented by 1, and the process is returned to step S2 to continue decomposition until the judgment condition is met or the maximum number of decomposed modes is reached. S4: Combine all modal components obtained from each projection direction, select the modal component with the highest energy value as the main signal according to the energy determination criterion, and suppress the remaining modal components as micro-Doppler signals, thereby completing the effective separation of micro-motion signals and main signals; By processing and analyzing simulation data and measured radar echo data, the effectiveness of the proposed method in suppressing micro-Doppler frequencies and separating signals under complex signal environments was verified.

[0024] For simulation data, since the high-speed rotation of the UAV rotor will introduce a high-frequency and periodic micro-Doppler modulation effect in the echo signal, this invention constructs an idealized UAV micro-motion signal model, as shown in Equation (13).

[0025] (13) Among them, the first item The second item represents the micro-motion signal caused by the drone rotor. This represents the echo signal from the main body of the drone. Considering that micro-motion signals typically have small amplitude and high frequency, this invention sets the relevant parameters as follows: micro-motion signal amplitude. =0.01, frequency =100Hz, main signal frequency =15HZ.

[0026] Figure 2 and Figure 3 The time-frequency diagrams of the composite signal before and after decomposition are shown. Figure 2 The image shows the time-frequency plot of the original mixed signal, where the bright yellow line in the middle represents the main signal, and the strip-shaped frequencies distributed around it correspond to the micro-Doppler frequencies and their harmonic components. Figure 3 The figure shows the result after decomposition using the method proposed in this invention. It is clear from the figure that the micro-Doppler frequency components have been effectively removed, the main signal has been successfully extracted, and effective separation of the main signal and the micro-motion signal has been achieved, verifying the signal separation capability of the proposed method in analog signal scenarios.

[0027] For the measured data, this invention uses a high-resolution radar to collect data on the drone target. The radar operates in the 9–10 GHz frequency band, and the target is a DJI M300 drone. The drone is flying at a horizontal distance of approximately 55 m and an altitude of approximately 200 m from the radar.

[0028] Figure 4 This is a time-frequency diagram of the echo signal acquired by radar. The highlighted part of the diagram represents the echo signal of the UAV itself, while the frequency strips distributed around it represent the micro-Doppler frequencies and their harmonics caused by rotor rotation.

[0029] For the measured signal, the SVMD_PSO algorithm proposed in this invention was used to separate the signal from the traditional EMD, VMD, and SVMD algorithms. The separation results are as follows: Figures 5-8 As shown, where Figure 5 The separation results of the SVMD_PSO algorithm, Figure 6 The SVMD algorithm separation results Figure 7 The result of the VMD algorithm separation. Figure 8The results show the separation results of the EMD algorithm. The extracted time-frequency distribution reveals significant differences in decomposition accuracy and anti-interference performance among different methods. The EMD method performs the worst, failing to completely extract the main signal and exhibiting considerable clutter and noise interference. While the VMD method can separate the main components, it still exhibits strong micro-Doppler components, indicating that its fixed mode number and cost parameter settings cannot simultaneously achieve signal smoothness and detail preservation. The SVMD method shows a significant improvement in separation accuracy compared to the previous two, with clearer extraction of the main signal, but still suffers from minor frequency interference, suggesting that its cost parameters require further optimization. In contrast, the SVMD-PSO method introduces the PSO algorithm based on SVMD, achieving adaptive optimization of the cost parameters, resulting in more accurate extraction of the main components and better noise suppression in the decomposition results.

[0030] To further quantify and evaluate the separation performance of each method, the entropy values ​​of the decomposition results under different algorithms were calculated, as shown in Table 1. The results show that the SVMD-PSO method has the lowest entropy value, indicating that its decomposed signal energy distribution is the most concentrated and its information redundancy is the lowest, demonstrating superior separation effect and signal purity.

[0031] Table 1 Comparison of entropy values ​​of the main signal extracted by different methods

[0032] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0033] The foregoing description illustrates and describes several preferred embodiments of the present invention. However, as previously stated, it should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

[0034] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition, characterized in that, include: S1: Acquire radar echo data in complex form, perform projection operations on it along multiple preset projection directions, and extract the real part of the signal in each projection direction as the input signal for subsequent decomposition. S2: Set the initial number of decomposition modes to 1, and process each real part signal of the projection obtained in S1 respectively; S3: Under the optimal parameter conditions described in S2, the SVMD algorithm is used to extract the mode component with the highest energy as the main signal; according to the preset threshold judgment condition, it is determined whether the currently obtained mode component meets the requirements of signal separation: if it meets the requirements, proceed to step S4; if it does not meet the requirements, the number of modes is incremented by 1, and the process is returned to step S2 to continue decomposition until the judgment condition is met or the maximum number of decomposed modes is reached. S4: Combine all modal components obtained from each projection direction, select the modal component with the highest energy value as the main signal according to the energy determination criterion, and suppress the remaining modal components as micro-Doppler signals, thereby completing the effective separation of the micro-motion signal and the main signal.

2. The micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition as described in claim 1, characterized in that, In step S1, the signal is projected onto the m-th direction to obtain a real-valued signal: (1)； in, It is a signal In direction The projection onto the surface is used as the input signal for subsequent decomposition.

3. The micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition as described in claim 1, characterized in that, Step S2 specifically includes: (1) Set the basic parameters of PSO, including the cost parameter search range [ [ ], maximum number of iterations T, particle swarm size N, etc.; (2) For the i-th particle ( The corresponding cost parameters Perform the SVMD decomposition process to obtain K eigenmode components. ; (2)； Take the mode component with the highest energy Spectrum As the main signal spectrum, the entropy value H is calculated using equation (3) and used as the fitness value of the i-th particle; (3)； Find the position with the minimum fitness value as the global optimum, which is the current optimal cost parameter; (3) By updating the position of the particle, i.e. the value of the cost parameter, repeat step (2), compare the changes in fitness value, and continuously adjust the global optimal position and the particle update direction. (4)； in, Let represent the cost parameter of particle i in the t-th iteration. Indicates its speed, Its historically optimal position; This represents the globally optimal position in the t-th iteration. , It is a random number between [0,1]. , It is a learning factor used to regulate the degree to which particles depend on individual and group experiences; Inertial weights are used to balance global and local search capabilities; larger ones... It facilitates global search, escaping local optima and avoiding getting trapped in local optima; while smaller... This approach facilitates local search, allowing the algorithm to quickly converge to the optimal solution. In solving practical optimization problems, it is often desirable to first employ a global search to quickly converge the search space to a certain region, and then use a local fine-grained search to obtain a high-precision solution. Therefore, an adaptive adjustment strategy is proposed, which linearly reduces the [value / size] as iteration progresses. The value of ; its iterative formula is equation (5): (5)； in, and These represent the maximum inertia weight and the minimum inertia weight, respectively. Indicates the current iteration number. Indicates the maximum number of iterations; (4) When the number of iterations reaches the set upper limit T, stop the iteration. At this time, output the cost parameter corresponding to the global optimal particle position. This parameter is the optimal cost parameter of SVMD decomposition.

4. The micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition as described in claim 1, characterized in that, In step S3, the specific process of the SVMD algorithm is as follows: (1) Take the real-valued signal obtained by projecting it onto the m-th direction from S1. The optimal particle position obtained in S2 is used as the cost parameter, representing the signal to be decomposed. Initialization parameters include the number of decomposed modes L=1, the number of iterations n=0, and the initial center frequency. Preset threshold , and Lagrange multiplier wait; (2) Update the Lth mode function of the decomposed function using equation (6). ; (6)； in, The modal function is obtained in the (n+1)th iteration. for The frequency domain expression, The center frequency of the Lth modal function in the nth iteration is... The Lagrange multiplier after the nth iteration; After modal update, the new center frequency is calculated by weighting its spectral energy distribution. : (7)； And update the Lagrange multipliers accordingly. : (8)； in, The step size factor is n; the value of n is continuously increased, and step (2) is executed repeatedly until the difference between adjacent iteration modes satisfies equation (9) and then terminates. (9)； (3) After each mode extraction is completed, determine whether the total reconstruction error of the current mode decomposition meets the set accuracy threshold. If it meets equation (10): (10)； in, This indicates the total length of the signal; if this condition is met, the overall decomposition process terminates; otherwise, the next mode is extracted until the termination criterion is met. The above is about real-valued signals. The process of SVMD decomposition yields a set of L modal components. ; (11) 5. The micro-Doppler frequency suppression method based on adaptive successive variational mode decomposition as described in claim 1, characterized in that, In step S4, the set of decomposition results of the complex signal Represented as: (12)； In the collection The mode component with the highest energy is the main signal that is needed, thus realizing the separation of micro-Doppler frequencies.

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