Residual-enhanced pole angle consistency improvement method
By mapping poles to real and imaginary parts, enhancing residues, and using optimization algorithms to adjust pole positions, the problem of poor pole angle consistency in radar target identification is solved, improving the accuracy of pole extraction and the integrity of the database, and supporting subsequent target identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- PLA PEOPLES LIBERATION ARMY OF CHINA STRATEGIC SUPPORT FORCE AEROSPACE ENG UNIV
- Filing Date
- 2026-02-15
- Publication Date
- 2026-06-02
Smart Images
Figure CN122132741A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of radar signal processing, target detection and recognition technology, and specifically to a method for improving pole angle consistency based on residue enhancement. Background Technology
[0002] In the modern information field, radar plays an indispensable role, with wide applications in meteorological monitoring and early warning, aviation and air traffic control, intelligent transportation, as well as medicine and agriculture. Traditional radar target identification methods mainly rely on optical region features or polarization features, which are sensitive to noise, incident direction, and target attitude angle. Therefore, they require the collection of a large number of feature templates for comparison, making the identification process complex and computationally intensive. In addition, low-observable targets such as stealth aircraft have low electromagnetic scattering intensity, making it difficult to detect target characteristics in the echo. Research shows that the target pole features in the radar resonance region are only related to the inherent properties of the target itself, such as shape, size, and material, and are not affected by factors such as target attitude and incident direction. Moreover, the electromagnetic scattering characteristics of the target in the resonance region are strong, which is more conducive to the identification of stealth targets. Therefore, using radar resonance region pole features for target identification has the advantages of high robustness, low computational cost, and small number of required feature template libraries, and has important research value.
[0003] Theoretically, target poles should have directional consistency. However, due to the imperfect characteristics of echo data in the resonant region and the influence of noise, there is a phenomenon of pole feature position shift. Based on actual simulations and pole extraction results from internal field data, it was found that although the pole extraction results for echoes from different azimuths of the same model are relatively consistent, they are not entirely identical, and the pole angle consistency is reduced. This is because the residue and energy contribution corresponding to the pole are related to the incoming wave direction and polarization. The residue of target poles extracted from certain directions is too small, and their energy contribution is too small when selecting feature poles, thus failing to meet the conditions and being discarded, or not being correctly extracted due to noise. According to previous experimental verification of various extraction algorithms, when extracting poles from echo data of the same target at different angles, an angle flickering phenomenon occurs, meaning that the extraction results of poles at the same location in echo data of the same target at different angles are not completely consistent. This significantly reduces the accuracy of target pole extraction, seriously affecting the accuracy of subsequent target detection and recognition based on radar resonant region characteristics. Existing methods to improve pole extraction accuracy generally involve filtering out high-frequency principal poles based on residue size and the number of times the same pole appears during multi-angle extraction, while removing other poles. However, existing methods only filter and do not effectively identify and correct poles that deviate from their correct positions due to low energy contribution. They do not address the root cause of pole angle flickering, resulting in omissions in pole extraction results and incomplete pole feature databases, leaving subsequent radar identification without detailed feature support. Summary of the Invention
[0004] In view of this, the present invention provides a pole angle consistency improvement method based on residue enhancement. augmented Pole The Angle Consistency Enhancement Method effectively solves the problem of pole angle flicker caused by low echo energy contribution during pole extraction. It corrects pole positions from the root, finds hidden poles, improves pole angle consistency, and generates a complete pole feature database, greatly improving the accuracy of pole extraction and providing effective data support for subsequent radar target identification.
[0005] The pole angle consistency improvement method based on residue enhancement of the present invention includes:
[0006] S1, extract the poles and residues of a radar resonant echo of the target; select the poles that deviate from the theoretical values of the poles as the poles to be optimized, P; S2, map the pole P to be optimized into two parts, real part and imaginary part, P=Re+Im, and calculate the enhanced residue R_new=R*k, where k is the residue enhancement factor, k>0; S3, optimize the real part Re and imaginary part Im of each pole P to be optimized: For each pole P to be optimized and its residue R, using the frequency response curve S_target reconstructed with the original pole P(Re, Im) and the enhanced residue R_new as the reference curve, calculate the waveform error of the frequency response curve S_orig reconstructed with the optimized and updated pole P_new(Re_new, Im_new) and the original residue R in the characteristic frequency band compared with the reference curve S_target. Taking the minimization of the waveform error as the optimization objective, optimize the real part Re and the imaginary part Im of the pole P to be optimized, and obtain the final optimized pole P*(Re*, Im*). S4. Replace the original pole P(Re, Im) with the optimized pole P*(Re*, Im) and put it into the pole feature template library to perform target recognition based on pole features.
[0007] Preferably, in S1, the poles and residues of the target resonant echo are extracted using the Cauchy algorithm, MPM algorithm, or Prony algorithm.
[0008] Preferably, in S1, the residue R corresponding to the pole P to be optimized is two to three orders of magnitude smaller than the residues corresponding to other poles that are consistent with the theoretical value.
[0009] Preferably, in S1, k is determined based on the deviation of the residue corresponding to the pole to be optimized from the residue corresponding to other poles that are consistent with the theoretical value.
[0010] Preferably, in step S3, the waveform error is Loss = |S_target - S_orig|.
[0011] Preferably, in step S3, particle swarm optimization, ant colony optimization, or genetic algorithm is used to optimize the real part Re and the imaginary part Im of the pole P.
[0012] Preferably, when the waveform error is less than a set threshold, or when the number of optimization loops reaches a set maximum value, the optimization ends, and the final Re* and Im* obtained are the desired values.
[0013] Beneficial effects: This invention designs a resonant radar echo fitting model based on residue enhancement, which maps the complex values of the pole features in the radar resonant region into two variables: real and imaginary. The particle swarm optimization algorithm is used to dynamically optimize the unnormalized real and imaginary poles, effectively correcting the position of the poles, especially the imaginary part (resonant frequency), thereby improving the accuracy of pole extraction and the consistency of pole angles. Attached Figure Description
[0014] Figure 1 The RCS amplitude at various angles is given at an illumination frequency of 0.476 GHz.
[0015] Figure 2 The RCS amplitude at various angles is given at an illumination frequency of 0.328 GHz.
[0016] Figure 3 The flowchart shows the pole angle consistency improvement method based on residue enhancement (taking the particle algorithm as an example).
[0017] Figure 4 This is the frequency response curve at a pitch angle of 30°.
[0018] Figure 5 This is the frequency domain fitting curve.
[0019] Figure 6 The results show the radar echo pole extraction at an elevation angle of 30°.
[0020] Figure 7 This is the frequency response curve at a pitch angle of 60°.
[0021] Figure 8 This is the frequency domain fitting curve.
[0022] Figure 9 The results show the radar echo pole extraction at an elevation angle of 60°.
[0023] Figure 10 This is the frequency response curve at a pitch angle of 70°.
[0024] Figure 11This is the frequency domain fitting curve.
[0025] Figure 12 The results show the radar echo pole extraction at an elevation angle of 70°.
[0026] Figure 13 The frequency response curve is reconstructed after residue enhancement.
[0027] Figure 14 The frequency response curve is reconstructed after residue enhancement.
[0028] Figure 15 To accurately reconstruct the frequency response curve at the poles.
[0029] Figure 16 To accurately reconstruct the frequency response curve at the poles.
[0030] Figure 17 This is a magnified view of a portion of the image.
[0031] Figure 18 The process of finding the first pole of data 4.
[0032] Figure 19 The process of finding the first pole of data 8.
[0033] Figure 20 The process of finding the second pole of the data.
[0034] Figure 21 The process of finding the second pole of the data is as follows.
[0035] Figure 22 Comparison of errors before and after extreme point optimization. Detailed Implementation
[0036] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0037] This invention provides a method for improving pole angle consistency based on residue enhancement.
[0038] Analysis of the results of previous experiments on pole extraction and residue shows that some pole extraction is inaccurate because the residue of the extracted target pole is too small. When selecting characteristic poles, the energy contribution of these poles is too small. Therefore, enhancing the residue is an important factor to make pole extraction more accurate.
[0039] In this experiment, taking the simulation data of a 1m thin rod with a pitch angle of 60 degrees and an azimuth angle of 0 degrees as an example, the modulus of the residues corresponding to the 4th and 8th poles, which were extracted inaccurately, was amplified, and the frequency response echo was restored using the amplified residues and the original poles.
[0040] To further explore the experimental principle of residue enhancement and the physical mechanism of pole angle scintillation, FEKO software was used to simulate multi-angle fixed-frequency irradiation of a thin rod. It was found that at an irradiation frequency of 0.476 GHz, the RCS amplitude was very small, almost zero, near an angle of 60 degrees. Figure 1 As shown; at an illumination frequency of 0.328 GHz, the RCS amplitude is very small near an angle of 70 degrees, such as... Figure 2 As shown.
[0041] The flowchart of the pole angle consistency improvement method based on residue enhancement of the present invention is as follows: Figure 3 As shown, it includes the following steps: Step 1: Use the pole extraction algorithm to extract the poles and residual values of a radar resonant echo of the target; Among them, appropriate pole extraction methods such as Cauchy, MPM, and Prony can be selected according to the specific signal-to-noise ratio and bandwidth of the target echo.
[0042] Step 2: Based on the extracted theoretical pole values of the target, select the poles P and their corresponding residues R that need to be optimized. Among the set of poles and residues extracted from the target, the residues corresponding to the poles that deviate from the theoretical values are smaller than the residues corresponding to other accurate poles, usually by two to three orders of magnitude.
[0043] Step 3: Map the pole to be optimized P to two parts, real and imaginary, P = Re + Im, and calculate the enhanced residue R_new = R * k, where k is the residue enhancement factor (k > 0). k is an empirical value estimated based on the deviation of the residue corresponding to the pole to be optimized from the residue corresponding to other accurate poles.
[0044] Step 4: Perform dynamic optimization on the real part Re and imaginary part Im of each pole P to be optimized: For each pole P to be optimized and its residue R, the frequency response curve S_target reconstructed with the original pole P (Re, Im) and the enhanced residue R_new is used as the reference curve. The waveform error of the frequency response curve S_orig reconstructed with the optimized and updated pole P_new (Re_new, Im_new) and the original residue R in the characteristic frequency band is calculated. The minimum waveform error is used as the optimization objective to optimize (Re, Im) of the pole P to be optimized. The waveform error is calculated as the absolute value of S_target - S_orig within the same frequency band. Optimization algorithms such as particle swarm optimization, ant colony optimization, and genetic optimization can be used to optimize the real part Re and the imaginary part Im of the pole P. Taking particle swarm optimization as an example, the coordinates of the particle are (Re, Im) of the pole P, and the error is used as the particle fitness. The particle position is optimized, and when the waveform error is less than a set threshold, the optimal particle position is obtained, which is the optimal real and imaginary part of the pole P.
[0045] Step 5: Replace the original extracted poles with the optimized poles and put them into the pole feature library for subsequent target recognition based on pole features.
[0046] Example The following experimental results will verify the effectiveness of this invention in improving pole angle consistency and pole extraction accuracy.
[0047] The radar resonant region pole characteristics were extracted using the Cauchy method based on the FEKO electromagnetic simulation software to simulate the model's scattering data. Simulation data (simulation parameters: frequency band 66.9M-1718.9M, interval 1M, number of frequency points 1653) of a standard thin rod with a length of 1m and a radius of 0.005m was used as an example, with elevation angles of 60° and 0° azimuth and 70° respectively. Pole optimization based on residue enhancement was performed. The echo data at 60° and 0° azimuth is designated as Data 1, and the echo data at 70° and 0° azimuth is designated as Data 2. Among the 91 echoes from elevation angles of 0° to 90°, the echo energy was highest at 30°, and the pole extraction was complete and accurate. Therefore, the pole extraction value of the 30° elevation echo was used as a reference value for pole error calculation.
[0048] Frequency response of echo data at a 30-degree pitch angle as follows Figure 4 As shown. The frequency domain fitting during pole extraction is as follows. Figure 5 As shown. The pole extraction results (displayed after normalization) are as follows. Figure 6 As shown in the figure. The results of pole and residue extraction are shown in Table 1.
[0049] Table 1. Pole retention values extracted from echo at a pitch angle of 30°
[0050] The Cauchy algorithm is used to extract poles from data 1 and data 2. The frequency domain echo and pole extraction process is shown below.
[0051] Frequency response of echo data at a 60-degree pitch angle as follows Figure 7 As shown. The frequency domain fitting during pole extraction is as follows. Figure 8 As shown. The pole extraction results (displayed after normalization) are as follows. Figure 9 As shown in the figure. The results of pole and residue extraction are shown in Table 2.
[0052] Table 2. Pole retention values extracted from echo at a 60° pitch angle.
[0053] Frequency response of echo data at a 70-degree pitch angle as follows Figure 10 As shown. The frequency domain fitting during pole extraction is as follows. Figure 11 As shown. The pole extraction results (displayed after normalization) are as follows. Figure 12 As shown in the figure. The results of pole and residue extraction are shown in Table 3.
[0054] Table 3. Pole retention values extracted from echo at 70° pitch angle
[0055] Pole error calculation method:
[0056] Methods for calculating accuracy improvement after pole optimization:
[0057] Suppose that the transfer function of a linear time-invariant (LTI) system is a rational function:
[0058] Expanding the partial fraction over all poles (including finite poles and poles at infinity) yields:
[0059] in, This is the k-th pole; The residue corresponding to the pole k is...
[0060] The polynomial part can be written as ,in If n=m, then only the constant term remains.
[0061] The partial fractional expansion of poles and residues is the most direct and physically clear way to express the frequency response. Each pole corresponds to the first (or second) dynamic mode of the system, and the residues determine the weight of that mode in the overall response.
[0062] Reconstructing the frequency response curve using poles and residues: The frequency domain echo reconstructed after a 10x amplification of the residue corresponding to the fourth pole extracted from the simulation data of a 1m thin rod with a pitch angle of 60 degrees and an azimuth angle of 0 degrees, is as follows: Figure 13As shown in the figure, the red curve represents the frequency response of the enhanced residue and pole restoration, while the blue curve represents the original echo (two-sided spectrum). After the residue corresponding to the 4th pole is enhanced, the RCS amplitude in the corresponding frequency range also increases accordingly.
[0063] The frequency domain echo reconstructed after a 50x amplification of the residue corresponding to the 8th pole extracted from simulation data of a 1m thin rod with a pitch angle of 60 degrees and an azimuth angle of 0 degrees, as shown below. Figure 14 As shown in the figure, the red curve represents the frequency response of the enhanced residue and pole restoration, while the blue curve represents the original echo (two-sided spectrum). After the residue corresponding to the 8th pole is enhanced, the RCS amplitude in the corresponding frequency range also increases accordingly.
[0064] The fourth inaccurate pole value extracted from the simulation data of a 1m thin rod with a pitch angle of 60 degrees and an azimuth angle of 0 degrees was replaced with an accurate pole value. The frequency response echo was then reconstructed using the replaced pole and the original residue. Figure 15 As shown in the figure, the red curve is the frequency response after the pole is changed and the original residue is restored, and the blue curve is the original echo (two-sided spectrum). It can be seen that after the fourth pole is replaced with the accurate pole value, the waveform of its corresponding frequency band shows the peak corresponding to that pole, and the RCS amplitude increases.
[0065] The 8th inaccurate pole value extracted from the simulation data of a 1m thin rod with a pitch angle of 60 degrees and an azimuth angle of 0 degrees was replaced with an accurate pole value. The frequency response echo was then reconstructed using the replaced pole and the original residue. Figure 16 As shown in the enlarged view, Figure 17 As shown, the red curve represents the frequency response after the poles are changed and the original residue is restored, while the blue curve represents the original echo (two-sided spectrum). It can be seen that after the 8th pole is replaced with the accurate pole value, the waveform of its corresponding frequency band shows the peak corresponding to that pole, and the RCS amplitude increases.
[0066] From the above theoretical derivation, it can be concluded that the influence of optimizing the pole position on the frequency response of the corresponding frequency band is consistent with the influence of enhancing the residue of the corresponding pole on the frequency response. Therefore, the principle of dynamic pole optimization is to map the complex value of the pole into two variables, real and imaginary parts, and use particle swarm optimization algorithms to dynamically optimize the unnormalized real and imaginary parts of the pole. During the optimization process, the frequency domain response echoes reconstructed by the optimized pole and the original residue are made closer to the frequency domain response echoes reconstructed by the enhanced residue and the original pole in the vicinity of the frequency range corresponding to the optimized pole.
[0067] The frequency response reconstruction module, the original pole-residue data loading module, the residue enhancement module, and the particle swarm optimization module are integrated into a single visual interface. The processor is opened, data one is loaded, the enhancement factor is input, and pole optimization based on residue enhancement is performed on the fourth pole of data one and its corresponding residue. Figure 18 As shown, after processing, the resonant frequency of the fourth pole changed from 0.192851 to 0.273382, the error decreased from 27.08% to 3.36%, and the accuracy improved by 87.59%.
[0068] For the 8th pole of Data 1 and its corresponding residue, pole optimization based on residue enhancement is performed, such as... Figure 19 As shown, after processing, the resonant frequency of the 8th pole changed from 0.532369 to 0.566732, the error decreased from 6.88% to 0.87%, and the accuracy was improved by 87.35%.
[0069] Open the residue enhancement processor, load Data 2, input the enhancement factor, and perform residue-based pole optimization on the third pole of Data 2 and its corresponding residue, such as... Figure 20 As shown, after processing, the resonant frequency of the third pole changed from 0.103777 to 0.203777, the error decreased from 44.81% to 8.37%, and the accuracy improved by 81.32%.
[0070] For the 6th pole of data 2 and its corresponding residue, pole optimization based on residue enhancement is performed, such as... Figure 21 As shown, after processing, the resonant frequency of the 6th pole changed from 0.370626 to 0.422705, the error decreased from 11.31% to 1.15%, and the accuracy was improved by 89.83%.
[0071] Accuracy comparison before and after pole optimization Figure 22 As shown, the pole errors have decreased significantly compared to those before optimization. Figure 22 In the data, poles 1, 2, 3, and 4 are data-1 pole 4, data-1 pole 8, data-2 pole 3, and data-2 pole 6, respectively.
[0072] In summary, the system's poles determine "where the response decays" (i.e., the decay rate and oscillation frequency), while the residue determines "how much the response decays" (i.e., the amplitude). These two are tightly coupled in the frequency domain. Moving a pole causes a shift in the center frequency (corresponding to the imaginary part) and bandwidth (corresponding to the real part) of the response, but the amplitude may change accordingly. Enhancing the residue directly increases the response amplitude at the corresponding frequency, but does not change the specific frequency at which the response occurs. The effect of optimizing the pole's position on the frequency response of the corresponding frequency band is in the same direction as the effect of enhancing the residue. Therefore, the principle of dynamic pole optimization is to map the complex value of the pole to two variables: a real part and an imaginary part. An optimization algorithm dynamically optimizes the unnormalized real and imaginary parts of the pole. During the optimization process, the frequency domain response echo reconstructed by the optimized pole and the original residue is made closer to the frequency domain response echo reconstructed by the enhanced residue and the original pole in the vicinity of the frequency range corresponding to the optimized pole.
[0073] A pole is usually a complex value, which is mapped to two variables: real and imaginary. The real and imaginary parts of the unnormalized pole are dynamically optimized using swarm optimization algorithms such as particle swarm optimization. The optimization thresholds for the real and imaginary parts are set according to the magnitude range of other accurate poles extracted from the same echo.
[0074] By leveraging the synergistic effect of pole placement fine-tuning and residue enhancement in the response direction, the frequency response curve of the optimized pole in its corresponding specific frequency band can be made closer to the maximum response amplitude (ideal echo peak) theoretically achievable by increasing the residue. This method effectively combines the spatial search of pole placement (adjusting frequency position) with the gain effect of residue amplitude (enhancing response intensity), solving the problem of response frequency misalignment that may be caused by relying solely on residue enhancement.
[0075] Experimental results based on particle swarm optimization show that this invention effectively solves the problem of pole angle flickering caused by low echo energy contribution during pole extraction, while keeping the target radar echo constant. It corrects pole positions at the root, identifies hidden poles, improves pole angle consistency, and generates a complete pole feature database. Furthermore, this invention compensates for echo energy issues that existing radar systems and extraction algorithms cannot address in improving pole extraction accuracy. Compared to existing methods that remove inaccurate poles based on residue size, this invention does not change the number of poles in the database. Based on the relationship between residue and poles, it dynamically optimizes poles using a reconstructed frequency response fitting curve, effectively improving pole angle consistency and providing a complete and accurate pole database for subsequent target identification.
[0076] 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 pole angle consistency improvement method based on residue enhancement, characterized in that, include: S1, extract the poles and residues of a radar resonant echo from the target; The poles that deviate from the theoretical values are selected as the poles to be optimized, P; S2, map the pole P to be optimized into two parts, real part and imaginary part, P=Re+Im, and calculate the enhanced residue R_new=R*k, where k is the residue enhancement factor, k>0; S3, optimize the real part Re and imaginary part Im of each pole P to be optimized: For each pole P to be optimized and its residue R, using the frequency response curve S_target reconstructed with the original pole P(Re, Im) and the enhanced residue R_new as the reference curve, calculate the waveform error of the frequency response curve S_orig reconstructed with the optimized and updated pole P_new(Re_new, Im_new) and the original residue R in the characteristic frequency band compared with the reference curve S_target. Taking the minimization of the waveform error as the optimization objective, optimize the real part Re and the imaginary part Im of the pole P to be optimized, and obtain the final optimized pole P*(Re*, Im*). S4. Replace the original pole P(Re, Im) with the optimized pole P*(Re*, Im) and put it into the pole feature template library to perform target recognition based on pole features.
2. The method as described in claim 1, characterized in that, In S1, the poles and residues of the target resonant echo are extracted using the Cauchy algorithm, MPM algorithm, or Prony algorithm.
3. The method as described in claim 1 or 2, characterized in that, In S1, the residue R corresponding to the pole P to be optimized is two to three orders of magnitude smaller than the residues corresponding to other poles that are consistent with the theoretical value.
4. The method as described in claim 3, characterized in that, In S1, k is determined based on the deviation of the residue corresponding to the pole to be optimized from the residue corresponding to other poles that are consistent with the theoretical value.
5. The method as described in claim 1, characterized in that, In S3, the waveform error is Loss = |S_target - S_orig|.
6. The method as described in claim 1 or 5, characterized in that, In S3, the real part Re and the imaginary part Im of the pole P are optimized using particle swarm optimization, ant colony optimization, or genetic algorithm.
7. The method as described in claim 1, characterized in that, When the waveform error is less than the set threshold, or when the number of optimization loops reaches the set maximum value, the optimization ends, and the final Re* and Im* obtained are the desired values.