A target initial ground distance inversion method based on tail flame abnormal echo

Abstract

This invention relates to a method for inverting the initial ground distance of a target based on anomaly echoes from its exhaust plume, belonging to the field of high-speed maneuvering target detection technology. This invention addresses the challenges of detecting, locating, and accurately inverting the initial distance of high-speed targets under complex backgrounds. The steps of this invention include: S1: ionospheric model simplification; S2: extraction of Bragg peak offset; S3: Doppler spectral feature extraction; S4: establishment of joint anomaly indices; S5: adaptive threshold detection and centroid localization; S6: nonlinear deviation fitting to obtain the true ground distance value. This invention establishes a complete closed-loop link from anomaly echo detection to quantitative estimation of the target's initial ground distance. By combining physical modeling and data-driven approaches, it effectively eliminates systematic biases in distance inversion, providing high-precision prior distance information for trajectory analysis and state identification of high-speed maneuvering targets.

Description

Technical Field

[0001] This invention relates to a method for inverting the initial ground distance of a target based on anomaly echoes from its exhaust plume, belonging to the field of high-speed maneuvering target detection technology. Background Technology

[0002] Skywave over-the-horizon radar utilizes the reflection and refraction of high-frequency electromagnetic waves by the ionosphere to overcome the limitations of the Earth's curvature, enabling over-the-horizon detection of targets thousands of kilometers away. It can be used for tasks such as sea state monitoring, high-speed target detection, and trajectory inversion. High-speed maneuvering targets, due to their high speed, strong maneuverability, rapid trajectory changes, and complex background environments, have become a core focus of early warning systems. Currently, high-speed target detection systems are evolving from simple early warning to detection and identification; however, there is still significant room for improvement in achieving a stable closed loop from early warning to identification in complex environments.

[0003] Currently, the main technical systems used for high-speed maneuvering target detection include space-based infrared early warning, ground-based / sea-based radar, skywave over-the-horizon radar, and detection and analysis methods based on rocket exhaust effect. Although the above technologies have made some progress, there are still some defects and shortcomings in the existing technologies: (1) Although the space-based infrared early warning system can achieve global wide-area surveillance, it is difficult to achieve high-confidence detection of weak targets in the early stage of ascent by relying solely on the infrared spectrum at ultra-long distances, and cross-domain sensor collaboration is required for confirmation. (2) Ground-based and sea-based radars have high accuracy, but due to the limitation of microwave straight-line propagation, there is a physical coverage blind zone for targets in the ascent stage below the horizon, which cannot provide sufficient early warning time. (3) Skywave over-the-horizon radar can break through the horizon constraint, but when detecting targets, it will be subject to complex backgrounds, such as time-varying ionospheric media, path fluctuations, multi-mode propagation, and strong clutter interference. (4) Detection methods based on exhaust effect utilize ionospheric cavities for early warning, but it is difficult to achieve high-precision real-time tracking and identification based solely on plasma depletion characteristics. Summary of the Invention

[0004] To address the challenges of detecting, locating, and accurately retrieving the initial distance of high-speed targets in complex environments, this invention proposes a target initial ground distance inversion method based on anomalous tail flame echoes.

[0005] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps: Step 1: Based on the tail flame disturbance echo data obtained by the skywave over-the-horizon radar, establish an ionospheric equivalent reflector model, and construct a geometric relationship model between radar, ionosphere, and target based on the curvature of the earth. Derive the nonlinear mapping relationship between slant range and ground distance, and extract multiple range gates from the RD spectrum. Step 2: For each range gate, extract the Bragg peak shift, Doppler spectral broadening characteristics and normalized energy of each range gate from the echo power matrix to construct a joint anomaly index; Step 3: Based on the joint anomaly index, an anomaly distance gate set is extracted from the background using an adaptive threshold, the anomaly centroid slant distance is calculated, and the inverse solution is used to obtain the initial estimate of the ground distance. Step 4: Based on the initial estimate of the ground distance, extract a multi-dimensional feature vector containing location, intensity, and morphological information. Correct systematic biases through nonlinear fitting and output the initial ground distance of the target.

[0006] Furthermore, step 1 specifically includes: Let the Earth's radius be... The geocentric distance of the equivalent virtual reflector is ,in The equivalent height of the virtual reflector in the ionosphere is given by the target's flight altitude. The geocentric distance corresponding to the target is Skywave radar is R High-speed target is T At the Earth's center O, the angle between radius OR and OA is... At the Earth's center O, the angle between radius OT and OA is... Based on the above parameters and the law of cosines, the propagation path length of the radar to the virtual reflection point is calculated. and the propagation path length from the virtual reflection point to the target. Obtain the equivalent propagation path length expression. ; Based on the equivalent propagation path length expression A nonlinear mapping relationship between slant range and ground distance is established, and multiple range gates are extracted from the RD spectrum based on this nonlinear mapping relationship. Path length of radar propagation to virtual reflection point The calculation formula is: (1); Length of the propagation path from the virtual reflection point to the target The calculation formula is: (2); Equivalent propagation path length expression for: (3); In formula (3), when the target enters the electromagnetic field and the electromagnetic rays are reflected by the ionosphere and reach the sea level, at this time... ; The nonlinear mapping relationship between slant range and ground distance is as follows: (4); In formula (4), x The distance between the radar and the scattering point on the ground; Ground distance between radar and scattering point x The calculation formula is: (5); In formula (5), when the scattering point height is 0, the propagation path is symmetrical about the virtual reflection point, that is... .

[0007] Furthermore, step 2 extracts the Bragg peak shift for each distance gate, including: According to radar transmission frequency Calculate the Bragg frequency of sea clutter According to the Bragg frequency of sea clutter Define the Bragg frequency range , ,in, In the radar echo Doppler spectrum, the first j A discrete frequency sampling point, The set frequency offset threshold; Based on Bragg frequency range The degree to which its energy deviates from the Bragg peak is calculated by distance-by-distance gate. Among them, when the energy of the distance gate is completely concentrated at the Bragg peak This indicates that the distance gate represents a normal sea surface echo; when the energy diffuses to the full Doppler band... This indicates that the distance gate is affected by the exhaust flame disturbance; Sea clutter Bragg frequency The calculation formula is: (6); In formula (6), g is the acceleration due to gravity. The speed of light; The degree to which the energy of the distance gate deviates from the Bragg peak The calculation formula is: (7); In formula (7), For the first A distance gate at the Doppler frequency The power value at that location, The total number of Doppler frequency points. To prevent the regularization constant from being divided by zero, the numerator in formula (7) is the sum of squared power within the Bragg interval, and the denominator is the sum of squared power across the entire frequency band.

[0008] Furthermore, in step 2, the Doppler spectral broadening features and normalized energy of each range gate are extracted from the echo power matrix, including: Calculate the power-weighted Doppler frequency standard deviation to obtain the Doppler spectral broadening characteristics of each range gate. ; Divide the total power of each distance gate by the maximum total power of all gates to obtain the normalized energy. ; Doppler spectral broadening characteristics of each distance gate The calculation formula is: (8); In formula (8), For the first i The power-weighted average Doppler frequency of each distance gate For the first i The power-weighted Doppler frequency standard deviation of the distance gate Here is the regularization constant; Normalized energy The calculation formula is: (9); In formula (9), k This is the index of the distance gate.

[0009] Furthermore, the joint anomaly indicator constructed in step 2 is as follows: (10); In formula (10), It is the soft energy threshold index. Used to detect the degree of Bragg frequency deviation. Used to measure Doppler broadening. Weak signal range gates are suppressed by compressing the energy dynamic range, while preventing high-energy gates from dominating detection.

[0010] Furthermore, step 3 employs an adaptive threshold to extract anomaly distance gate sets from the background, including: Repeat step 2 to obtain the joint anomaly index for all distance gates. Use the statistical outlier criterion based on interquartile range to automatically determine the adaptive threshold using the median and interquartile range of the data distribution. ; Based on adaptive threshold Extract the set of abnormal distance gates; Adaptive threshold The calculation formula is: (11); In formula (11), The upper quartile of the joint set of anomaly indicators. It represents the lower quartile of the joint set of anomalies.

[0011] Furthermore, step 3 calculates the slant distance of the anomaly centroid and obtains the initial estimate of the ground distance through inverse kinematics, including: Using joint anomaly indicators as weights, the weighted centroid slant range of the anomaly distance gate set is calculated. Combining this with the nonlinear mapping relationship between slant range and ground distance, the weighted centroid slant range is inversely solved to obtain the initial estimate of the ground distance. ; Preliminary estimate of ground distance The calculation formula is: (12).

[0012] In formula (12), This is a set of abnormal distance gates.

[0013] Furthermore, step 4 specifically includes: Based on the set of anomaly distance gates, the following features are extracted: weighted centroid ground distance of anomaly gates, ground distance of peak gates of joint indices, number of anomaly gates, ground width of anomaly zone, peak value of joint indices, total Doppler energy of peak gates, Bragg deviation of peak gates, and Doppler coverage of peak gates, forming an eight-dimensional feature vector. Based on the multidimensional feature vector and the initial estimate of the ground distance, with the actual ground distance as the optimization objective, a gradient boosting regressor is used for least squares fitting to establish the systematic offset law between the geometric inversion distance and the actual distance. Based on the systematic offset pattern, the initial estimate of the ground distance is corrected to obtain the true ground distance. ; The systematic offset pattern between the geometrically inverted distance and the true distance is as follows: (13); In formula (13), These are, respectively, the ground distance of the weighted centroid of the anomaly gate, the ground distance of the peak gate of the joint index, the number of anomaly gates, the ground width of the anomaly zone, the peak value of the joint index, the total Doppler energy of the peak gate, the Bragg deviation of the peak gate, and the Doppler coverage of the peak gate.

[0014] The beneficial effects of this invention are: (1) This invention addresses the problem of physical blind spots or missing information dimensions in a single detection system. It integrates two types of information sources: the over-the-horizon detection capability of skywave radar and the ionospheric disturbance effect of the tail flame. Without changing the existing radar system, the disturbance of the ionosphere by the tail flame is transformed into an anomaly in the skywave radar echo spectrum. The initial state of the target is inverted from the anomaly, breaking through the limitation of a single means remaining at the level of "detecting anomalies". This promotes the improvement of the ability of skywave radar from "long-distance detection and early warning" to "long-distance identification".

[0015] (2) Through multi-dimensional feature fusion and adaptive threshold mechanism, the present invention can automatically complete the robust detection and positioning of abnormal distance gate in complex and ever-changing ionospheric environment and sea clutter background without manual parameter adjustment, and has the ability to adapt to different sea conditions and different disturbance intensities.

[0016] (3) This invention establishes a complete closed-loop link from abnormal echo detection to quantitative estimation of the initial ground distance of the target. By combining physical modeling and data-driven methods, it effectively eliminates systematic biases in distance inversion and provides high-precision distance prior information for trajectory analysis and state recognition of high-speed maneuvering targets. Attached Figure Description

[0017] Figure 1 A flowchart of a target initial ground range inversion method based on anomalous tail flame echo; Figure 2 This is a schematic diagram of the equivalent path based on the curvature of the Earth. Figure 3 Schematic diagram of ray tracing perturbation Figure 4 This is a schematic diagram of the abnormal echo spectrum of a skywave radar. Detailed Implementation

[0018] The overall method of this invention includes six core steps: ionospheric model simplification and equivalent path modeling, Bragg peak offset extraction, Doppler spectral feature extraction, joint anomaly index construction, adaptive threshold detection and centroid localization, and nonlinear deviation fitting.

[0019] First, based on the assumption of an equivalent reflective layer of the ionosphere, a nonlinear mapping relationship between slant range and ground distance considering the curvature of the Earth is established, such as... Figure 2 As shown; secondly, regarding the abnormal broadening of the RD spectrum caused by the ionospheric electron density voids resulting from the exhaust flame disturbance, such as... Figure 3 and Figure 4 As shown, three complementary features—Bragg peak deviation, Doppler spectrum broadening standard deviation, and normalized energy—are extracted from the RD spectrum power matrix through a distance-gated process and fused into a joint anomaly index. Subsequently, an anomaly distance gate is separated from the background using an adaptive thresholding method based on interquartile range. The anomaly centroid slant distance is calculated using the joint index as weights, and the initial ground distance estimate is obtained through geometric model inversion. Finally, an 8-dimensional feature vector containing location, intensity, and morphological information is extracted from the above detection process, as shown in Table 1. A gradient boosting regressor is used to correct the systematic bias of the geometric inversion, outputting a high-precision estimate of the initial ground distance of the target.

[0020] Table 1

[0021] Using the above method, the present invention can combine physical modeling derivation with nonlinear fitting based on the geometric mapping relationship between the distance gate position of the anomalous region in the echo spectrum and the initial ground distance, thereby achieving a high-precision solution for the initial ground distance of the target.

[0022] like Figure 1 As shown, the steps of the target initial ground range inversion method based on the anomalous echo of the tail flame described in this embodiment include: S1: Simplified ionospheric model; Further derivation considering the geometric relationships of a spherical Earth. Let the Earth's radius be... The geocentric distance of the equivalent virtual reflector is The target flight altitude is The geocentric distance corresponding to the target is .like Figure 1 As shown, R represents skywave radar, and T represents a high-speed target. Let OA be the angle between radius OR and OA at the Earth's center O. Let O be the point at the Earth's center, and let OT be the angle between radius OT and OA. According to the law of cosines, the path length of the radar propagation to the virtual reflection point can be expressed as: (1); The propagation path length from the virtual reflection point to the target can be expressed as: (2); This leads to the final equivalent propagation path expression: (3); In formula (3), when the target enters the electromagnetic field and the electromagnetic rays are reflected by the ionosphere and reach the sea level, at this time... ; The equivalent path length can be expressed as: (4); For sea surface echoes from a monostatic radar (scattering point height is 0), the propagation path is symmetrical about the virtual reflection point, i.e. The ground distance between the radar and the scattering point is... Substituting into the previous equation, we obtain the relationship between the slant distance and the ground distance: (5); The exhaust plume disturbance creates electron concentration holes in the ionosphere, causing Doppler broadening in radar echoes passing through the disturbed region. Observations show that there are typically 1 to 3 range gates in the RD spectrum, whose power is anomalously broadened across the entire Doppler frequency axis, appearing as "bright horizontal lines" in the RD spectrum. The rays corresponding to these range gates pass precisely through the region where the exhaust plume disturbance is most intense. Based on this, anomaly indicators are extracted from the RD spectrum power matrix range gate by range gate using the following steps. S2: Extract Bragg peak shift; Calculate the Bragg frequency of sea clutter based on the radar transmission frequency. Define the Bragg frequency range For each distance gate Calculate the degree to which its energy deviates from the Bragg peak: (6); In formula (7), For the first A distance gate at the Doppler frequency The power value at that location, The total number of Doppler frequency points. To prevent the regularization constant from being divided by zero, the numerator in formula (7) is the sum of squared power within the Bragg interval, and the denominator is the sum of squared power across the entire frequency band.

[0023] When the energy of a certain distance gate is completely concentrated at the Bragg peak This indicates that the echo is a normal sea surface echo; when the energy diffuses to the full Doppler band... This indicates that the gate was affected by the exhaust flame disturbance.

[0024] S3: Doppler spectral feature extraction; Calculate the power-weighted Doppler frequency standard deviation as a direct measure of broadening: (8); In formula (8), For the first i The power-weighted average Doppler frequency of each distance gate For the first i The power-weighted Doppler frequency standard deviation of the distance gate It is the regularization constant; the energy of the normal gate is concentrated in nearby, Smaller; the disturbed anomaly gate energy diffuses across a wide frequency band. Significantly increased. Simultaneously, normalized energy is calculated by dividing the total power of each distance gate by the maximum total power of all gates, normalizing it to the [0, 1] interval: (9); In formula (9), k This is the index of the distance gate.

[0025] S4: Establish joint anomaly indicators; Combine the three quantities in S2 and S3 into a joint anomaly indicator: (10); In formula (10), , is the soft energy threshold index. Used to detect the degree of Bragg frequency deviation. Used to measure Doppler broadening. Weak signal range gates are suppressed by compressing the energy dynamic range, while preventing high-energy gates from dominating detection. The product of these three factors constitutes an adaptive metric: under different data conditions, the factor with the highest contrast automatically dominates anomaly gate localization.

[0026] S5: Adaptive threshold detection and centroid localization; To obtain the joint index of all distance gates Then, a threshold needs to be automatically determined. This separates the anomalous gates from the background. Since most range gates are normal sea surface echoes, The values ​​are concentrated at low levels, with only a few affected doors. The values ​​are significantly high, exhibiting a typical right-skewed distribution. Therefore, this paper adopts a statistical outlier criterion based on the interquartile range, automatically determining an adaptive threshold using the median and interquartile range of the data distribution. (11); In formula (11), The upper quartile of the joint set of anomaly indicators. It represents the lower quartile of the joint set of anomalies.

[0027] Next, the slope distance of the anomaly centroid is calculated using the joint index as weights, and the initial estimate of the ground distance is obtained by inversely solving the slope distance-ground distance geometric relationship in S1: (12).

[0028] In formula (12), This is a set of abnormal distance gates.

[0029] S6: Nonlinear deviation fitting to obtain the true ground distance value; Not the actual initial ground distance of the tail flame There is a systematic bias between the two, because It is derived by inversely calculating the slant range of the abnormal peak gate. However, the exhaust perturbation region affects the ray path, making it no longer symmetrical, thus affecting the accuracy of the inverse calculation formula. Furthermore, the positioning of the broadened peak gate also has errors: when the perturbation region is concentrated and the peak gate positioning is clear, The deviation is relatively small; however, when the disturbance region spans multiple distance gates and has an asymmetrical shape, the peak gate may deviate from the true disturbance center, leading to... This itself introduces additional errors. Therefore, and The true relationship contains nonlinear components and needs to be corrected by fitting a model.

[0030] Further auxiliary observations reflecting the spatial morphology of the disturbance area are extracted from the detection process of S2-S5 to form a feature space. Examples include distance features; among which, location features ( All features are transformed from slant range space to ground distance space; the rest are intensity and morphological characteristics of anomaly regions. Features in the feature space are used as input, along with the true ground distance. To achieve the objective, a least-squares fit is performed using a gradient boosting regressor (GBR): (13); In formula (13), These are, respectively, the ground distance of the weighted centroid of the anomaly gate, the ground distance of the peak gate of the joint index, the number of anomaly gates, the ground width of the anomaly zone, the peak value of the joint index, the total Doppler energy of the peak gate, the Bragg deviation of the peak gate, and the Doppler coverage of the peak gate.

[0031] Its core task is to fit the observed ground distance. Distance from actual ground To determine the offset between the two points, GBR uses location features to learn how this offset varies with distance, and uses morphological and intensity features to compensate for the differences in offset under different perturbation conditions. Ultimately, the true ground distance is obtained. The value of .

[0032] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for inverting the initial ground range of a target based on anomaly echoes of the exhaust plume, characterized in that, include: Step 1: Based on the tail flame disturbance echo data obtained by the skywave over-the-horizon radar, establish an ionospheric equivalent reflector model, and construct a geometric relationship model between radar, ionosphere, and target based on the curvature of the earth. Derive the nonlinear mapping relationship between slant range and ground distance, and extract multiple range gates from the RD spectrum. Step 2: For each range gate, extract the Bragg peak shift, Doppler spectral broadening characteristics and normalized energy of each range gate from the echo power matrix to construct a joint anomaly index; Step 3: Based on the joint anomaly index, an anomaly distance gate set is extracted from the background using an adaptive threshold, the anomaly centroid slant distance is calculated, and the inverse solution is used to obtain the initial estimate of the ground distance. Step 4: Based on the initial estimate of the ground distance, extract a multi-dimensional feature vector containing location, intensity, and morphological information. Correct systematic biases through nonlinear fitting and output the initial ground distance of the target.

2. The target initial ground range inversion method based on the anomalous echo of the tail flame as described in claim 1, characterized in that, Step 1 specifically includes: Let the Earth's radius be... The geocentric distance of the equivalent virtual reflector is ,in The equivalent height of the virtual reflector in the ionosphere is given by the target's flight altitude. The geocentric distance corresponding to the target is Skywave radar is R High-speed target is T At the Earth's center O, the angle between radius OR and OA is... At the Earth's center O, the angle between radius OT and OA is... Based on the above parameters and the law of cosines, the propagation path length of the radar to the virtual reflection point is calculated. and the propagation path length from the virtual reflection point to the target. Obtain the equivalent propagation path length expression. ; Based on the equivalent propagation path length expression A nonlinear mapping relationship between slant range and ground distance is established, and multiple range gates are extracted from the RD spectrum based on this nonlinear mapping relationship. Path length of radar propagation to virtual reflection point The calculation formula is: （1）； Length of the propagation path from the virtual reflection point to the target The calculation formula is: （2）； Equivalent propagation path length expression for: （3）； In formula (3), when the target enters the electromagnetic field and the electromagnetic rays are reflected by the ionosphere and reach the sea level, at this time... ; The nonlinear mapping relationship between slant range and ground distance is as follows: （4）； In formula (4), x The distance between the radar and the scattering point on the ground; Ground distance between radar and scattering point x The calculation formula is: （5）； In formula (5), when the scattering point height is 0, the propagation path is symmetrical about the virtual reflection point, that is... .

3. The target initial ground range inversion method based on the anomalous echo of the tail flame as described in claim 1, characterized in that, Step 2 extracts the Bragg peak shift for each distance gate, including: According to radar transmission frequency Calculate the Bragg frequency of sea clutter According to the Bragg frequency of sea clutter Define the Bragg frequency range , ,in, In the radar echo Doppler spectrum, the first j A discrete frequency sampling point, The set frequency offset threshold; According to the Bragg frequency range The degree to which its energy deviates from the Bragg peak is calculated by distance-by-distance gate. Among them, when the energy of the distance gate is completely concentrated at the Bragg peak This indicates that the distance gate represents a normal sea surface echo; when the energy diffuses to the full Doppler band... This indicates that the distance gate is affected by the exhaust flame disturbance; Sea clutter Bragg frequency The calculation formula is: （6）； In formula (6), g is the acceleration due to gravity. The speed of light; The degree to which the energy of the distance gate deviates from the Bragg peak The calculation formula is: （7）； In formula (7), For the first A distance gate at the Doppler frequency The power value at that location, The total number of Doppler frequency points. To prevent the regularization constant from being divided by zero, the numerator in formula (7) is the sum of squared power within the Bragg interval, and the denominator is the sum of squared power across the entire frequency band.

4. The target initial ground range inversion method based on the anomalous echo of the tail flame as described in claim 1, characterized in that, Step 2 involves extracting the Doppler spectral broadening features and normalized energy for each range gate from the echo power matrix, including: Calculate the power-weighted Doppler frequency standard deviation to obtain the Doppler spectral broadening characteristics of each range gate. ; Divide the total power of each distance gate by the maximum total power of all gates to obtain the normalized energy. ; Doppler spectral broadening characteristics of each distance gate The calculation formula is: （8）； In formula (8), For the first i The power-weighted average Doppler frequency of each distance gate For the first i The power-weighted Doppler frequency standard deviation of the distance gate Here is the regularization constant; Normalized energy The calculation formula is: （9）； In formula (9), k This is the index of the distance gate.

5. The target initial ground range inversion method based on the anomalous echo of the tail flame as described in claim 1, characterized in that, The joint anomaly index constructed in step 2 is as follows: （10）； In formula (10), It is the soft energy threshold index. Used to detect the degree of Bragg frequency deviation. Used to measure Doppler broadening. Weak signal range gates are suppressed by compressing the energy dynamic range, while preventing high-energy gates from dominating detection.

6. The target initial ground range inversion method based on the anomalous echo of the tail flame as described in claim 1, characterized in that, Step 3 uses an adaptive threshold to extract anomaly distance gate sets from the background, including: Repeat step 2 to obtain the joint anomaly index for all distance gates. Use the statistical outlier criterion based on interquartile range to automatically determine the adaptive threshold using the median and interquartile range of the data distribution. ; Based on adaptive threshold Extract the set of abnormal distance gates; Adaptive threshold The calculation formula is: （11）； In formula (11), The upper quartile of the joint set of anomaly indicators. It represents the lower quartile of the joint set of anomalies.

7. The target initial ground range inversion method based on the anomalous echo of the tail flame as described in claim 1, characterized in that, Step 3 involves calculating the slant distance of the anomaly centroid and obtaining an initial estimate of the ground distance using an inverse solution, including: Using joint anomaly indicators as weights, the weighted centroid slant range of the anomaly distance gate set is calculated. Combining this with the nonlinear mapping relationship between slant range and ground distance, the weighted centroid slant range is inversely solved to obtain the initial estimate of the ground distance. ; Preliminary estimate of ground distance The calculation formula is: （12）。 In formula (12), This is a set of abnormal distance gates.

8. The target initial ground range inversion method based on the anomalous echo of the tail flame as described in claim 1, characterized in that, Step 4 specifically includes: Based on the set of anomaly distance gates, the following features are extracted: weighted centroid ground distance of anomaly gates, ground distance of peak gates of joint indices, number of anomaly gates, ground width of anomaly zone, peak value of joint indices, total Doppler energy of peak gates, Bragg deviation of peak gates, and Doppler coverage of peak gates, forming an eight-dimensional feature vector. Based on the multidimensional feature vector and the initial estimate of the ground distance, with the actual ground distance as the optimization objective, a gradient boosting regressor is used for least squares fitting to establish the systematic offset law between the geometric inversion distance and the actual distance. Based on the systematic offset pattern, the initial estimate of the ground distance is corrected to obtain the true ground distance. ; The systematic offset pattern between the geometrically inverted distance and the true distance is as follows: （13）； In formula (13), These are, respectively, the ground distance of the weighted centroid of the anomaly gate, the ground distance of the peak gate of the joint index, the number of anomaly gates, the ground width of the anomaly zone, the peak value of the joint index, the total Doppler energy of the peak gate, the Bragg deviation of the peak gate, and the Doppler coverage of the peak gate.

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