A high-resolution three-dimensional point-trace aggregation method based on prior data

Abstract

The present invention provides a high-resolution three-dimensional point trace condensation method based on prior data, which belongs to the field of radar target detection technology. The specific process is: a radar video projection data warehouse of three-dimensional point traces of medium and high altitude neighboring targets is constructed through a radar video simulator. The envelope characteristics of radar video data in three dimensions of distance, azimuth and pitch are described in a manner similar to "contour lines". The characteristics include pole amplitude, pole number, inter-pole gradient, and pole radar video data unit span. The sample data in the data warehouse is used to form a neighboring target envelope matching template. The neighboring target queries the corresponding template according to the multi-dimensional index, and uses relative feature data to complete the matching of multiple envelope sampling points. The matching envelope information is used to complete the segmentation of the target video data, and the segmented video data is subjected to distance condensation and angle condensation to form the target three-dimensional point trace information.

Description

Technical Field

[0001] The invention belongs to the technical field of radar target detection. Background Art

[0002] The main task of the radar system is to determine whether the target exists, and to accurately detect and track multiple batches of multiple targets, and the point extraction of echo data is the basis for all these tasks. A point extraction system with good performance can accurately and effectively extract the target, which is of vital importance to the performance of the radar system. The ideal target echo should be manifested as the broadening of the radar antenna pattern in azimuth, while the distance depends on the pulse compression waveform used by the signal processor. Therefore, after the echo signal is processed by the front end, a target may output multiple over-threshold signals at different distances, different azimuths and different pitch beams at the same time. The problem of how to determine the true distance center, azimuth center and pitch degree of the target is solved by three-dimensional point condensation.

[0003] The ability of a radar to distinguish targets in azimuth and elevation is mainly determined by the azimuth and elevation beamwidths. The interval between two identical targets A and B at almost the same distance is slightly larger than the beamwidth. When the beam sweeps over them, the radar receives the echo from target A first, and then receives the echo from target B. Targets A and B are easy to distinguish in azimuth. If the interval between the same two targets is less than the beamwidth, when the beam sweeps over them, the radar still receives the echo from target A first, and then receives the echo from target B. However, before the radar stops receiving the echo from target A, it starts receiving the echo from target B, so the echoes from the two targets are mixed together. In radar operation, under the influence of antenna pattern modulation and detection threshold, the actual radar angular resolution is smaller than one beamwidth. A 3dB beamwidth is usually used as a measure of radar angular resolution (Introduction to Airborne Radar (Second Edition)).

[0004] Different radar systems have different target echo forms and parameters, and the criteria for target point trace resolution and merging are also different, but the basic process is the same. In the document "Design of Three-Coordinate Radar Point Trace Extraction System" (Ship Electronic Countermeasures, 2010, Vol.33, No.5pp:78-82), a three-coordinate radar point trace extraction method using the principle of "peak search in distance, and finding the center of mass in elevation and azimuth" is proposed; in the document "A Point Trace Condensation Method Based on Three-Coordinate Radar" (Radar and Countermeasures, 2013, Vol.33, No.4pp:46-50), a method of using multiple repeated cycle accumulation and statistics to improve the authenticity of the trace is proposed; in the document "Research on Target Accumulation Detection and Point Trace Condensation Technology", the radar video data after signal processing is first resolved and merged in distance, then resolved and merged in azimuth, and finally the distance and angle information of the trace is obtained using the centroid method. The common point trace condensation method adopts the connected merging process without prior information in the condensation process. Therefore, the radar azimuth resolution and mid-to-high altitude pitch resolution are generally greater than or equal to 2 times the 3dB beam width, and the range resolution is greater than or equal to C / 2B, where C is the speed of light and B is the radar equivalent bandwidth. The low-altitude pitch resolution of the radar is usually interfered by the multipath effect, which is different from the azimuth resolution. Summary of the invention

[0005] In traditional point trace condensation, the connected merging process without prior information is usually adopted. Limited by the aliasing of target echoes, under the influence of antenna pattern modulation and detection threshold, the radar azimuth resolution and mid-to-high altitude pitch resolution are generally greater than or equal to 2 times the 3dB beam width, and the distance resolution is greater than or equal to C / 2B, where C is the speed of light and B is the radar equivalent bandwidth. In order to improve the radar's ability to resolve adjacent targets, the present invention constructs a radar video projection data warehouse of mid-to-high altitude adjacent target three-dimensional point traces through a radar video simulator. The radar video data is processed by pulse compression, pattern modulation and detection threshold filtering, and usually has envelope characteristics similar to the sinc function in the distance dimension, azimuth dimension and pitch dimension. Therefore, "contour lines" are used to describe the video data projected in three dimensions, including the pole amplitude, the number of poles, the gradient between poles, and the span of the pole radar video data unit. The sample data in the radar video projection data warehouse is used to form an adjacent target envelope matching template. In the radar working scene, the neighboring target queries the corresponding video data envelope template based on the multi-dimensional index, and uses the relative feature data to complete the matching of the envelope multi-sampling points. The matching envelope information is used to complete the segmentation of the target video data, and the distance and angle condensation are performed based on the segmented video data to form the target 3D point information.

[0006] The present invention is realized by the following technical scheme: performing "contour line" three-dimensional projection on the radar echo video, performing envelope matching with a three-dimensional point trace database constructed by radar video simulator modeling, and performing high-resolution point trace condensation processing after forming matching point traces.

[0007] Furthermore, the modeling method of the three-dimensional point trace database is as follows: Step 1: construct a radar video projection data bin of the three-dimensional point traces of the mid- and high-altitude neighboring targets through a radar video simulator; Step 2: use "contour lines" to describe the video data projected in the three dimensions of distance, azimuth and elevation, including the pole amplitude, the number of poles, the gradient between poles, and the span of the radar video data unit between poles. Step 3: use the sample data in the radar video projection data bin to form an envelope matching template of the neighboring targets in the three dimensions of distance, azimuth and elevation.

[0008] Furthermore, the maintenance method of the three-dimensional point trace database is: through the radar video simulator, the radar is classified according to different working modes, and the prior data is generated according to ① the distance segment between the center of the adjacent target line and the radar station site, ② the adjacent angle of the adjacent target azimuth, ③ the adjacent angle of the adjacent target elevation, and ④ the adjacent distance spacing of the adjacent target. The storage of prior data adopts a multi-layer index nested tree structure, and the multi-layer index tree contains: ① radar working mode -> ② the distance between the center of the adjacent target line and the radar station site -> ③ the angle between the adjacent target line and the radar line of sight and the adjacent target distance spacing. The prior data is stored in the corresponding position according to the index, and the "flattening" processing method is used to compress the three-dimensional prior data to obtain the radar video projection data of the distance dimension, azimuth dimension and pitch dimension, and extract its envelope features, including: pole amplitude A, number of poles M, pole gradient G, pole radar video data unit span (CellNum S ,CellNum E ).

[0009] Furthermore, the high-resolution point trace condensation processing method is as follows: Step 1: In the radar working scenario, when the position between targets is smaller than the traditional resolution capability of the radar, high-resolution point trace condensation processing is performed; Step 2: Select the matching prior data envelope as the template through a multi-layer index tree; Step 3: Perform a "flattened" projection on the intercepted three-dimensional measured target video data to obtain a three-dimensional envelope; Step 4: Match the template envelope and the measured envelope, and if the match is successful, segment the three-dimensional measured target video data according to the feature range of the template envelope, and perform conventional three-dimensional condensation on the segmented three-dimensional measured target video data to achieve high-resolution point trace condensation processing; Step 5: If the match is unsuccessful, perform conventional three-dimensional condensation directly, and prompt the host computer.

[0010] Among them, the matching process is performed in the form of a sliding window, and the matching process steps are as follows: ① pole search; ② template translation; ③ template scaling; ④ multi-sampling point matching. Step 1: Pole search: In the pole search, the number of poles M of the envelope template, the polarity of the pole gradient G, and the span of the pole radar video data unit are used for searching. The pole distribution of the actual data is estimated by the proportional relationship between the actual data size and the sample data size, and the polarity of the pole gradient G is determined by voting. If the pole distribution characteristics of the actual data in three dimensions are consistent with the template, the match is successful, otherwise the match fails, and the high-resolution point trace condensation process is exited, and conventional three-dimensional point trace condensation processing is performed. The poles are described as: the number of poles M, the gradient G between the poles: {P1(G + ,G - ),...,P m (G + ,G - )}Pole radar video data unit span: Where P1 to P m is the number of poles, G + represents the positive gradient, G - Represents the negative gradient. The order of positive and negative gradients in () represents the property of this extreme point, whether it is a maximum or a minimum. CellNum S ,CellNum E Represents the starting data unit number and the ending data unit number; Step 2: Template translation: According to the results of the pole search, a sliding window method is used to refine the start and end range of the actual data poles. From the template envelope, in the order of distance from near to far, azimuth from small to large, and pitch from small to large, align the poles on the template envelope with the poles of the actual data to complete the template translation. During the template envelope translation process, the overlapping parts of the data units are numerically superimposed, and the broken data units are numerically interpolated; Step 3: Template scaling: Use the pole amplitude A in the template envelope data, the gradient P on both sides of the pole (G + ,G - ), polar radar video data unit span (CellNum S ,CellNum E ), calculate the value of the template envelope data at the pole zero point, use the amplitude of the pole of the actual data, according to the gradient on both sides of the pole in the template envelope data, take the value at the pole zero point in the template envelope data as the termination condition, calculate the span of the pole radar video data unit, and complete the enlargement or reduction of the template envelope in three dimensions; Step 4: Multi-sampling point matching: Use the multi-sampling point matching method to judge the envelope consistency. In order to ensure the accuracy of the judgment while reducing the amount of calculation, the number of selected sampling points ≥ the number of poles × 4. The consistency judgment is realized by hypothesis testing.

[0011] The beneficial effects of the present invention include:

[0012] (1) Compared with the traditional method of "nine-square grid" traversal, the data compression processing and envelope multi-point matching method reduces the amount of calculation by 50%, and the extra time resources are equivalent to the performance improvement space;

[0013] (2) When a neighboring target is approaching, the amplitude and size of its echo are affected by target echo overlap, target shielding, and signal-to-noise ratio, and there are numerical fluctuations. The decision criteria for point trace condensation processing in traditional methods are fixed, and the fluctuation of target echoes can cause target false alarms or target missed detections. During the matching process, the method of the present invention can be dynamically adjusted according to the mathematical characteristics of the model. Under the premise of the same target missed detection rate, the target false alarm rate is reduced by 50%. The target point traces after template matching segmentation have losses in width and size, but their position accuracy is not lost;

[0014] (3) The method of the present invention can improve the spatial resolution of the radar for adjacent targets. The angular resolution is increased from ≥2 times the 3dB beam width to ≥1 times the 3dB beam width, and the distance resolution is increased from ≥C / 2B to ≤C / 2B. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Flow chart of high-resolution three-dimensional point condensation processing based on prior data;

[0016] Figure 2 Schematic diagram of classification and combination of simulation data samples;

[0017] Figure 3 Multi-layer index tree structure diagram;

[0018] Figure 4 Schematic diagram of the mathematical description of the envelope curve;

[0019] Figure 5 Schematic diagram of the matching process. DETAILED DESCRIPTION

[0020] In order to better understand the technical solution of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0021] The present invention proposes a high-resolution three-dimensional point trace condensation method based on prior data, performs "contour line" three-dimensional projection on the radar echo video, performs envelope matching with the three-dimensional point trace database constructed by radar video simulator modeling, and forms matching point traces before high-resolution point trace condensation processing. The present invention improves the spatial resolution of adjacent point targets, the angular resolution is increased from ≥2 times the 3dB beam width to ≥1 times the 3dB beam width, and the distance resolution is increased from ≥C / 2B to ≤C / 2B. Compared with the "nine-square grid" traversal method in the traditional method, the amount of calculation can be reduced by 50%. Under the premise of the same target missed detection rate, the target false alarm rate is reduced by 50%, and the condensed point traces have no loss in position accuracy.

[0022] The present invention Figure 1 As shown, the specific process is:

[0023] Generation and maintenance of prior data:

[0024] (1) Through the radar video simulator, the simulation of adjacent targets below the radar resolution capability is completed. By counting the scenes where sea targets and air targets generate overlapping echoes, the number of adjacent targets N is taken as 2. The distance R between the center of the adjacent target line and the radar site is set to 5km: 25km: 250km. The angle θ between the center of the adjacent target line and the radar line of sight in the range-azimuth is set to 5°: 15°: 360°. The angle α between the center of the adjacent target line and the radar line of sight in the range-elevation is set to 5°: 15°: 360°. When the adjacent targets are simulated for azimuth angle, the distance between the targets is d = R × 2 times the 3dB azimuth beam width. When the adjacent targets are simulated for elevation angle, the distance between the targets is d = R × 2 times the 3dB elevation beam width. When the adjacent targets are simulated for distance, the distance between the targets is d = C / 2B. The simulation data samples are as follows: Figure 2 As shown;

[0025] (2) In order to improve the management efficiency of sample data and the search efficiency during matching processing and the real-time requirements of the system, the data storing the sample data is designed to be nested. The multi-layer index includes: 1 radar working mode -> 2 the distance between the center of the adjacent target line and the radar site -> 3 the angle between the adjacent target line and the radar line of sight and the distance interval between the adjacent targets, as shown in the following figure. Figure 3 As shown;

[0026] (3) The three-dimensional video data is stored in the corresponding position according to the index. In order to obtain the data envelope in the distance dimension, azimuth dimension and pitch dimension, the three-dimensional video data is "flattened" by averaging or taking the larger of them to generate radar video projection data in three dimensions. Assume that the interception range of the three-dimensional video data is the distance unit start and end: d1-d l , azimuth unit start and end: θ1-θ n , pitch unit start and end: α1-αm The calculation formula is as follows:

[0027]

[0028]

[0029]

[0030] (4) Extract the amplitude information of the radar video projection data to form a video projection data envelope. Perform multi-dimensional smoothness fitting on the envelope curve obtained by multiple simulations. Perform mathematical modeling on the fitted envelope curve and describe it as the pole amplitude A, pole number M, pole gradient G, pole radar video data unit span (CellNum S ,CellNum E ). Figure 4 shown.

[0031] Detailed process of high-resolution point trace condensation processing:

[0032] (1) In the radar working scenario, when an antenna cycle ends, the target track position information including distance, azimuth, pitch and motion information including heading, speed and update time are used to predict the relationship between the position of adjacent targets and the traditional resolution of the radar at the next antenna scanning time. Assume that target 1 has a distance of Dis1, azimuth Azi1, pitch Ele1, speed XVelocity1, YVelocity1, ZVelocity1 and update time T1; assume that target 2 has a distance of Dis2, azimuth Azi2, pitch Ele2, speed XVelocity2, YVelocity2, ZVelocity2 and update time T2. The antenna scanning cycle is △T, and the traditional resolution of the radar is set to the distance resolution △R, the azimuth resolution △θ, and the pitch resolution △α. The calculation formula is as follows:

[0033]

[0034] If △Dis≤△R and △Azi≤△θ and △Ele≤△α, then enter the high-resolution point trace condensation process, otherwise perform the conventional three-dimensional point trace condensation process;

[0035] (2) Determine the mode index value according to the current working mode of the radar, calculate the distance index value (Dis / 25+1) according to the distance information Dis of the center position of the target line, calculate the angle index value (β / 10+1) between the center of the adjacent target line and the radar line of sight in the distance-azimuth according to the angle β between the target azimuth line and the radar line of sight, and calculate the angle index value (γ / 10+1) between the center of the adjacent target line and the radar line of sight in the distance-elevation according to the angle γ between the target azimuth line and the radar line of sight. Combine the above index values ​​at all levels to determine the adjacent target envelope matching template;

[0036] (3) According to the location distribution of the adjacent targets, start and end according to the distance unit: d a -d b , azimuth unit start and end: θ c -θ d , pitch unit start and end: α e -α f Intercept the 3D video data of the neighboring target, perform data “compression” processing on the 3D video data, and generate the envelope of the radar video projection data in three dimensions. The calculation formula is the same as “Generation and maintenance of prior data (3)”.

[0037] (4) Matching the envelope of the three-dimensional video projection data of the neighboring target with the corresponding neighboring target envelope matching template. The matching process is performed in the form of a sliding window. The matching process steps are as follows: ① pole search; ② template translation; ③ template scaling; ④ multi-sampling point matching.

[0038] Pole search: Considering that the peak value of the target envelope in the actual scene is related to the signal-to-noise ratio, the pole number M of the envelope template, the polarity of the pole gradient G, and the span of the pole radar video data unit are used for searching. The pole in the template is described as:

[0039] The number of poles M, the pole gradient G: {P1(G + ,G _ ),...,P m (G + ,G _ )}

[0040] Pole radar video data unit span:

[0041] Where P1 to P m is the number of poles, G + represents the positive gradient, G _ Represents the negative gradient. The order of positive and negative gradients in () represents the property of this extreme point, whether it is a maximum or a minimum. CellNum S ,CellNum ERepresents the start data unit sequence number and the end data unit sequence number.

[0042] For each dimension of the video projection data envelope, a proportional relationship is generated based on the actual data size and sample data size. For example, if the actual data size is 8 data units and the sample is 10 data units, the scale is 4:5, with the actual data in front. The expected pole distribution of the actual data is obtained by scaling the span of the template's pole radar video data unit {△CellNum expect_1 ,...,△CellNum expect_m-1}, in each segment △CellNum expect The polarity of adjacent video data units is calculated and voted. The voting adopts the 7:3 criterion, that is, the gradient polarity with a number exceeding 70% in the result is used as the △CellNum of this segment. expect If the pole distribution characteristics of the actual data in three dimensions are consistent with the template, the match is successful, otherwise the match fails, the high-resolution point trace condensation process is exited, and the conventional three-dimensional point trace condensation process is performed.

[0043] Template translation: Based on the results of the pole search in ①, estimate the pole position range of the actual data in three dimensions. Use a sliding window method in each pole position range to refine the start and end range of the pole, and perform weighted average on the amplitude values ​​corresponding to the data units in the start and end range to determine the amplitude of the current pole and the corresponding data unit number. From the template envelope, in the order of distance from near to far, azimuth from small to large, and pitch from small to large, align the peaks corresponding to the poles on the template envelope with the data unit numbers corresponding to the poles on the three-dimensional envelope of the actual data to complete the template translation. During the translation process, the overlapping parts of the data units are numerically superimposed, and the broken data units are numerically interpolated.

[0044] Template scaling: For the template envelope and actual data envelope after alignment, use the extreme point amplitude A and the gradient P(G + ,G _ ), polar radar video data unit span (CellNum S ,CellNum E ), calculate the value at the pole zero point in the template envelope data, use the amplitude of the pole of the actual data, according to the gradient on both sides of the pole in the template envelope data, take the value at the pole zero point in the template envelope data as the termination condition, calculate the span of the pole radar video data unit, and complete the enlargement or reduction of the template envelope.

[0045] Multi-sampling point matching: For the template envelope after scaling and the actual data envelope, the multi-sampling point matching method is used to judge the envelope consistency. In order to ensure the accuracy of the judgment while reducing the amount of calculation, the number of selected sampling points is ≥ the number of poles × 4. The consistency judgment is carried out by hypothesis testing. Assuming that the difference between the actual data envelope and the template envelope after scaling satisfies the normal distribution with a mean of 0 and a standard deviation of σ0, the judgment formula for each sampling point is as follows:

[0046] Assumption: μ=μ0,σ=σ0

[0047] Construct the hypothesized statistic:

[0048] Rejection region: W = {|U|>Z α / 2}

[0049] Through hypothesis testing, it is determined that the match is successful. Otherwise, if the match fails, the high-resolution point trace condensation process is exited and the conventional 3D point trace condensation process is performed. The successfully matched radar video data is segmented and extracted according to the template envelope shape at the time of matching, and the actual radar video data in the corresponding distance unit, azimuth unit and pitch unit are composed of 3D video data. The 3D video data is subjected to conventional 3D point trace condensation processing. The processing diagram is as follows Figure 5 shown.

Claims

1. A high-resolution three-dimensional point condensation method based on prior data, characterized by: The radar echo video is projected in three dimensions as "contour lines" and envelope matched with the three-dimensional point trace samples constructed by radar video simulator modeling. After the matching points are formed, high-resolution point trace condensation processing is performed; The spatial volume of the radar echo video is measured from three dimensions: radial distance, horizontal azimuth and vertical pitch. In order to describe the two-dimensional envelope characteristics of the radar echo video, the radar echo video is projected onto three two-dimensional planes: horizontal azimuth + vertical pitch, radial distance + vertical pitch and radial distance + horizontal azimuth. For the missing third dimension on each two-dimensional plane, the "contour" processing of the dimensional data can be realized by averaging or taking the larger one. The modeling method of the three-dimensional point trace sample constructed by the radar video simulator modeling method includes: Step 1: Construct a radar video projection data warehouse of three-dimensional point traces of mid- and high-altitude neighboring targets through a radar video simulator, including: through a radar video simulator, classify according to different working modes of the radar, and combine according to ① the distance segment between the center of the neighboring target line and the radar station site, ② the neighboring target azimuth neighboring angle, ③ the neighboring target elevation neighboring angle, and ④ the neighboring target distance neighboring spacing to complete the generation of prior data; the storage of prior data adopts a multi-layer index nested tree structure, and the multi-layer index tree includes: ① radar working mode -> ② the distance between the center of the neighboring target line and the radar station site -> ③ the angle between the neighboring target line and the radar line of sight and the neighboring target distance spacing; the prior data is stored in the corresponding position according to the index, and the three-dimensional prior data is compressed by the "flattening" processing method to obtain the radar video projection data of the distance dimension, azimuth dimension and elevation dimension, and extract its envelope features, including the pole amplitude A, the number of poles M, the pole gradient G, the pole radar video data unit span (CellNum S ,CellNum E ); Step 2: Use "contour lines" to describe the video data projected in three dimensions: distance, azimuth, and elevation, including the pole amplitude, the number of poles, the gradient between poles, and the span of radar video data units between poles; Step 3: Use the sample data in the radar video projection data bin to form an envelope matching template of the adjacent target in three dimensions: distance, azimuth and elevation; The high-resolution point trace condensation processing method comprises: Step 1: In the radar working scenario, when the distance between targets is smaller than the traditional resolution capability of the radar, high-resolution point condensation processing is performed; Step 2: Select the matching prior data envelope as a template through the multi-layer index tree; Step 3: Perform "flattening" projection on the intercepted 3D measured target video data to obtain a 3D envelope; Step 4: Match the template envelope and the measured envelope. If the match is successful, segment the 3D measured target video data according to the feature range of the template envelope, and perform conventional 3D condensation on the segmented 3D measured target video data to achieve high-resolution point trace condensation processing; Step 5: If the matching is unsuccessful, directly perform conventional three-dimensional condensation and notify the host computer.

2. The high-resolution three-dimensional point trace condensation method based on prior data according to claim 1, characterized in that: The envelope matching before the high-resolution point trace condensation is performed in the form of a sliding window, including: Step 1: Pole search: In the pole search, the number of poles M of the envelope template, the polarity of the pole gradient G, and the span of the pole radar video data unit are used for searching; the pole distribution of the actual data is estimated by the proportional relationship between the actual data size and the sample data size, and the polarity of the pole gradient G is determined by voting; if the pole distribution characteristics of the actual data in three dimensions are consistent with the template, the match is successful, otherwise the match fails, and the high-resolution point trace condensation processing is exited and the conventional three-dimensional point trace condensation processing is performed; the pole is described as: the number of poles M, the gradient G between poles: {P1(G + ,G - ),...,P m (G + ,G - )}Pole radar video data unit span: Where P1 to P m is the number of poles, G + represents the positive gradient, G - Represents the negative gradient. The order of positive and negative gradients in () represents the property of this extreme point, whether it is a maximum or a minimum. CellNum S ,CellNum E Represents the start data unit sequence number and the end data unit sequence number; Step 2: Template translation: Based on the results of the pole search, a sliding window method is used to refine the start and end ranges of the actual data poles; from the template envelope, the poles on the template envelope are aligned with the poles of the actual data in the order of distance from near to far, azimuth from small to large, and elevation from small to large, to complete the template translation; during the template envelope translation process, the overlapping parts of the data units are numerically superimposed, and the broken data units are numerically interpolated; Step 3: Template scaling: Use the extreme point amplitude A and the gradient P(G + ,G - ), polar radar video data unit span (CellNum S ,CellNum E ), calculate the value of the template envelope data at the pole zero point, use the amplitude of the pole of the actual data, according to the gradient on both sides of the pole in the template envelope data, take the value at the pole zero point in the template envelope data as the termination condition, calculate the span of the pole radar video data unit, and complete the enlargement or reduction of the template envelope in three dimensions; Step 4: Multi-sampling point matching: The envelope consistency judgment is performed using the multi-sampling point matching method. In order to reduce the amount of calculation while ensuring the accuracy of the judgment, the number of selected sampling points ≥ the number of poles × 4; the consistency judgment is implemented using hypothesis testing.

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