CN109459753A - Weather radar data coordinate converts Fast Interpolation method - Google Patents
Weather radar data coordinate converts Fast Interpolation method Download PDFInfo
- Publication number
- CN109459753A CN109459753A CN201710959444.1A CN201710959444A CN109459753A CN 109459753 A CN109459753 A CN 109459753A CN 201710959444 A CN201710959444 A CN 201710959444A CN 109459753 A CN109459753 A CN 109459753A
- Authority
- CN
- China
- Prior art keywords
- interpolation
- value
- dimensional
- sinc
- data block
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 45
- 239000013598 vector Substances 0.000 claims abstract description 59
- 239000011159 matrix material Substances 0.000 claims abstract description 45
- 238000006073 displacement reaction Methods 0.000 claims abstract description 10
- 238000006243 chemical reaction Methods 0.000 claims abstract description 3
- 238000013139 quantization Methods 0.000 claims description 10
- 238000013507 mapping Methods 0.000 claims description 8
- 238000004364 calculation method Methods 0.000 claims description 5
- 230000009466 transformation Effects 0.000 description 10
- 238000005070 sampling Methods 0.000 description 6
- 238000010586 diagram Methods 0.000 description 3
- 238000009499 grossing Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000017105 transposition Effects 0.000 description 2
- 102000003745 Hepatocyte Growth Factor Human genes 0.000 description 1
- 108090000100 Hepatocyte Growth Factor Proteins 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000006855 networking Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/95—Radar or analogous systems specially adapted for specific applications for meteorological use
- G01S13/958—Theoretical aspects
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/418—Theoretical aspects
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
- Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- Computer Networks & Wireless Communication (AREA)
- General Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
本发明提供了一种天气雷达数据坐标转换快速插值方法,根据预设的插值核点数和量化位移预先计算sinc插值核表格;计算待转换到的地理坐标系的均匀三维网格中的每个网络点的网格点坐标值所对应的以当前雷达自身为中心的极坐标系下的坐标,计算其在均匀极坐标离散网格中所处的位置;根据位置值的整数部分,从给定的离散化保存的天气雷达体积扫描数据中抽取一个三维矩阵数据块;根据位置值的小数部分从sinc插值核表格中查询并得到表格中的三行元素以分别组成列向量和利用三维矩阵数据块和得到二维矩阵数据块;利用二维矩阵数据块和得到一维列向量;利用一维列向量与得到当前网格值的插值结果。本发明提升了插值速度。
The invention provides a fast interpolation method for coordinate conversion of weather radar data. The sinc interpolation kernel table is pre-calculated according to the preset number of interpolation kernel points and the quantized displacement; each network in the uniform three-dimensional grid of the geographic coordinate system to be converted is calculated. The grid point coordinate value of the point corresponds to the coordinates in the polar coordinate system centered on the current radar itself, and calculates its position in the uniform polar coordinate discrete grid; according to the integer part of the position value, from the given Extract a three-dimensional matrix data block from the weather radar volume scan data saved by discretization; query from the sinc interpolation kernel table according to the fractional part of the position value and obtain three rows of elements in the table to form column vectors respectively and Using 3D matrix data blocks and Get a two-dimensional matrix data block; use the two-dimensional matrix data block and Get a one-dimensional column vector; use the one-dimensional column vector and Get the interpolation result of the current grid value. The present invention improves the interpolation speed.
Description
技术领域technical field
本发明涉及天气雷达信号与数据处理领域,尤其涉及一种用于天气雷达数据坐标转换的快速插值方法。The invention relates to the field of weather radar signal and data processing, in particular to a fast interpolation method for coordinate transformation of weather radar data.
背景技术Background technique
天气雷达得到的数据产品通常处于以雷达自身为中心的极坐标,包含气象目标的距离,方位和俯仰坐标。对于多部天气雷达组网观测的应用,需要构建统一的坐标系,例如由经度、维度和高度组成的地理坐标系作为基准,各雷达得到的数据产品均通过插值方法由自身极坐标系变换至新的坐标系下,从而方便天气雷达数据的组网拼图。由于大部分气象目标,例如云在空间上具有连续性,并且有很多细尺度结构,因而希望插值后的散射率场在空间上要保持连续性,同时在内插过程中应最大限度地保留雷达资料中存在的原始回波结构特征。常见的插值方法包括:最近邻居法、线性内插法和sinc核插值法。其中,最近邻居法虽然速度快,但是精度过低,易导致插值后的雷达散射率在空间上不连续;线性内插法对原始插值前数据引入较大的平滑,因而易损失原有散射率细尺度结构特征。sinc核插值法是根据奈奎斯特采样定理进行插值的方法,精度最高,但是通常情况下计算复杂度较高。The data products obtained by the weather radar are usually in polar coordinates centered on the radar itself, including the distance, azimuth and pitch coordinates of the meteorological target. For the application of networked observation of multiple weather radars, a unified coordinate system needs to be constructed. For example, the geographic coordinate system composed of longitude, latitude and height is used as the benchmark. The data products obtained by each radar are transformed from their own polar coordinate system to Under the new coordinate system, it is convenient for the networking puzzle of weather radar data. Since most meteorological objects, such as clouds, are spatially continuous and have many fine-scale structures, it is hoped that the interpolated scatter rate field should be spatially continuous, and the radar should be preserved as much as possible during the interpolation process. The original echo structural features present in the data. Common interpolation methods include: nearest neighbor method, linear interpolation method and sinc kernel interpolation method. Among them, although the nearest neighbor method is fast, its accuracy is too low, which easily leads to the spatial discontinuity of the interpolated radar scattering rate; the linear interpolation method introduces a large smoothing to the original data before interpolation, so it is easy to lose the original scattering rate Fine-scale structural features. The sinc kernel interpolation method is a method of interpolation according to the Nyquist sampling theorem, which has the highest accuracy, but usually has a high computational complexity.
发明内容SUMMARY OF THE INVENTION
鉴于上述技术问题,本发明提供了一种用于天气雷达数据坐标转换的快速插值方法。In view of the above technical problems, the present invention provides a fast interpolation method for coordinate transformation of weather radar data.
本发明中的天气雷达数据坐标转换快速插值方法,包括:步骤1,根据预设的插值核点数和量化位移预先计算sinc插值核表格;步骤2,通过映射关系计算出待转换到的地理坐标系的均匀三维网格中的每个网络点的网格点坐标值所对应的以当前雷达自身为中心的极坐标系下的坐标;步骤3,对于步骤2计算得到的某一个具体的距离、俯仰和方位坐标,计算其在天气雷达体积扫描数据的均匀极坐标离散网格中所处的位置;步骤4,根据步骤3得到的所述位置的位置值的整数部分,从给定的离散化保存的天气雷达体积扫描数据中抽取一个三维矩阵数据块;步骤5,分别根据步骤3得到的所述位置的位置值的小数部分,从sinc插值核表格中查询并得到表格中的三行元素以分别组成列向量和步骤6,利用步骤4得到的三维矩阵数据块和步骤5得到的列向量进行加权运算,得到二维矩阵数据块;步骤7,利用步骤6得到的二维矩阵数据块和步骤5得到的列向量进行加权运算,得到一维列向量;步骤8,利用步骤7得到的一维列向量,与步骤5得到的列向量进行加权运算,得到当前网格值的插值结果。The fast interpolation method for coordinate conversion of weather radar data in the present invention includes: step 1, pre-calculating a sinc interpolation kernel table according to a preset number of interpolation kernel points and quantized displacement; step 2, calculating a geographic coordinate system to be converted to through a mapping relationship The coordinates in the polar coordinate system with the current radar itself as the center corresponding to the grid point coordinate value of each network point in the uniform three-dimensional grid; step 3, for a specific distance, pitch calculated in step 2 and azimuth coordinates, calculate its position in the uniform polar coordinate discrete grid of the weather radar volume scan data; step 4, according to the integer part of the position value of the position obtained in step 3, save from the given discretization A three-dimensional matrix data block is extracted from the weather radar volume scanning data of ; Step 5, according to the fractional part of the position value of the position obtained in step 3, query from the sinc interpolation kernel table and obtain three rows of elements in the table to respectively make up a column vector and Step 6, use the three-dimensional matrix data block obtained in step 4 and the column vector obtained in step 5 Carry out weighted operation to obtain a two-dimensional matrix data block; Step 7, utilize the two-dimensional matrix data block obtained in step 6 and the column vector obtained in step 5 Perform a weighted operation to obtain a one-dimensional column vector; step 8, use the one-dimensional column vector obtained in step 7, and the column vector obtained in step 5 Perform a weighting operation to obtain the interpolation result of the current grid value.
优选地,所述步骤1中,所述的插值核点数P的典型取值是6~16间的任一偶数,量化位移1/L中的L的典型取值为大于等于10的偶数;Preferably, in the step 1, the typical value of the interpolation kernel number P is any even number between 6 and 16, and the typical value of L in the quantization displacement 1/L is an even number greater than or equal to 10;
所述的sinc插值核表格是L+1行,P列的数值表格;The sinc interpolation kernel table is a numerical table of row L+1 and column P;
所述sinc插值核表格的第i行,第j列的元素wi,j的值通过以下公式计算得到The value of the element w i,j of the i-th row and the j-th column of the sinc interpolation kernel table is calculated by the following formula
其中,i=1,2,...L+1,j=1,2,...P,sin c(x)=sin(πx)/(πx)表示sinc函数。Among them, i=1,2,...L+1, j=1,2,...P, sin c(x)=sin(πx)/(πx) represents the sinc function.
优选地,所述步骤2中,由地理坐标系的网格点坐标值(xlat,m′,ylon,n′,hk′)到以当前雷达自身为中心的极坐标系坐标的映射关系的表达式为:Preferably, in the step 2, the mapping from the grid point coordinate values (x lat,m' ,y lon,n' ,h k' ) of the geographic coordinate system to the coordinates of the polar coordinate system centered on the current radar itself The expression for the relationship is:
其中,(xr,yr,hr)为天气雷达自身位置的经纬高坐标,R表示地球半径,s=R×arccos[sin(xlat,m′)sin(xr)+cos(xlat,m′)cos(xr)cos(ylon,n′-yr)]xlat,m′,ylon,n′,hk′分别表示网格所代表的第m′个纬度、第n′个经度和第k′个高度坐标。Among them, (x r , y r , hr ) is the longitude, latitude and altitude coordinates of the weather radar itself, R represents the earth’s radius, s=R×arccos[sin(x lat,m′ )sin(x r )+cos(x lat,m′ )cos(x r )cos(y lon,n′ -y r )]x lat,m′ ,y lon,n′ ,h k′represent the m′th latitude, The n'th longitude and the k'th altitude coordinate.
优选地,所述步骤3中,由某一个具体的距离、俯仰和方位坐标计算其在天气雷达体积扫描数据的均匀极坐标离散网格Preferably, in the step 3, a specific distance, pitch and azimuth coordinates Calculate its uniform polar discrete grid in weather radar volume scan data
中所处的位置(x1,x2,x3)的方法为 The method for the position (x1,x2,x3) in the
优选地,所述步骤4包括:Preferably, the step 4 includes:
步骤41,分别对x1,x2,x3取整,得到 其中表示取整算子;Step 41, round up x1, x2, and x3 respectively to get in represents the rounding operator;
步骤S42,在给定的离散化保存的天气雷达体积扫描数据中,其中m=1,2,...M,n=1,2,...N,k=1,2,...K,按第一个维度的索引从n1-(P/2-1)、n1-P/2、n1-P/2+1、…、n1+P/2,第二个维度的索引从n2-(P/2-1)、n2-P/2、n2-P/2+1、…、n2+P/2,第三个维度的索引从n3-(P/2-1)、n3-P/2、n3-P/2+1、…、n3+P/2,抽取出一个P×P×P维的三维矩阵数据块s(i,j,l),i,j,l=1,2,...P。Step S42, the weather radar volume scan data saved in the given discretization , where m=1,2,...M, n=1,2,...N, k=1,2,...K, indexed by the first dimension from n 1 -(P/ 2-1), n 1 -P/2, n 1 -P/2+1, ..., n 1 +P/2, the second dimension is indexed from n 2 -(P/2-1), n 2 -P/2, n 2 -P/2+1, ..., n 2 +P/2, the third dimension is indexed from n 3 -(P/2-1), n 3 -P/2, n 3 -P/2+1,...,n 3 +P/2, extract a P×P×P dimensional three-dimensional matrix data block s(i,j,l), i,j,l=1,2,. ..P.
优选地,所述步骤5包括:Preferably, the step 5 includes:
计算x1的小数部分将其除以量化位移1/L的值并四舍五入为整数其中表示取整算子,查询sinc插值表格并选定插值表中第L+1-m1行的元素作为加权值组成行向量round()表示四舍五入取整算子;Calculate the fractional part of x1 Divide it by the value of the quantization shift 1/L and round to an integer in Indicates the rounding operator, queries the sinc interpolation table and selects the elements of the L+1-m1 row in the interpolation table as the weighted value to form a row vector round() indicates the rounding operator;
计算x2的小数部分将其除以量化位移1/L的值并四舍五入为整数查询sinc插值表格并选定插值表中第L+1-m2行的元素作为加权值组成行向量 Calculate the fractional part of x2 Divide it by the value of the quantization shift 1/L and round to an integer Query the sinc interpolation table and select the elements of the L+1-m2 row in the interpolation table as the weighted value to form a row vector
计算x3的小数部分将其除以量化位移1/L的值并四舍五入为整数查询sinc插值表格并选定插值表中第L+1-m3行的元素作为加权值组成行向量 Calculate the fractional part of x3 Divide it by the value of the quantization shift 1/L and round to an integer Query the sinc interpolation table and select the elements of the L+1-m3 row in the interpolation table as the weighted value to form a row vector
优选地,所述步骤6包括:Preferably, the step 6 includes:
在三维矩阵数据块sP×P×P中,针对某个固定的索引对(j,l),将三维矩阵数据块sP×P×P的P个数据元素s(1,j,l),s(2,j,l),...,s(P,j,l)组成列向量然后求取该向量与列向量的内积作为一个P×P二维矩阵数据块s′P×P×P的第j行,第l列的数据元素,其中,上标T表示矩阵或向量转置。对所有的索引对(j,l),j,l=1,2,...P进行遍历,直到计算得到P×P二维矩阵数据块s′P×P×P。In the three-dimensional matrix data block s P×P×P , for a fixed index pair (j,l), the P data elements s(1,j,l) of the three-dimensional matrix data block s P×P×P , s(2,j,l),...,s(P,j,l) form a column vector Then find the vector and the column vector inner product of As a data element of the jth row and the lth column of a P×P two-dimensional matrix data block s′ P×P×P , the superscript T represents the matrix or vector transposition. All index pairs (j,l), j,l=1,2,...P are traversed until a P×P two-dimensional matrix data block s′ P×P×P is obtained by calculation.
优选地,所述步骤7中的一维列向量的表达式为:Preferably, the expression of the one-dimensional column vector in the step 7 is:
其中,为一维列向量,s′P×P×P为二维矩阵数据块,为列向量,T表示矩阵或向量转置。in, is a one-dimensional column vector, s′ P×P×P is a two-dimensional matrix data block, is a column vector, and T represents the matrix or vector transpose.
优选地,所述步骤8中,当前网格值的插值结果为:Preferably, in the step 8, the interpolation result of the current grid value is:
其中,T表示矩阵或向量转置。where T represents matrix or vector transpose.
从上述技术方案可以看出,本发明具有以下有益效果:As can be seen from the above technical solutions, the present invention has the following beneficial effects:
(1)本发明技术方案中天气雷达数据坐标变换使用sinc核插值,插值精度较高,有助于保留气象目标散射率的细尺度结构特征;(1) In the technical solution of the present invention, the coordinate transformation of weather radar data uses sinc kernel interpolation, and the interpolation accuracy is high, which is helpful to retain the fine-scale structural characteristics of the scattering rate of meteorological targets;
(2)本发明技术方案中插值的实现是通过查询预先计算好的sinc插值核表格获得加权值,避免了实时计算复杂度较高的sinc函数的过程,提升了插值速度。(2) The implementation of the interpolation in the technical solution of the present invention is to obtain the weighted value by querying the pre-calculated sinc interpolation kernel table, which avoids the process of calculating the sinc function with high complexity in real time, and improves the interpolation speed.
附图说明Description of drawings
图1为本发明实施例天气雷达进行体积扫描示意图;1 is a schematic diagram of volume scanning performed by a weather radar according to an embodiment of the present invention;
图2为本发明实施例中使用的sinc核插值原理示意图。FIG. 2 is a schematic diagram of a sinc kernel interpolation principle used in an embodiment of the present invention.
图3为本发明实施例一种用于天气雷达数据坐标转换的快速插值方法的流程图。FIG. 3 is a flowchart of a fast interpolation method for coordinate transformation of weather radar data according to an embodiment of the present invention.
具体实施方式Detailed ways
为使本领域技术人员更好的理解本发明的技术方案,下面结合附图和具体实施方式对本发明作详细说明。In order to make those skilled in the art better understand the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
本发明技术方案中天气雷达数据坐标变换使用sinc核插值,插值精度较高,有助于保留气象目标散射率的细尺度结构特征;插值的实现是通过查询预先计算好的sinc插值核表格获得加权值,避免了实时计算复杂度较高的sinc函数的过程,提升了插值速度。In the technical solution of the present invention, sinc kernel interpolation is used for the coordinate transformation of weather radar data, and the interpolation accuracy is high, which is helpful for retaining the fine-scale structural features of the scattering rate of meteorological targets; the interpolation is realized by querying the pre-calculated sinc interpolation kernel table to obtain the weighting value, avoids the process of real-time calculation of the sinc function with high complexity, and improves the interpolation speed.
本发明的实施方式是针对天气雷达数据由自身极坐标数据变换到其它坐标系如由经纬高表示的地理坐标系进行的。在详细介绍本发明的实施方式的细节之前,首先简要介绍利用数据插值实现坐标变换的原理。The embodiments of the present invention are carried out for the transformation of weather radar data from polar coordinate data to other coordinate systems such as geographic coordinate systems represented by latitude, longitude and altitude. Before introducing the details of the embodiments of the present invention in detail, the principle of realizing coordinate transformation by data interpolation is briefly introduced first.
请参考图1所示,通常,天气雷达进行体积扫描,可获取气象目标在极坐标系下的距离r、方位角俯仰角θ坐标的雷达散射率因子的基本数据产品,设其表示为设数据实施坐标变换到地理坐标系后的数据应当为Z′(xlat,ylon,h),其中xlat表示经度坐标,ylon表示维度坐标,h表示高度坐标。对于某个具体的坐标值(xlat,ylon,h)处的气象目标,坐标变换后的数据Z′(xlat,ylon,h)是由通过坐标映射得到的:Please refer to Figure 1. Usually, the weather radar performs volume scanning to obtain the distance r and azimuth angle of the meteorological target in the polar coordinate system. The basic data product of the radar scatter factor of the pitch angle θ coordinate, let it be expressed as Assuming that the data after the coordinate transformation of the data to the geographic coordinate system should be Z'(x lat , y lon , h), where x lat represents the longitude coordinate, y lon represents the dimensional coordinate, and h represents the height coordinate. For a meteorological target at a specific coordinate value (x lat , y lon , h), the coordinate-transformed data Z′ (x lat , y lon , h) is given by Obtained by coordinate mapping:
其中,r(xlat,ylon,h),θ(xlat,ylon,h),可通过大圆几何学理论求得,设天气雷达自身位置的经纬高坐标为(xr,yr,hr),则Among them, r(x lat ,y lon ,h),θ(x lat ,y lon ,h), It can be obtained through the theory of great circle geometry. If the latitude and longitude coordinates of the weather radar's own position are (x r , y r , hr ) , then
其中,R表示地球半径,s的表达式为Among them, R is the radius of the earth, and the expression of s is
s=R×arccos[sin(xlat)sin(xr)+cos(xlat)cos(xr)cos(ylat-yr)]s=R×arccos[sin(x lat )sin(x r )+cos(x lat )cos(x r )cos(y lat -y r )]
通常情况下,天气雷达体扫描获取的数据是在极坐标系下均匀网格分布的,离散化保存的数据的,m=1,2,...M,n=1,2,...N,k=1,2,...K。M,N和K分别表示插值前极坐标系上天气雷达数据在距离、俯仰和方位方向的数据维度。某个具体的地理坐标系坐标值(xlat,ylon,h)所对应映射的极坐标r(xlat,ylon,h),θ(xlat,ylon,h),不一定正好处于极坐标系上的整数网格点上,需要利用其周围网格点上的数据通过插值方法得到变换后的数据Z′(xlat,ylon,h)。Typically, data obtained from weather radar volume scans It is uniformly grid distributed in the polar coordinate system, and the data stored in discretization , m=1,2,...M, n=1,2,...N, k=1,2,...K. M, N, and K represent the data dimensions of the weather radar data in the range, pitch, and azimuth directions in the polar coordinate system before interpolation, respectively. Polar coordinates r(x lat ,y lon ,h),θ(x lat , y lon , h), It is not necessarily exactly on the integer grid point on the polar coordinate system, and the transformed data Z'(x lat , y lon , h) needs to be obtained by interpolation method using the data on the surrounding grid points.
常见的插值方法包括:最近邻居法、线性内插法和sinc核插值法。其中,最近邻居法虽然速度快,但是精度过低,易导致插值后的雷达散射率在空间上不连续;线性内插法对原始插值前数据引入较大的平滑,因而易损失原有散射率细尺度结构特征。sinc核插值法是根据奈奎斯特采样定理进行插值的方法,精度最高,但是通常情况下计算复杂度较高。Common interpolation methods include: nearest neighbor method, linear interpolation method and sinc kernel interpolation method. Among them, although the nearest neighbor method is fast, its accuracy is too low, which easily leads to the spatial discontinuity of the interpolated radar scattering rate; the linear interpolation method introduces a large smoothing to the original data before interpolation, so it is easy to lose the original scattering rate Fine-scale structural features. The sinc kernel interpolation method is a method of interpolation according to the Nyquist sampling theorem, which has the highest accuracy, but usually has a high computational complexity.
本发明的实施方式中插值是基于sinc核插值进行的。在详细介绍本发明的实施方式的细节之前,还需先简单描述sinc核插值的一些概念和原理。In the embodiment of the present invention, the interpolation is performed based on sinc kernel interpolation. Before introducing the details of the embodiments of the present invention in detail, it is necessary to briefly describe some concepts and principles of sinc kernel interpolation.
通常,在满足信号带限和采样率大于奈奎斯特采样频率的前提下,离散序列s[i],i=1,2,...可以通过sinc核插值得到任意非整数采样点x上的高精度的插值结果s′(x),表示如下:Generally, on the premise of satisfying the signal band limit and the sampling rate is greater than the Nyquist sampling frequency, the discrete sequence s[i], i=1,2,... can be obtained by sinc kernel interpolation to obtain any non-integer sampling point x The high-precision interpolation result s'(x) is expressed as follows:
其中,sin c(x)=sin(πx)/(πx)称为sinc插值核,上述插值公式表示,任意非整数采样点x上信号值可以通过对离散序列s[i]的加权和得到,而各离散序列样点的权值是sinc插值核。Among them, sin c(x)=sin(πx)/(πx) is called the sinc interpolation kernel. The above interpolation formula indicates that the signal value at any non-integer sampling point x can be obtained by the weighted sum of the discrete sequence s[i], The weight of each discrete sequence sample point is the sinc interpolation kernel.
图2为本发明实施例中使用的sinc核插值原理示意图,一般情况下,无需对所有样点均计算sinc核权值,而是使用非整数采样点x周围的8~16点的离散序列s[i]的样本值参与插值运算,例如图2中,需要插值计算非整数样点x处的值,则使用其左右各4个整数样点值(x处左右各4个“o”符号表示的样点值)和对应的sinc函数权值(用“□”表示的sinc函数样点值)进行加权求和。进行sinc核插值公式计算时,由于根据输入的x的值计算插值核sinc(x)的值的过程涉及到三角函数运算,计算复杂度较高,为克服这个缺点,本发明专利将预先计算好的插值核以表格方式存储以避免实时计算,从而提升插值速度。FIG. 2 is a schematic diagram of the sinc kernel interpolation principle used in the embodiment of the present invention. Generally, it is not necessary to calculate the sinc kernel weights for all sample points, but a discrete sequence s of 8 to 16 points around the non-integer sample point x is used. The sample value of [i] is involved in the interpolation operation. For example, in Figure 2, if the value at the non-integer sample point x needs to be interpolated, then four integer sample point values on the left and right of it are used (the four “o” symbols on the left and right of x represent the The sample value of ) and the corresponding weight of the sinc function (the sample value of the sinc function represented by "□") are weighted and summed. When calculating the sinc kernel interpolation formula, since the process of calculating the value of the interpolation kernel sinc(x) according to the input x value involves trigonometric function operations, the computational complexity is high. In order to overcome this shortcoming, the patent of the present invention will pre-calculate The interpolation kernels are stored in a table format to avoid real-time calculations, thereby increasing the interpolation speed.
图1是根据本发明实施例的一种用于天气雷达数据坐标转换的快速插值方法的流程图。请参考图1,在本发明的一个实施例中,提供了一种用于天气雷达数据坐标转换的快速插值方法,该方法可以包括:FIG. 1 is a flowchart of a fast interpolation method for coordinate transformation of weather radar data according to an embodiment of the present invention. Referring to FIG. 1, in one embodiment of the present invention, a fast interpolation method for coordinate transformation of weather radar data is provided, and the method may include:
步骤S1,根据预设的插值核点数P和量化位移1/L预先计算sinc插值核表格,如表1所示;Step S1, pre-calculate the sinc interpolation kernel table according to the preset number of interpolation kernel points P and the quantization displacement 1/L, as shown in Table 1;
所述的插值核点数P的典型取值是6~16间的任一偶数,量化位移1/L中的L的典型取值为大于等于10的偶数;The typical value of the number of interpolation kernel points P is any even number between 6 and 16, and the typical value of L in the quantization displacement 1/L is an even number greater than or equal to 10;
所述的sinc插值核表格是L+1行,P列的数值表格;The sinc interpolation kernel table is a numerical table of row L+1 and column P;
所述sinc插值核表格的第i行,第j列的元素wi,j的值通过以下公式计算得到The value of the element w i,j of the i-th row and the j-th column of the sinc interpolation kernel table is calculated by the following formula
其中,i=1,2,...L+1,j=1,2,...P,sinc(x)=sin(πx)/(πx)表示sinc函数。Among them, i=1,2,...L+1, j=1,2,...P, sinc(x)=sin(πx)/(πx) represents the sinc function.
表1为在P=8,L=12时的13行8列的插值核表格Table 1 is the interpolation kernel table of 13 rows and 8 columns when P=8, L=12
步骤S2,设要转换到的地理坐标系的均匀三维网格为Ω={(xlat,m′,ylon,n′,hk′)|m′=1,2,...M′,n′=1,2,...N′,k′=1,2,...K′},其中xlat,m′,ylon,n′,hk′分别表示网格所代表的第m′个纬度、第n′个经度和第k′个高度坐标,M,N和K分别表示网格的尺寸维度,对于所有网格点中每一个具体的网格点坐标值(xlat,m′,ylon,n′,hk′),首先通过映射关系f计算出其对应的以当前雷达自身为中心的极坐标系下的坐标然后都重复执行下述步骤S3~S8,其中r′,θ′,分别表示映射的极坐标系下的距离、俯仰角和方位角坐标;Step S2, set the uniform three-dimensional grid of the geographic coordinate system to be converted to Ω={(x lat,m′ ,y lon,n′ ,h k′ )|m′=1,2,...M′ , n′=1,2,...N′, k′=1,2,...K′}, where x lat,m′ ,y lon,n′ ,h k′represent the grid represented by The m'th latitude, n'th longitude and k'th height coordinates of , M, N and K respectively represent the size dimension of the grid, for each specific grid point coordinate value of all grid points (x lat,m′ ,y lon,n′ ,h k′ ), first calculate the corresponding coordinates in the polar coordinate system centered on the current radar itself through the mapping relationship f Then, the following steps S3 to S8 are repeatedly executed, wherein r′, θ′, Represent the distance, pitch and azimuth coordinates in the polar coordinate system of the mapping;
所述的由地理坐标系的网格点坐标值(xlat,m′,ylon,n′,hk′)到以当前雷达自身为中心的极坐标系坐标的映射关系f的表达式为:The expression of the mapping relationship f from the grid point coordinate values of the geographic coordinate system (x lat, m′ , y lon, n′ , h k′ ) to the coordinates of the polar coordinate system centered on the current radar itself is: :
其中,(xr,yr,hr)为天气雷达自身位置的经纬高坐标,R表示地球半径,s的表达式为Among them, (x r , y r , hr ) is the latitude, longitude and altitude coordinates of the weather radar itself, R is the radius of the earth, and the expression of s is
s=R×arccos[sin(xlat,m′)sin(xr)+cos(xlat,m′)cos(xr)cos(ylon,n′-yr)]s=R×arccos[sin(x lat,m′ )sin(x r )+cos(x lat,m′ )cos(x r )cos(y lon,n′ -y r )]
步骤S3,对于步骤S2计算得到的某一个具体的距离、俯仰和方位坐标计算其在天气雷达体积扫描数据的均匀极坐标离散网格中所处的位置(x1,x2,x3),其表示距离坐标r′位于rm序列中的第x1个样点,m=1,2,...M;俯仰坐标θ′位于θn序列中的第x2个样点,n=1,2,...N;方位坐标位于序列中的第x3个样点,k=1,2,...K;x1,x2,x3为不小于1的整数或非整数;Step S3, for a specific distance, pitch and azimuth coordinates calculated in step S2 Calculate its uniform polar discrete grid in weather radar volume scan data The position (x1, x2, x3) in , which indicates that the distance coordinate r' is located at the x1th sample point in the rm sequence, m =1, 2,...M; the pitch coordinate θ' is located in the θ n sequence The x2th sample point in , n=1,2,...N; azimuth coordinates lie in The x3th sample point in the sequence, k=1,2,...K; x1,x2,x3 are integers or non-integers not less than 1;
所述的由某一个具体的距离、俯仰和方位坐标计算其在天气雷达体积扫描数据的均匀极坐标离散网格中所处的位置(x1,x2,x3)的方法为:described by a specific distance, pitch and azimuth coordinates Calculate its uniform polar discrete grid in weather radar volume scan data The method for the position (x1, x2, x3) in the :
步骤S4,根据步骤S3得到的x1,x2,x3位置值的整数部分,从给定的离散化保存的天气雷达体积扫描数据m=1,2,...M,n=1,2,...N,k=1,2,...K中,抽取出一个P×P×P维的三维矩阵数据块s(i,j,l),i,j,l=1,2,...P,其中整数P为所述步骤s1所示的预设的插值核点数P;Step S4, according to the integer part of the x1, x2, x3 position values obtained in step S3, from the given discretized saved weather radar volume scan data m=1,2,...M, n=1,2,...N, k=1,2,...K, extract a P×P×P dimensional three-dimensional matrix data block s( i,j,l), i,j,l=1,2,...P, wherein the integer P is the preset number of interpolation kernel points P shown in the step s1;
所述的根据x1,x2,x3位置值的整数部分,从给定的离散化保存的天气雷达体积扫描数据m=1,2,...M,n=1,2,...N,k=1,2,...K中,抽取出一个P×P×P维的三维矩阵数据块s(i,j,l),i,j,l=1,2,...P的步骤又可以包含:Said weather radar volume scan data saved from a given discretization according to the integer parts of the x1, x2, x3 position values m=1,2,...M, n=1,2,...N, k=1,2,...K, extract a P×P×P dimensional three-dimensional matrix data block s( i,j,l), i,j,l=1,2,...P The steps can include:
子步骤S41:分别对x1,x2,x3取整,得到 其中表示取整算子;Sub-step S41: respectively round x1, x2, and x3 to obtain in represents the rounding operator;
子步骤S42:对于给定的离散化保存的天气雷达体积扫描数据m=1,2,...M,n=1,2,...N,k=1,2,...K中,按第一个维度的索引从n1-(P/2-1)、n1-P/2、n1-P/2+1、…、n1+P/2,第二个维度的索引从n2-(P/2-1)、n2-P/2、n2-P/2+1、…、n2+P/2,第三个维度的索引从n3-(P/2-1)、n3-P/2、n3-P/2+1、…、n3+P/2,抽取出一个P×P×P维的三维矩阵数据块s(i,j,l),i,j,l=1,2,...P;Sub-step S42: Weather radar volume scan data saved for a given discretization In m=1,2,...M, n=1,2,...N, k=1,2,...K, according to the index of the first dimension from n 1 -(P/2- 1), n 1 -P/2, n 1 -P/2+1, ..., n 1 +P/2, the second dimension is indexed from n 2 -(P/2-1), n 2 -P /2, n 2 -P/2+1, ..., n 2 +P/2, the third dimension is indexed from n 3 -(P/2-1), n 3 -P/2, n 3 -P /2+1,...,n 3 +P/2, extract a P×P×P dimensional three-dimensional matrix data block s(i,j,l), i,j,l=1,2,... P;
步骤S5:分别根据步骤S3得到的x1,x2,x3位置值的小数部分,从sinc插值核表格中查询并得到表格中的三行元素,分别组成列向量和 Step S5: According to the fractional parts of the x1, x2, and x3 position values obtained in step S3, query from the sinc interpolation kernel table and obtain three rows of elements in the table, which form column vectors respectively and
所述的根据x1,x2,x3位置值的小数部分,从sinc插值核表格中查询并得到表格中的三行元素,分别组成列向量和的方法是:According to the fractional part of the position value of x1, x2, x3, query from the sinc interpolation kernel table and obtain three rows of elements in the table, which form column vectors respectively and The method is:
计算x1的小数部分将其除以量化位移1/L的值并四舍五入为整数其中表示取整算子,查询sinc插值表格并选定插值表中第L+1-m1行的元素作为加权值组成行向量round()表示四舍五入取整算子;Calculate the fractional part of x1 Divide it by the value of the quantization shift 1/L and round to an integer in Indicates the rounding operator, queries the sinc interpolation table and selects the elements of the L+1-m1 row in the interpolation table as the weighted value to form a row vector round() indicates the rounding operator;
计算x2的小数部分将其除以量化位移1/L的值并四舍五入为整数查询sinc插值表格并选定插值表中第L+1-m2行的元素作为加权值组成行向量 Calculate the fractional part of x2 Divide it by the value of the quantization shift 1/L and round to an integer Query the sinc interpolation table and select the elements of the L+1-m2 row in the interpolation table as the weighted value to form a row vector
计算x3的小数部分将其除以量化位移1/L的值并四舍五入为整数查询sinc插值表格并选定插值表中第L+1-m3行的元素作为加权值组成行向量 Calculate the fractional part of x3 Divide it by the value of the quantization shift 1/L and round to an integer Query the sinc interpolation table and select the elements of the L+1-m3 row in the interpolation table as the weighted value to form a row vector
步骤S6,利用步骤S4得到的三维矩阵数据块sP×P×P和步骤S5得到的列向量进行加权运算,得到P×P二维矩阵数据块s′P×P×P;Step S6, use the three-dimensional matrix data block s P×P×P obtained in step S4 and the column vector obtained in step S5 Perform a weighted operation to obtain a P×P two-dimensional matrix data block s′ P×P×P ;
所述的利用三维矩阵数据块sP×P×P和列向量进行加权运算的过程为:The use of three-dimensional matrix data blocks s P×P×P and column vectors The process of performing the weighting operation is as follows:
在三维矩阵数据块sP×P×P中,针对某个固定的索引对(j,l),将三维矩阵数据块sP×P×P的P个数据元素s(1,j,l),s(2,j,l),...,s(P,j,l)组成列向量然后求取该向量与列向量的内积作为一个P×P二维矩阵数据块s′P×P×P的第j行,第l列的数据元素,其中,上标T表示矩阵或向量转置。对所有的索引对(j,l),j,l=1,2,...P进行遍历,直到计算得到P×P二维矩阵数据块s′P×P×P;In the three-dimensional matrix data block s P×P×P , for a fixed index pair (j,l), the P data elements s(1,j,l) of the three-dimensional matrix data block s P×P×P , s(2,j,l),...,s(P,j,l) form a column vector Then find the vector and the column vector inner product of As a data element of the jth row and the lth column of a P×P two-dimensional matrix data block s′ P×P×P , the superscript T represents the matrix or vector transposition. Traverse all index pairs (j,l), j,l=1,2,...P until the P×P two-dimensional matrix data block s′ P×P×P is obtained by calculation;
步骤S7,利用步骤S6得到的二维矩阵数据块s′P×P×P和步骤S5得到的列向量进行加权运算,得到包含P个元素的一维列向量 Step S7, use the two-dimensional matrix data block s′ P×P×P obtained in step S6 and the column vector obtained in step S5 Perform a weighted operation to get a one-dimensional column vector containing P elements
所述的利用二维矩阵数据块s′P×P×P和列向量进行加权运算,利用的是向量和矩阵的乘法,其表达式为:The described use of two-dimensional matrix data blocks s′ P×P×P and column vectors The weighting operation is performed using the multiplication of vectors and matrices, and its expression is:
得到一个包含P个元素的一维列向量其中,上标T表示矩阵或向量转置;get a 1D column vector with P elements Among them, the superscript T represents the matrix or vector transpose;
步骤S8,利用步骤S7得到的包含P个元素的一维向量与步骤S5得到的列向量进行加权运算,得到当前网格值的插值结果,表达式为Step S8, use the one-dimensional vector containing P elements obtained in step S7 with the column vector obtained in step S5 Perform a weighted operation to get the interpolation result of the current grid value, the expression is
其中,上标T表示矩阵或向量转置。where the superscript T represents the matrix or vector transpose.
以上实施例仅为本发明的示例性实施例,不用于限制本发明,本发明的保护范围由权利要求书限定。本领域技术人员可以在本发明的实质和保护范围内,对本发明做出各种修改或等同替换,这种修改或等同替换也应视为落在本发明的保护范围内。The above embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and the protection scope of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent replacements to the present invention within the spirit and protection scope of the present invention, and such modifications or equivalent replacements should also be regarded as falling within the protection scope of the present invention.
Claims (9)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201710959444.1A CN109459753B (en) | 2017-10-16 | 2017-10-16 | Weather radar data coordinate conversion fast interpolation method |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201710959444.1A CN109459753B (en) | 2017-10-16 | 2017-10-16 | Weather radar data coordinate conversion fast interpolation method |
Publications (2)
Publication Number | Publication Date |
---|---|
CN109459753A true CN109459753A (en) | 2019-03-12 |
CN109459753B CN109459753B (en) | 2022-10-11 |
Family
ID=65606156
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201710959444.1A Active CN109459753B (en) | 2017-10-16 | 2017-10-16 | Weather radar data coordinate conversion fast interpolation method |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN109459753B (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN110261857A (en) * | 2019-07-17 | 2019-09-20 | 南京信息工程大学 | A kind of weather radar spatial interpolation methods |
CN110412551A (en) * | 2019-07-20 | 2019-11-05 | 中国船舶重工集团公司第七二四研究所 | A kind of cross-platform handover coordinate transformation method of over-the-horizon detection target information |
CN110940978A (en) * | 2019-12-09 | 2020-03-31 | 上海眼控科技股份有限公司 | Radar PPI image display method and device, electronic equipment and storage medium |
Citations (10)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6384766B1 (en) * | 1997-06-18 | 2002-05-07 | Totalförsvarets Forskningsinstitut | Method to generate a three-dimensional image of a ground area using a SAR radar |
JP2010278873A (en) * | 2009-05-29 | 2010-12-09 | Victor Co Of Japan Ltd | Color conversion apparatus |
CN102117227A (en) * | 2011-03-09 | 2011-07-06 | 南京恩瑞特实业有限公司 | Multi-core parallel calculation method for weather radar data |
CN102393520A (en) * | 2011-09-26 | 2012-03-28 | 哈尔滨工程大学 | Sonar moving target imaging method based on target echo Doppler characteristics |
CN103197299A (en) * | 2013-03-25 | 2013-07-10 | 南京信息工程大学 | Extraction and quantitative analysis system of weather radar radial wind information |
CN103530627A (en) * | 2013-10-23 | 2014-01-22 | 东南大学 | ISAR image restoration method based on two-dimensional scattering center set grid model |
CN103630901A (en) * | 2013-03-29 | 2014-03-12 | 中国科学院电子学研究所 | Method for imaging of airborne down-looking array 3-D SAR |
CN105204005A (en) * | 2015-10-19 | 2015-12-30 | 中国电子科技集团公司第二十八研究所 | VTS system radar return video display method based on geographic coordinate system |
CN105701859A (en) * | 2016-02-22 | 2016-06-22 | 武汉华信联创技术工程有限公司 | Radar single-station polar coordinate data three-dimensional grid processing method and system |
CN107180014A (en) * | 2017-04-28 | 2017-09-19 | 华讯方舟科技有限公司 | A kind of quick sinc interpolation methods and system |
-
2017
- 2017-10-16 CN CN201710959444.1A patent/CN109459753B/en active Active
Patent Citations (10)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6384766B1 (en) * | 1997-06-18 | 2002-05-07 | Totalförsvarets Forskningsinstitut | Method to generate a three-dimensional image of a ground area using a SAR radar |
JP2010278873A (en) * | 2009-05-29 | 2010-12-09 | Victor Co Of Japan Ltd | Color conversion apparatus |
CN102117227A (en) * | 2011-03-09 | 2011-07-06 | 南京恩瑞特实业有限公司 | Multi-core parallel calculation method for weather radar data |
CN102393520A (en) * | 2011-09-26 | 2012-03-28 | 哈尔滨工程大学 | Sonar moving target imaging method based on target echo Doppler characteristics |
CN103197299A (en) * | 2013-03-25 | 2013-07-10 | 南京信息工程大学 | Extraction and quantitative analysis system of weather radar radial wind information |
CN103630901A (en) * | 2013-03-29 | 2014-03-12 | 中国科学院电子学研究所 | Method for imaging of airborne down-looking array 3-D SAR |
CN103530627A (en) * | 2013-10-23 | 2014-01-22 | 东南大学 | ISAR image restoration method based on two-dimensional scattering center set grid model |
CN105204005A (en) * | 2015-10-19 | 2015-12-30 | 中国电子科技集团公司第二十八研究所 | VTS system radar return video display method based on geographic coordinate system |
CN105701859A (en) * | 2016-02-22 | 2016-06-22 | 武汉华信联创技术工程有限公司 | Radar single-station polar coordinate data three-dimensional grid processing method and system |
CN107180014A (en) * | 2017-04-28 | 2017-09-19 | 华讯方舟科技有限公司 | A kind of quick sinc interpolation methods and system |
Non-Patent Citations (4)
Title |
---|
HAN KUOYE 等: ""Efficient Pseudopolar Format Algorithm for Down-Looking Linear-Array SAR 3-D Imaging"", 《IEEE GEOSCIENCE AND REMOTE SENSING LETTERS》 * |
JIN-PING SUN 等: ""The Polar Format Imaging Algorithm for Forward-looking Bistatic SAR"", 《7TH EUROPEAN CONFERENCE ON SYNTHETIC APERTURE RADAR》 * |
芜晓丹: ""SAR极坐标格式处理波前弯曲补偿方法研究"", 《硕士电子期刊》 * |
郭江哲: ""高分辨机载SAR两维自聚焦处理及FPGA实现"", 《万方数据》 * |
Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN110261857A (en) * | 2019-07-17 | 2019-09-20 | 南京信息工程大学 | A kind of weather radar spatial interpolation methods |
CN110261857B (en) * | 2019-07-17 | 2022-04-15 | 南京信息工程大学 | Spatial interpolation method for weather radar |
CN110412551A (en) * | 2019-07-20 | 2019-11-05 | 中国船舶重工集团公司第七二四研究所 | A kind of cross-platform handover coordinate transformation method of over-the-horizon detection target information |
CN110412551B (en) * | 2019-07-20 | 2021-02-26 | 中国船舶重工集团公司第七二四研究所 | Cross-platform handover coordinate conversion method for beyond-the-horizon detection target information |
CN110940978A (en) * | 2019-12-09 | 2020-03-31 | 上海眼控科技股份有限公司 | Radar PPI image display method and device, electronic equipment and storage medium |
Also Published As
Publication number | Publication date |
---|---|
CN109459753B (en) | 2022-10-11 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN109545072B (en) | Map construction pose calculation method, map construction pose calculation device, map construction pose storage medium and map construction pose calculation system | |
CN109459753B (en) | Weather radar data coordinate conversion fast interpolation method | |
Kiseleva et al. | Theory of continuous optimal set partitioning problems as a universal mathematical formalism for constructing voronoi diagrams and their generalizations. I. Theoretical foundations | |
CN105654483A (en) | Three-dimensional point cloud full-automatic registration method | |
CN112345084B (en) | Three-dimensional temperature field construction method and device based on digital twin environment | |
CN108802669A (en) | Two-dimensional direction of arrival estimation method, two-dimensional direction of arrival estimation device and terminal | |
CN115457202B (en) | Method, device and storage medium for updating three-dimensional model | |
CN109685841B (en) | Registration method and system of three-dimensional model and point cloud | |
Shiri et al. | An FPGA implementation of singular value decomposition | |
CN114677494A (en) | Method, device and equipment for calculating radar detection capability based on subdivision grids | |
CN104615880A (en) | Rapid ICP (inductively coupled plasma) method for point cloud matching of three-dimensional laser radar | |
CN113936046A (en) | Object positioning method and device, electronic equipment and computer readable medium | |
CN112363122A (en) | Extraction method and application of weak harmonic signals in high-frequency ground wave radar ionosphere noise | |
JP2017106907A (en) | Efficient covariance matrix update | |
CN106157258B (en) | A kind of satellite-borne SAR image geometric correction method | |
CN112782647B (en) | Information-combined quadratic constraint least square radiation source positioning method | |
CN106908760B (en) | Single-station passive positioning method based on array autocorrelation matrix | |
CN104778260A (en) | Method for modeling dynamic radar environment knowledge base | |
Hansen | Transformations useful in certain antenna calculations | |
CN117232523A (en) | Navigation route planning method, device, equipment and medium for orchard robot | |
CN115049813A (en) | Coarse registration method, device and system based on first-order spherical harmonics | |
CN109507634A (en) | A kind of blind far-field signal Wave arrival direction estimating method based on sensing operator under any sensor array | |
An et al. | A fast numerical algorithm for calculating electromagnetic scattering from an object above a rough surface | |
Monakov | Localization algorithm for multilateration systems | |
CN113447887A (en) | Full-space positioning method, device, equipment and computer readable storage medium |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |