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列米波雷达 altimeter based super-resolution digital terrain matching array

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Publication number
CN102288944A
CN102288944A CN 201110120849 CN201110120849A CN102288944A CN 102288944 A CN102288944 A CN 102288944A CN 201110120849 CN201110120849 CN 201110120849 CN 201110120849 A CN201110120849 A CN 201110120849A CN 102288944 A CN102288944 A CN 102288944A
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method
vector
steering
target
elevation
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CN 201110120849
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Chinese (zh)
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CN102288944B (en )
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朱伟
杨明磊
陈伯孝
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西安电子科技大学
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Abstract

The invention discloses a super-resolution height measuring method based on topographic matching for a digital array meter wave radar, which is mainly used for solving the problem of high height measuring error of a fluctuating position in the prior art. The method comprises the following implementation steps of: performing clutter cancellation and interference cancellation processing on a targetsignal received by the radar to obtain a cancelled target signal; roughly measuring a target elevation angle by using a beam forming method; determining a maximum likelihood search range according tothe roughly-measured elevation angle and searching in the search range; computing a ground reflection point coordinate corresponding to each array element and a direct wave path and a reflection wavepath of each target relative to each array element according to a search elevation angle; computing a corresponding direct steering vector and a multipath steering vector by using the direct wave path and the reflection wave path; constructing a synthetic steering vector and computing a projection matrix of the synthetic steering vector; and performing maximum likelihood estimation to obtain a target accurate elevation angle. In the method, an altitude parameter of a radar position and the synthetic steering vector are introduced into super-resolution height measurement, so that the measuringaccuracy is increased; and the method can be applied to target tracking.

Description

基于地形匹配的数字阵列米波雷达超分辨测高方法列米波雷达 altimeter based super-resolution digital terrain matching array

技术领域 FIELD

[0001] 本发明属于雷达信号处理技术领域,涉及米波雷达测高,具体地说是针对数字阵列米波雷达,提出一种基于地形匹配的超分辨测高方法,可用于目标跟踪。 [0001] The present invention belongs to the technical field of radar signal processing, relates VHF radar altimeter, particularly for digital array 列米波雷达, we proposed a super-resolution terrain height measurement method based matching can be used for target tracking.

背景技术 Background technique

[0002] 按照仰角波束的形成方式和扫描方式,三坐标3D雷达可分为堆积波束雷达、频扫雷达、相扫雷达和数字波束形成雷达。 [0002] manner and formed according to the elevation beam scanning, the radar can be divided into bulk 3D coordinate beam radar, frequency sweeping the radar, and the radar sweep phase digital beam forming radar.

[0003] 堆积波束雷达把同时形成的接收波束在仰角上垂直堆积起来,并在方位上机械扫描,以实现搜索目标和目标三坐标的测量。 [0003] The stacked-beam radar reception beams formed simultaneously stacked vertically in elevation and azimuth mechanical scanning, to achieve measurement of a search target and the target coordinate. 例如,美国的陆基S波段三坐标AN/TPS-43雷达, 以6个仰角波束覆盖20°的仰角范围。 For example, US land-based coordinate S band AN / TPS-43 radar to six elevation beam coverage range of elevation angles of 20 °. L波段三坐标S713Martell0雷达用8个堆积波束覆盖20°的仰角范围。 Coordinate S713Martell0 L-band radar coverage range of elevation angles of 20 ° with 8 beams stacked.

[0004] 频率扫描雷达通过控制频率的变化在口径面上产生不同的相位变化梯度,从而通过电控的方法使波束指向所需的仰角,例如,S波段舰载三坐标AN/SPS-39、AN/SPS-48雷达。 [0004] The frequency scanning radar to cause different phase gradient change in diameter by controlling the frequency plane, so that the desired elevation beam pointing electrically controlled by a method, for example, S-band carrier coordinate AN / SPS-39, AN / SPS-48 radar.

[0005] 相控阵三坐标雷达采用移相器在仰角上扫描或控制笔形窄波束扫描。 [0005] The phased array radars use phase shifter coordinate scan control pencil or narrow beam scanning in elevation. 例如L波段远程三坐标AN/TPS-59战术机动雷达。 For example, L-band remote coordinate AN / TPS-59 tactical mobile radar.

[0006] 可见,目前三坐标雷达主要是工作在S波段和L波段等微波波段。 [0006] it is seen that the current coordinate radar mainly working in L-band and S-band and other microwave band. 而在米波波段, 波束较宽,波束因地、海面反射而导致波瓣分裂。 In the UHF band, a wider beam, due to the beam, caused by sea surface reflection lobe division. 因此,过去的米波雷达均为两坐标雷达,而两坐标雷达又不能满足现代战争的要求。 Therefore, past VHF radar are two coordinate radar, and the two coordinate radar can not meet the requirements of modern warfare.

[0007] 国内外雷达界普遍认为,米波雷达具有反隐身能力。 [0007] abroad radar field that, with a VHF radar anti-stealth capability. 但是米波雷达因受波长长、天线尺寸和架高有限等因素的限制,天线波束宽度宽、角分辨力低,更重要的是因地、海面反射即所谓“多径”问题使其难以探测低空目标,且在多径环境下难以测高,故米波雷达的测高问题一直是雷达界尚未很好解决的难题。 However, due to a long wavelength limit VHF radar, antenna size and elevated limited and other factors, the antenna beamwidth wide, low angular resolution, more importantly because of the ground, sea surface reflection so-called "multi-path" problems make it difficult to detect low-altitude targets, and difficult to measure in high multipath environments, so the VHF radar altimetry has been the radar community has not yet solved the problem.

[0008] 为较好地解决米波测高难题,最主要的技术途径是增大天线在高度维的孔径,以减小天线垂直面的波束宽度。 [0008] The UHF altimeter solve the problem, the most important technical approach is to increase the height dimension of the antenna aperture, in order to reduce the vertical antenna beamwidth. 而对于低空目标,即使增大天线在高度维的孔径,因无法避开“多径”问题,其解决测高问题主要有三类技术: For low-altitude targets, even if the increase in the height dimension of the antenna aperture, inability to avoid the "multipath" problem, which solves the problem altimetry technology are mainly three types:

[0009] (1)穿越波束法,也就是单频波瓣分裂法,利用目标穿越波束时回波幅度的变化进行估高。 [0009] (1) through the beam method, i.e. single frequency lobe division method, use of echo amplitude variation across the beam for target overestimated. 这种方法要求较长的时间,只能估高而不能测高。 This method requires a long time, can not be overestimated and altimeter.

[0010] (2)多频波瓣分裂测高法。 [0010] (2) splitting multiple frequency lobe altimetry. 利用多个工作频率时分工作,但要求多个频率的工作带宽较宽。 A plurality of operating frequencies using the time division of work, but requires a wider operating bandwidth of the plurality of frequencies. 这种方法在理论可行,但实际系统较复杂,目前还没有这种实用系统。 This method is feasible in theory, but the actual system is more complex, there is no such a practical system.

[0011] C3)基于波瓣分裂的米波雷达测高方法。 [0011] C3) based on the high VHF radar lobe division. 利用不同天线分裂波瓣的相位关系,确定目标所在仰角区间,对接收信号进行比幅处理提取归一化误差信号,最后根据归一化误差信号和仰角区间查表得到目标的高度。 Splitting phase relationships with different antenna lobe, determining a target elevation angle range where the received signal amplitude ratio extraction process the normalized error signal, the final height of the target obtained according to the normalized error signal and the elevation range lookup table. 陈伯孝等在2006年在《电子学报》和雷达年会上介绍了“基于波瓣分裂的米波雷达测高方法”。 Chen Boxiao etc. in 2006 in the "Journal of Electronics" and radar at the annual meeting "based VHF radar altimeter lobe splitting." 这是一种在垂直维只需3根天线的米波雷达的低仰角测高方法。 This is a low elevation VHF radar altimetry method only the vertical dimension of the three antennas. 该方法只适合于平坦阵地,对阵地的平坦性要求较高,且测高精度只能达到距离的1%,难以满足一些精度较高的实际使用要求。 This method is only suitable for flat position, flatness requirements for higher positions, and can accurately measure the distance of up to 1%, accuracy is difficult to meet some of the higher actual requirements. [0012] (4)阵列超分辨处理测高。 [0012] (4) an array of super-resolution processing altimetry. 把阵列信号处理中的超分辨技术应用于分辨直达波信号和多径信号。 The array signal processing technology for super resolution to distinguish the direct wave signals and multipath signals. 因为直达波信号和多径信号是相干的,所以这类算法主要是估计相干源波达方向DOA的超分辨算法,先使用空间平滑和Topelitz变换等方法解相干,然后利用信号子空间、噪声子空间和子阵旋转不变性等来测角。 Since the direct wave signals and multipath signals are coherent, so this type of super-resolution estimation algorithm mainly DOA algorithm of DOA, and to the use of spatial smoothing Topelitz decorrelation transform method, and then using the signal subspace, noise subspace and rotation invariant spatial sub-array to measure the angle and the like. 例如,赵光辉等人于2009年2月在《电子与信息学报》发表的论文“基于差分预处理的米波雷达低仰角处理算法”和胡铁军等人于2009年8月在《电波科学学报》发表的论文“阵列内插的波束域ML米波雷达测高方法”,以及胡晓琴等于2008年8月在《电波科学学报》发表的论文“米波雷达测高多径模型研究”, 提出了考虑多径延时差的米波雷达阵列信号综合模型。 For example, Zhao Guanghui, who in February 2009 in the "Electronics & Information Technology" papers "low elevation meter wave radar based pre-processing algorithms of the differential" and Hu Tiejun, who in August 2009 in the "Journal of Radio Science "papers" interpolated array beamspace ML VHF radar altimetry method ", and Hu Xiaoqin equal in August 2008 in the" Journal of radio Science "papers" high VHF radar more research path model "proposed consider VHF radar array synthesizer model multipath delay time difference. 该方法是基于平坦阵地模型,同时存在瓶颈,那就是分辨既相干,空间位置又近的目标。 The method is based on a flat front model, while there is a bottleneck, and that is both coherent resolution, spatial location and close to the goal.

[0013] 上述几种测高方法均只适用于平坦阵地模型,即各天线接收的直达波与地面反射波的波程差满足近似线性关系。 [0013] The altimeter Several methods are only applicable to model flat position, i.e., the direct wave and the wave retardation ground reflected wave received by each antenna satisfies an approximately linear relationship. 但是对于复杂雷达阵地,大型阵列各天线的地面发射点的起伏较大,各天线直达多径波程差不满足近似线性关系,因此在复杂阵地模型下,现有的各种测高方法测角误差较大,不再适用。 However, for complex radar position, undulating ground transmission points large arrays of each antenna is large, each antenna multipath direct wave path difference does not satisfy the approximate linear relationship, the positions in the complex model, the existing methods of measuring various high angle measurement error is large, no longer applies.

发明内容 SUMMARY

[0014] 本发明的目的在于克服上述已有技术的不足,提出一种基于地形匹配的超分辨测高方法,消除非线性的直达多径波程差对测角的影响,提高复杂阵地模型下的测角精度和雷达的阵地适应能力。 [0014] The object of the present invention is to overcome the disadvantages of the above prior art, to provide a match based on the super-resolution terrain height measurement method, to eliminate the influence of nonlinear multipath direct wave path difference of the measured angle, increase the complexity of the model position positions and the ability to adapt the radar angle measurement accuracy.

[0015] 为实现上述目的,本发明通过各阵元地面反射点的两维坐标,来计算不同阵元的直达波波程与地面反射波波程,再利用直达波波程和反射波波程构造合成导向矢量进行超分辨处理,具体步骤包括如下: [0015] To achieve the above object, the present invention is by two-dimensional coordinates of each reflection point of the array element surface, the different array elements to calculate the linear drive with the ground reflected wave Da Bobo process, and then reflected by the linear drive wave Cheng Da Bobo constructing a composite steering vector super-resolution process, comprising the following specific steps:

[0016] (1)从雷达回波中提取目标信号,并对该目标信号进行杂波对消和干扰对消处理, 得到对消后目标信号; [0016] (1) extracting a target from the radar echo signals, and clutter cancellation and target interference cancellation processing on the signal obtained after the cancellation of the target signal;

[0017] (2)使用波束形成法对对消后目标信号进行仰角粗测,得到目标信号的粗测仰角φ ; [0017] (2) using the beam forming method of the target elevation signal for eliminating coarse, rough measurement to obtain the elevation angle φ of the target signal;

[0018] (3)根据目标信号的粗测仰角^确定最大似然的搜索范围,当<j、于Ψ/2时,搜索范围为0〜Ψ,否则搜索范围为^-^//2-^ + ^///2,其中Ψ表示半功率波束宽度; [0018] (3) The coarse elevation angle of the target signal determining a maximum likelihood ^ search, when <j, in Ψ / 2, the search range 0~Ψ, otherwise the search range of ^ - ^ @ 2- /// ^ + ^ 2, where Ψ represents a half power beam width;

[0019] (4)在步骤C3)确定的搜索范围内搜索,根据搜索仰角,确定各阵元对应的地面反射点坐标: [0019] (4) searching the search range in step C3) is determined, the elevation angle based on the search, determining coordinates of the ground reflection point corresponding to the array element:

[0020] (4a)将反射区地面海拔按照1米间隔分层,根据搜索仰角,计算阵元在各层上的反射点; [0020] (4a) according to the altitude of the ground reflection region stratified 1 m intervals, according to the search elevation angle, calculating the reflection point on the array element layers;

[0021] (4b)查找雷达阵地海拔图上下两侧最近的反射点,记为a和b ; [0021] (4b) finds the closest reflection point position radar altitude FIG upper and lower sides, referred to as a and B;

[0022] (4c)将a点和b点垂直投影到雷达阵地海拔图,得到投影点c和d,利用c点和d 点之间的阵地海拔数据做曲线拟合,得到曲线cd ; [0022] (4c) the point a and point b to the radar position vertically projected elevation view obtain projection points c and d, using the front elevation data between point c and point d do curve fitting, curve obtained CD;

[0023] (4d)将直线ab和曲线Cd的交点作为阵元在起伏地面上的反射点; [0023] (4d) the linear and curved Cd ab as the intersection point on the reflective array elements undulating ground;

[0024] (5)根据地面反射点,计算目标相对各阵元的直达波波程和反射波波程; [0024] (5) The surface reflection point is calculated for each target relative linear array element and reflected wave Da Bobo Cheng Cheng;

[0025] (6)利用直达波波程和反射波波程,计算相应的直达导向矢量和多径导向矢量; [0025] (6) and reflected by the linear drive Da Bobo wave drive calculated steering vector corresponding direct and multipath steering vector;

[0026] (7)使用直达导向矢量和多径导向矢量计算合成导向矢量As : [0026] (7) steering vector using direct and multipath guide synthesized vector calculating steering vector As:

[0027] As = Ad+Ai;[0028] 其中:Ad为直达导向矢量,Ai为多径导向矢量; [0027] As = Ad + Ai; [0028] wherein: Ad is a direct steering vector, Ai multipath steering vector;

[0029] (8)计算合成导向矢量As的投影矩阵; [0029] (8) calculates a combined vector As guide projection matrix;

[0030] (9)根据投影矩阵和对消后目标信号的协方差矩阵进行最大似然估计,得到目标精确仰角。 [0030] (9) The maximum likelihood estimation the projection matrix and a covariance matrix after the cancellation of the target signal, to obtain accurate target elevation.

[0031] 本发明与现有技术相比具有如下优点: [0031] The prior art and the present invention has the following advantages:

[0032] (1)本发明由于使用直达波波程和反射波波程构造合成导向矢量,通过合成导向矢量进行测角处理,从而消除了非线性的直达多径波程差对测角的影响,提高了测角精度; [0032] (1) of the present invention is the use of direct and reflected wave drive Da Bobo process of constructing a composite steering vector angle measurement processing performed by synthesizing a steering vector, thus eliminating the influence of nonlinear multipath direct wave path difference of angle measurement to improve the angle measurement accuracy;

[0033] (2)本发明由于使用了雷达阵地海拔图,将雷达阵地海拔参数引入测角算法中,从而提高了雷达的阵地适应能力; [0033] (2) according to the present invention, since a front elevation of FIG radar, the radar position parameter elevation angle measurement algorithm is introduced, thereby improving the ability to adapt to the position of the radar;

[0034] (3)本发明由于采用反射区海拔分层和曲线拟合的方法来计算反射点,因此简化了起伏地面上各阵元发射点的计算过程,减少了算法运算量。 [0034] (3) The method of the present invention adopts the hierarchical and altitude curve fitting to calculate the reflection region reflection point, thus simplifying the calculation process for each array element on the emission point undulating ground, reducing the amount of arithmetic operations.

附图说明 BRIEF DESCRIPTION

[0035] 图1是本发明的流程图; [0035] FIG. 1 is a flow chart of the present invention;

[0036] 图2是本发明中雷达接收信号模型图; [0036] FIG. 2 is a radar receiver according to the present invention, FIG signal model;

[0037] 图3是本发明中地面反射点计算示意图; [0037] FIG. 3 is a reflecting surface in the present invention, a schematic view point calculation;

[0038] 图4是本发明仿真使用的雷达阵地海拔图; [0038] FIG. 4 is a front elevation of a simulation using the radar of the present invention;

[0039] 图5是用本发明在理想阵地模型下仿真的各阵元直达波和地面反射波的波程差图; [0039] FIG. 5 is a simulation of the present invention in position over the model of each array element and the wave of the direct wave path difference FIG ground reflected wave;

[0040] 图6是用本发明在图4模型下仿真的各阵元直达波和地面反射波的波程差图; [0040] FIG. 6 is a simulation of the present invention in FIG. 4 each array element model direct wave and the reflected wave path difference FIG ground wave;

[0041] 图7是用不同方法在图4模型下对高仰角目标随信噪比变化的测角精度仿真图; [0041] FIG. 7 is a high elevation angle in different ways and the target SNR with changing angle measurement accuracy in the simulation of FIG. 4 FIG model;

[0042] 图8是用不同方法在图4模型下对低仰角目标随信噪比变化的测角精度仿真图; [0042] FIG. 8 is different methods for low elevation angle measurement accuracy simulation target SNR variation with FIG. 4 in FIG model;

[0043] 图9是针对实测数据的处理结果图。 [0043] FIG 9 is a processing result for the measured data of FIG.

具体实施方式 detailed description

[0044] 下面结合附图详细说明本发明的内容和效果。 [0044] The following detailed description of the content and effects of the invention in conjunction with the accompanying drawings.

[0045] 参照图1,本发明包括如下步骤: [0045] Referring to FIG 1, the present invention comprises the steps of:

[0046] 步骤1 :对雷达接收的目标信号进行杂波对消和干扰对消处理,得到对消后目标信号。 [0046] Step 1: the target signal received by the radar clutter cancellation and interference cancellation process, to obtain a target signal after cancellation.

[0047] 本发明中雷达接收目标信号的模型如图2所示。 [0047] In the present invention, the model receives the radar target signal as shown in FIG. 图2中一个远场的窄带信号入射到M个阵元组成的均勻线阵,天线的倾斜角为θ a,架高为ha(l,阵元间隔为d,以第一根天线在海平面的投影点为坐标原点,D点为第m个阵元的地面投影点,E点为目标的地面投影点, 〜为等效地球半径,Rt为目标距离,θ为搜索仰角,C点为地心,A点为第m个阵元,A点水平坐标和垂直坐标分别为hax(m)和hay(m),T点为目标,T点水平坐标和垂直坐标分别为htx 和hty,G(m)表示D点与E点的水平距离,其中: ULA narrowband signal in FIG. 2 is incident to a far-field consisting of M array elements, the antenna tilt angle is θ a, frame height ha (l, array element spacing is d, a first antenna at sea level origin of coordinates projected point, D point of the m-th array element in the floor projection point, E point of the target floor projection point, - an equivalent Earth radius, Rt is the target distance, the elevation angle [theta] for the search, C to point heart, A point of the m-th array element, A point of the horizontal and vertical coordinates, respectively HAX (m) and Hay (m), T point target, horizontal coordinate T and vertical coordinates, respectively htx and hty, G ( m) D represents the horizontal distance between point E and point, wherein:

[0048] hax (m) = -d (m-1) cos θ a,m = 1,2L, M [0048] hax (m) = -d (m-1) cos θ a, m = 1,2L, M

[0049] hay (m) = ha0+d(ml)sin θ a,m = 1,2L,M [0049] hay (m) = ha0 + d (ml) sin θ a, m = 1,2L, M

Figure CN102288944AD00071

[0052] G(m) = htx-hax(m); [0052] G (m) = htx-hax (m);

[0053] B点为目标对应第m个阵元的地面反射点,B点水平坐标和垂直坐标分别为hbx(m) 和hby(m),第m个阵元的目标直达波和地面反射波的波程分别为和氏(m),Ri(Hi)= R1 (m) +R2 (m),R1 (m)和R2 (m)分别为B点与A点的距离和B点与T点的距离。 [0053] B point corresponding to a target m-th array element surface reflection point, B point of the horizontal and vertical coordinates, respectively HBx (m) and hby (m), the m-th array element of the target direct wave and the ground reflected wave the beam path, respectively, and s (m), Ri (Hi) = R1 (m) + R2 (m), R1 (m), and R2 (m) respectively point B and point a distance and point B and point T distance.

[0054] 从图2信号模型中得到第m个阵元接收的目标信号χ (m) [0054] m-th array element obtained from the received signal model of FIG. 2 target signal [chi] (m)

[0055] χ (m) = xd (m) +Xi (m) +c (m) +g (m) +n (m), m = 1, 2L, M [0055] χ (m) = xd (m) + Xi (m) + c (m) + g (m) + n (m), m = 1, 2L, M

[0056] 其中xd(m)为目标直达波信号,xd(m)= se-jkRd(m),Xi(m)为目标反射波信号, Xi(M) = STe-jkRi(m),, c (m)为杂波信号,g(m)为干扰信号,n(m)为均值为零、方差为ο 2的高斯白噪声,s为雷达发射信号,κ为波数,Γ为地面反射系数。 [0056] where xd (m) is the direct wave target signal, xd (m) = se-jkRd (m), Xi (m) is the target signal reflected wave, Xi (M) = STe-jkRi (m) ,, c (m) is noise signal, G (m) is an interference signal, n-(m) is zero-mean, white Gaussian noise with variance ο 2, s is a radar transmit signal, [kappa] is a wave number, Gamma] is the ground reflection coefficient.

[0057] 对χ (m)通过自适应滤波来对消杂波和干扰,得到对消后目标信号 [0057] The χ (m) by adaptive filtering of the clutter and interference cancellation, the cancellation of the target signal to obtain

[0058] [0058]

Figure CN102288944AD00072

[0059] 将对消后目标信号用矢量X表示为: [0059] After the target signal cancellation will be represented by a vector X is:

[0060] [0060]

Figure CN102288944AD00073

[0061] 其中:上标T表示转置。 [0061] wherein: the superscript T represents transposition.

[0062] 步骤2 :使用波束形成法对对消后目标信号进行仰角粗测,得到目标信号的粗测 [0062] Step 2: beam forming method using a target elevation signal for eliminating coarse, rough measurement to obtain a target signal

仰角识: Elevation know:

[0063] [0063]

Figure CN102288944AD00074

[0064] 其中:arg max为寻找具有最大评分的参量,abs为求模运算, [0064] wherein: arg max to find parameter having the maximum score, abs is the modulo operation,

[0065] [0065]

Figure CN102288944AD00075

,κ表示波数,Μ表示阵元个数,R为对消后信号的协方差矩阵,R = ΧΧΗ,上标T表示转置,上标H表示共轭转置,X为对消后目标信 , [Kappa] represents the wave number, [mu] represents the array element number, R is the covariance matrix cancellation after signal, R = ΧΧΗ, superscript T denotes transpose, a superscript H denotes a conjugate transpose, X is the elimination target channel to

号矢量。 No. vector.

[0066] 步骤3 :根据目标信号的粗测仰角袖角定最大似然的搜索范围,当<j、于Ψ/2时,搜索范围为0〜Ψ,否则搜索范围为φ-ψ//2-φ + ψ/2,其中Ψ表示半功率波束宽度。 [0066] Step 3: The fixed sleeve coarse elevation angle search range of the target signal of maximum likelihood, when <j, in Ψ / 2, the search range 0~Ψ, otherwise the search range of φ-ψ // 2 -φ + ψ / 2, where Ψ represents the half-power beamwidth.

[0067] 步骤4 :在步骤(3)确定的搜索范围内搜索,根据搜索仰角,确定各阵元对应的地面反射点坐标。 [0067] Step 4: searching within a search range determined in step (3), the elevation angle based on the search, determining coordinates of the ground reflection point corresponding to the array element.

[0068] 由于反射点位于阵地海拔图上,而阵地海拔图难以使用数学表达式表示,因此反射点坐标不易直接求解,在此使用海拔分层和曲线拟合的方式进行求解,其求解步骤参照图3,包括如下: [0068] Since the reflection point located on the front elevation view and front elevation of FIG mathematical expression is difficult to use, said reflection point coordinates so easily solved directly used herein solve delamination and altitude curve fitting manner, with reference to which solution steps Figure 3, comprising:

[0069] (4a)将反射区地面海拔按照1米间隔分层,根据搜索仰角,计算阵元在各层上的反射点水平坐#hx(m,η)和垂直坐标hy(m,n),图3中横轴表示与雷达阵地的水平距离,纵轴表示海拔高度,阴影表示雷达阵地海拔,横虚线表示海拔分层,+表示阵元在各层上的反射点: [0069] (4a) according to the altitude of the ground reflection region stratified 1 m intervals, according to the search elevation array element is calculated reflection point on the horizontal layers sit #hx (m, η) and vertical coordinates hy (m, n) FIG 3 the horizontal axis represents the horizontal distance from the radar position, the vertical axis represents the altitude, altitude radar position hatched, dotted line elevation cross-hierarchical, + represents the reflection point on the array element layers:

Figure CN102288944AD00081

[0072] 其中:m表示第m个阵元,M表示阵元个数,η表示反射区海拔分层的第η层,N 为反射区地面海拔起伏高度,hx(m, η)和hy(m,η)分别为第m个阵元在第η层反射点的水平坐标和垂直坐标,G(m)为目标与第m个阵元的地面水平距离,hax(m)为第m个阵元 [0072] wherein: m represents the m-th array element, M is the number of array elements, η represents elevation layered reflective layer Zone [eta], N is a relief height above sea floor reflection area, hx (m, η) and HY ( m, η) are the m-th array element the horizontal and vertical coordinates at the [eta] layer reflection point, G (m) target with the m-th array element ground horizontal distance, hax ​​(m) is the m-th array yuan

的水平坐标,ρ为临时变量 The horizontal coordinate, ρ is a temporary variable

Figure CN102288944AD00082

ξ为临时变量, ξ is a temporary variable,

Figure CN102288944AD00083

,ae为等效地球半径,hay (m)为第m个阵元的垂直坐标,hty为 , AE is the equivalent radius of the Earth, the vertical coordinate Hay (m) is the m-th array element, is HTY

目标的垂直坐标; Vertical coordinates of the target;

[0073] (4b)查找雷达阵地海拔图上下两侧最近的反射点,记为a和b ; [0073] (4b) finds the closest reflection point position radar altitude FIG upper and lower sides, referred to as a and B;

[0074] (4c)将a点和b点垂直投影到雷达阵地海拔图,得到投影点c和d,图3中竖虚线表示垂直投影,利用c点和d点之间的阵地海拔数据做曲线拟合,得到曲线Cd ; [0074] (4c) the point a and point b to the radar position vertically projected elevation view obtain projection points c and d, the vertical dashed line in Figure 3 represents a vertical projection, front elevation data between points c and d by doing curve points obtained by fitting curves of Cd;

[0075] (4d)将直线ab和曲线Cd的交点作为阵元在起伏地面上的反射点。 [0075] (4d) the linear and curved Cd ab as the intersection point on the reflective array elements undulating ground.

[0076] 步骤5 :根据地面反射点,通过如下三角公式计算目标至各阵元的直达波波程Rd (m)和反射波波程: [0076] Step 5: The surface reflection point is calculated by the following trigonometric formula to each of the target array element linear Da Bobo Cheng Rd (m) and the reflection wave range:

[0077] [0077]

Figure CN102288944AD00084

[0078] Ri (m) = R1 (m) +R2 (m), m = 1,2, L, M [0078] Ri (m) = R1 (m) + R2 (m), m = 1,2, L, M

[0079] 其中:m表示第m个阵元,M表示阵元个数,&(m)为目标至第m个阵元的直达波波程,hay(m)为第m个阵元的垂直坐标,〜为等效地球半径,hty为目标的垂直坐标,G (m)为目标与第m个阵元的地面水平距离,Ri(Hi)为目标至第m个阵元的反射波波程,R1(Hi)为第m个阵元与第m个阵元对应地面反射点的距离,为目标与第m个阵元对应地面反射点的距尚, [0079] wherein: m represents the m-th array element, M is the number of array elements, & (m) of the target m-th array element to a straight path Da Bobo, hay (m) is the m-th array element perpendicular coordinates, ~ an equivalent Earth radius, HTY target vertical coordinate, G (m) as the target level with the floor of the m-th array element distance, Ri (Hi) for the target to the m-th array element drive reflected wave , R1 (Hi) is the m-th array element corresponding to the m-th array element and the ground reflection point distance, a target m-th array element and the corresponding point of reflection from the ground yet,

[0080] [0080]

Figure CN102288944AD00085
Figure CN102288944AD00086

[0082] hbx(m)和hby(m)分别为第m个阵元对应地面反射点的水平坐标和垂直坐标,hax(m) 为第m个阵元的水平坐标。 [0082] hbx (m) and HBY (m) respectively corresponding to the m-th array element surface reflection point of the horizontal and vertical coordinates, hax ​​(m) is the horizontal coordinate of the m-th array element.

[0083] 步骤6 :利用直达波波程&011)和反射波波程氏(111),计算相应的直达导向矢量Α,(θ)和多径导向矢量Ai(Q): [0083] Step 6: using a linear drive Da Bobo & 011) and a reflective wave Cheng (111), a direct calculation of the corresponding steering vector [alpha], ([theta]) and multipath steering vector Ai (Q):

[0084] Ad ( θ ) = [ad(l),ad (2),L,ad (M) ]τ [0084] Ad (θ) = [ad (l), ad (2), L, ad (M)] τ

[0085] Ai ( θ ) = [ai(D, Bi (2),L,Bi (M) ]τ [0085] Ai (θ) = [ai (D, Bi (2), L, Bi (M)] τ

[0086]其中:ad(m) = e-JKRAm') ,Cii(Jn) = Te-m(jn'),m = 1,2,L,M,m 表示第m 个阵元,M 表示阵元个数,κ表示波数,Γ为地面反射系数,上标T表示转置。 [0086] wherein: ad (m) = e-JKRAm '), Cii (Jn) = Te-m (jn'), ​​m = 1,2, L, M, m denotes the m-th array element, M is the array number of neurons, [kappa] represents the wave number, Gamma] is the ground reflection coefficients, the superscript T represents transposition.

[0087] 步骤7 :使用直达导向矢量Ad(e)和多径导向矢量&(9)计算合成导向矢量As(0): [0087] Step 7: Direct steering vector Ad (e) and the steering vector & multipath (9) calculates a combined steering vectors As (0):

[0088] Ks(Q) = Ad( θ )+Ai( θ )[0089] 其中:θ为搜索仰角。 [0088] Ks (Q) = Ad (θ) + Ai (θ) [0089] where: θ is an elevation angle search.

[0090] 步骤8:使用合成导向矢量As( θ )计算合成导向矢量的投影矩阵Ρ( θ): [0090] Step 8: Synthesis of steering vectors As (θ) calculates a combined vector guide projection matrix Ρ (θ):

[0091 ] [0091]

Figure CN102288944AD00091

[0092] 其中:θ为搜索仰角,上标H表示共轭转置,上标-1表示矩阵求逆。 [0092] where: θ is a search angle of elevation, the superscript H denotes the conjugate transpose and the superscript -1 represents matrix inversion.

[0093] 步骤9 :根据投影矩阵和对消后目标信号的协方差矩阵进行最大似然估计,得到目标精确仰角: [0093] Step 9: The maximum likelihood estimation the projection matrix and a covariance matrix after the cancellation of the target signal, to obtain accurate target elevation:

[0094] [0094]

Figure CN102288944AD00092

[0095] 其中:θ为目标精确仰角,arg max为寻找具有最大评分的参量,tr为矩阵求迹, Ρ(θ)为投影矩阵,R为对消后信号的协方差矩阵。 [0095] where: θ is the precise elevation target, arg max to find parameter having the maximum score, tr is the trace matrix, Ρ (θ) is the projection matrix, R is the covariance matrix of the signal after cancellation.

[0096] 本发明的效果可以通过以下仿真结果和实测数据处理结果进一步说明。 [0096] The effect of the present invention can be further illustrated by the following simulation results and the actual data processing result.

[0097] 1.仿真环境及条件 [0097] 1. simulation environment and conditions

[0098] 仿真环境使用图4所示的雷达阵地海拔图。 [0098] Position Elevation Radar simulation environment shown in FIG. 4 to FIG. 横轴表示与雷达阵地的水平距离,纵轴表示海拔高度,阴影表示雷达阵地海拔。 The horizontal axis represents the horizontal distance radar position of the vertical axis represents altitude, elevation shaded radar position. 雷达阵地的水平450米以内为起伏地形,水平450米以外为海平面。 Radar level positions undulating terrain within 450 meters, 450 meters beyond the level of sea level.

[0099] 仿真条件为以下雷达参数:天线架高6米,倾角6°,阵元个数22,阵元间隔为半波长,快拍数10。 [0099] The simulation condition parameters of the radar: antenna mount 6 meters, angle 6 °, the number of array elements 22, a half wavelength array element spacing, 10 snapshots.

[0100] 2.仿真内容 [0100] 2. simulation content

[0101] 仿真1,用本发明在理想阵地模型下对各阵元的直达波和地面反射波的波程差进行仿真,仿真结果如图5所示。 [0101] Simulation 1, with the present invention is to simulate wave path difference of each array element of the ground reflected wave and direct wave at a position over the model, the simulation results shown in Fig. 其中横轴表示目标海拔高度从1000米至15000米变化,纵轴表示直达波和地面反射波的波程差。 Wherein the horizontal axis represents the target altitude from 1000 to 15,000 m changes, the vertical axis represents the ground reflected wave and direct wave of the wave path difference. 图5中显示了目标与雷达水平距离50千米,目标海拔高度按照横轴变化时第1、6、11、16和22个阵元的直达波和地面反射波的波程差。 FIG. 5 shows a radar target horizontal distance 50 km, the horizontal axis in accordance with the target altitudes Change 1,6,11,16 and 22 of array element ground reflected wave and direct wave of the wave path difference. 从图5可以得出,在理想阵地模型下,各阵元的直达波和地面反射波的波程差满足线性变化。 Can be derived from FIG 5, in the ideal position model, each wave path difference array element ground reflected wave and direct wave satisfies linear.

[0102] 仿真2,用本发明在图4模型下对各阵元的直达波和地面反射波的波程差进行仿真,仿真结果如图6所示。 [0102] 2 simulation, with the present invention is to simulate wave path difference of each array element of the ground reflected wave and direct wave at the model of FIG. 4, the simulation results shown in Figure 6. 其中横轴表示目标海拔高度从1000米至15000米变化,纵轴表示直达波和地面反射波的波程差。 Wherein the horizontal axis represents the target altitude from 1000 to 15,000 m changes, the vertical axis represents the ground reflected wave and direct wave of the wave path difference. 图6中显示了目标与雷达水平距离50千米,目标海拔高度按照横轴变化时第1、6、11、16和22个阵元的直达波和地面反射波的波程差。 In FIG. 6 shows a radar target and horizontal distance 50 km, while the horizontal axis in accordance with a target altitude change 1,6,11,16 and 22 of array element ground reflected wave and direct wave of the wave path difference. 从图6可以得出,在起伏阵地模型下,各阵元的直达波和地面反射波的波程差不满足线性变化。 Can be derived from FIG. 6, in the position fluctuation model wave path difference of each array element ground reflected wave and direct wave does not satisfy a linear change.

[0103] 仿真3,用现有的波束形成算法、前后向空间平滑MUSIC算法和本发明分别在图4 模型下对高仰角目标进行测角精度仿真,仿真结果如图7所示。 [0103] 3 simulation, with conventional beam forming algorithm, respectively, before and after the high elevation angle measurement accuracy target spatial smoothing MUSIC algorithm simulation and the model of the present invention in FIG. 4, the simulation results shown in Fig. 其中横轴表示信噪比从-5 分贝至15分贝变化,纵轴表示测角误差。 Wherein the horizontal axis represents SNR from -5 dB to 15 dB variation, the vertical axis represents the angle measurement error. 仿真选取的目标参数:目标仰角4度,目标与雷达距离50千米,蒙特卡罗实验次数100次。 Simulation parameters selected targets: target elevation 4 degrees, the target distance from the radar 50 km, 100 times the number of Monte Carlo experiment. 图7中DBF表示波束形成算法在信噪比按照横轴变化时的测角误差,SSMUSIC表示前后向空间平滑MUSIC算法在信噪比按照横轴变化时的测角误差,GSVML表示本发明在信噪比按照横轴变化时的测角误差。 Figure 7 represents a DBF beamforming algorithm according to the measured SNR of the horizontal axis change angle error, SSMUSIC represent forward and backward spatial smoothing MUSIC algorithm in accordance with the measuring angle error when the SNR of the horizontal axis changes, GSVML the present invention in a letter angle measurement error changes according to the horizontal axis noise ratio. 从图7可以得出,对高仰角目标现有的波束形成算法、前后向空间平滑MUSIC算法测角误差偏大,而本发明的测角误差最小。 Can be derived from FIG. 7, a high elevation angle is formed algorithm target beam current, measured before and after the spatial smoothing MUSIC algorithm to the angle error is too large, while the minimum angle measurement error of the present invention.

[0104] 仿真4,用现有的波束形成算法、前后向空间平滑MUSIC算法和本发明分别在图4 模型下对低仰角目标进行测角精度仿真,仿真结果如图8所示。 [0104] 4 simulation, a conventional beam forming algorithm, respectively, before and after the target low elevation angle measurement accuracy spatial smoothing MUSIC algorithm simulation and the model of the present invention in FIG. 4, the simulation results shown in Fig. 其中横轴表示信噪比从-5 分贝至15分贝变化,纵轴表示测角误差。 Wherein the horizontal axis represents SNR from -5 dB to 15 dB variation, the vertical axis represents the angle measurement error. 仿真选取的目标参数:目标仰角1度,目标与雷达距离200千米,蒙特卡罗实验次数100次。 Simulation selected target parameter: 1 degree elevation target, the target distance from the radar 200 km, 100 times the number of Monte Carlo experiment. 图8中DBF表示波束形成算法在信噪比按照横轴变化时的测角误差,SSMUSIC表示前后向空间平滑MUSIC算法在信噪比按照横轴变化时的测角误差,GSVML表示本发明在信噪比按照横轴变化时的测角误差。 FIG 8 represents the DBF beamforming algorithm according to the SNR measuring angle error when the horizontal axis changes, SSMUSIC represent forward and backward spatial smoothing MUSIC algorithm in accordance with the measuring angle error when the SNR of the horizontal axis changes, GSVML the present invention in a letter angle measurement error changes according to the horizontal axis noise ratio. 从图8可以得出,对低仰角目标现有的波束形成算法、前后向空间平滑MUSIC算法测角误差偏大,而本发明的测角误差最小。 Can be derived from FIG. 8, a conventional algorithm for low elevation target beam, before and after the spatial smoothing MUSIC algorithm to the angle error is too large, while the minimum angle measurement error of the present invention.

[0105] 3.对某警戒雷达实测数据的测角结果 [0105] 3. The angle measurement results of the measured data for a surveillance radar

[0106] 该警戒雷达架设阵地海拔图如图9(a)所示,其中横轴表示与雷达阵地的水平距离,纵轴表示海拔高度,实线表示雷达阵地海拔,雷达阵地的水平6千米以内为起伏地形, 水平6千米以外为海平面。 [0106] The surveillance radar altitude erected position shown in Figure 9 (a), in which the horizontal axis represents the horizontal distance from the radar position, the vertical axis represents the altitude, the solid line indicates the position above sea level radar, radar positions 6km within undulating terrain, outside level 6km sea level.

[0107] 用现有的波束形成算法、前后向空间平滑MUSIC算法和本发明对该警戒雷达实测数据进行测角处理,测角处理结果如图9(b)所示,其中横轴表示目标与阵地的距离,纵轴表示距离随横轴变化时的测角误差。 [0107] with a conventional beam forming algorithm, before and after angle measurement process to the MUSIC algorithm and the spatial smoothing of the present invention, the surveillance radar measurement data, angle measurement processing result in FIG. 9 (b), in which the horizontal axis represents the target and distance positions, and the vertical axis represents the angle measurement error of the distance changes with the horizontal axis. 图9(b)中DBF表示波束形成算法的测角误差,SSMUSIC 表示前后向空间平滑MUSIC算法的测角误差,GSVML表示本发明的测角误差。 FIG. 9 (b) represents the angle measurement error DBF beamforming algorithm, SSMUSIC angle error measurement represents the forward and backward spatial smoothing MUSIC algorithm, GSVML angle error measurement represents the present invention. 从图9(b)可以得出,现有的波束形成算法、前后向空间平滑MUSIC算法测角误差偏大,而本发明的测角误差最小。 Can be derived from FIG. 9 (b), a conventional beamforming algorithm, before and after the spatial smoothing MUSIC algorithm angle error is too large, while the minimum angle measurement error of the present invention.

Claims (7)

1. 一种基于地形匹配的数字阵列米波雷达超分辨测高方法,包括以下步骤:(1)从雷达回波中提取目标信号,并对该目标信号进行杂波对消和干扰对消处理,得到对消后目标信号;(2)使用波束形成法对对消后目标信号进行仰角粗测,得到目标信号的粗测仰角P ;(3)根据目标信号的粗测仰角^确定最大似然的搜索范围,当Vh于Ψ/2时,搜索范围为0〜Ψ,否则搜索范围为识-^/2~^ + 1///2,其中Ψ表示半功率波束宽度;(4)在步骤C3)确定的搜索范围内搜索,根据搜索仰角,确定各阵元对应的地面反射点坐标:(4a)将反射区地面海拔按照1米间隔分层,根据搜索仰角,计算阵元在各层上的反射占.(4b)查找雷达阵地海拔图上下两侧最近的反射点,记为a和b ; (4c)将a点和b点垂直投影到雷达阵地海拔图,得到投影点c和d,利用c点和d点之间的阵地海拔数据做曲线拟合,得到曲线cd An array of digital terrain matching based super-resolution high 列米波雷达 measuring method, comprising the steps of: (1) extracting a target from the radar echo signals, and clutter cancellation and target interference cancellation processing on the signal to give the target signal cancellation; (2) using the beam forming method of the target signal cancellation for elevation coarse, resulting coarse elevation P target signal; (3) ^ determined according to the coarse elevation angle of the target signal maximum likelihood the search range, when Vh to [Psi] / 2, the search range 0~Ψ, otherwise the search range of knowledge - ^ / 2 + 1 /// ~ ^ 2, where [Psi] denotes a half power beam width; (4) at step C3) within the search range determined by the search, the search according to the elevation angle, ground reflection determining coordinates corresponding to each array element: (4a) according to the altitude of the ground reflection region 1 m intervals layered on the elevation angle based on the search, computing array element layers reflection accounts (4b) to find upper and lower sides of FIG altitude radar position nearest point of reflection, referred to as a and b;. (4c) and the point a to point b radar position vertically projected elevation view obtain projection points c and d, using the elevation data positions between the point c and the point d do curve fitting, curve obtained cd ;(4d)将直线ab和曲线cd的交点作为阵元在起伏地面上的反射点;(5)根据地面反射点,计算目标相对各阵元的直达波波程和反射波波程;(6)利用直达波波程和反射波波程,计算相应的直达导向矢量和多径导向矢量;(7)使用直达导向矢量和多径导向矢量计算合成导向矢量As : As = Ad+Aj,其中:Ad为直达导向矢量,Ai为多径导向矢量;(8)计算合成导向矢量As的投影矩阵;(9)根据投影矩阵和对消后目标信号的协方差矩阵进行最大似然估计,得到目标精确仰角。 ; (4D) and the straight line ab cd curve as the intersection point on the reflective array elements undulating ground; (5) The surface reflection point is calculated for each target relative linear array element and reflected wave Cheng Cheng Da Bobo; (6 ) and reflected by the linear drive Da Bobo wave drive calculated steering vector corresponding direct and multipath steering vector; (7) steering vector using direct and multipath guide synthesized vector calculating steering vector As: As = Ad + Aj, wherein: Ad is a direct steering vector, Ai multipath steering vector; (8) calculates a combined steering vectors as projection matrix; (9) maximum likelihood estimation according to the projection matrix and a covariance matrix of the target signal cancellation, to give the object precisely elevation.
2.根据权利要求1所述的米波雷达超分辨测高方法,其中步骤(¾所述的使用波束形成法对对消后目标信号进行仰角粗测,是通过如下公式进行:φ = arg maxφ(l / abs(aH (φ)Ra(φ)))其中W为目标粗测仰角,arg max为寻找具有最大评分的参量,abs为求模运算, a(φ) = [ejK-0-smin(φ),ejK-l-sin(φ)L,ejk.(M-1).sin(φ)W]Tκ表示波数,M表示阵元个数,上标T表示转置, 上标H表示共轭转置,R为对消后信号的协方差矩阵。 VHF radar according to claim 1, wherein said ultra-high resolution measuring method, wherein step (¾ of the beam forming method using the target signal for eliminating coarse elevation angle, is performed by the following equation: φ = arg maxφ (l / abs (aH (φ) Ra (φ))) wherein W is a certain coarse elevation, arg max to find parameter having the maximum score, abs is the modulo operation, a (φ) = [ejK-0-smin (φ), ejK-l-sin (φ) L, ejk. (M-1) .sin (φ) W] Tκ represents wave number, M is the number of array elements, the superscript T denotes the transpose, the superscript H denotes conjugate transpose, R is the covariance matrix of the signal after cancellation.
3.根据权利要求1所述的米波雷达超分辨测高方法,其中步骤Ga)所述将反射区地面海拔按照1米间隔分层,根据搜索仰角,计算阵元在各层上的反射点,是通过如下公式进行: 3. The VHF radar altimeter according to claim 1 a super-resolution method, wherein the step of Ga) the elevation of the ground reflection region according to a hierarchical meter intervals, the elevation angle based on the search, the reflection point is calculated on the array element layers , is performed by the following formula:
Figure CN102288944AC00021
其中:m表示第m个阵元,M表示阵元个数,η表示反射区海拔分层的第η层, N为反射区地面海拔起伏高度,hx(m,η)和hy(m,η)分别为第m个阵元在第η层反射点的水平坐标和垂直坐标,G(m)为目标与第m个阵元的水平距离,G(m)=htx-hax(m),ρ 为临时变量 Wherein: m represents the m-th array element, M is the number of array elements, η represents elevation layered reflective layer Zone [eta], N is a relief height above sea floor reflection area, hx (m, η) and hy (m, η ) are the m-th array element the horizontal and vertical coordinates at the η layer reflection point, G (m) target with the m-th array element of the horizontal distance, G (m) = htx-hax (m), ρ temporary variable
Figure CN102288944AC00022
为临时变量, Temporary variables,
Figure CN102288944AC00031
hax(m)为第m个阵元的水平坐标,htx为目标的水平坐标, HAX (m) is the horizontal coordinate of the m-th array element, the horizontal coordinate of the target HTX,
Figure CN102288944AC00032
,ae为等效地球半径,ha¥ (m)为第m个阵元的垂直坐标,hty为目标的垂直坐标 , Ae is the equivalent radius of the Earth, ha ¥ (m) is the vertical coordinate of the m-th array element, hty target vertical coordinate
Figure CN102288944AC00033
为目标距离,θ为搜索仰角。 Target distance, θ is a search angle of elevation.
4.根据权利要求1所述的米波雷达超分辨测高方法,其中步骤(¾所述计算目标相对各阵元的直达波波程和反射波波程,是通过如下三角公式进行: VHF radar according to claim 1, wherein said ultra-high resolution measuring method, wherein the step (¾ of the target is calculated for each array element relative to a straight path and Da Bobo reflected wave drive is performed by the following trigonometric formula:
Figure CN102288944AC00034
其中:m表示第m个阵元,M表示阵元个数,&(m)为第m个阵元的直达波波程,hay (m)为第m个阵元的垂直坐标,〜为等效地球半径,hty为目标的垂直坐标,G(m)为目标与第m个阵元的水平距离,Ri(Iii)为第m个阵元的反射波波程,R1(Hi)为第m个阵元与第m个阵元对应地面反射点的距离,R2 (m)为目标与第m个阵元对应地面反射点的距离, Wherein: m represents the m-th array element, M is the number of array elements, & (m) is the m-th array element straight away Da Bobo, Hay (m) is the vertical coordinate of the m-th array element, and the like - is effective radius of the Earth, hty target vertical coordinate, G (m) target with the m-th array element horizontal distance, Ri (Iii) of the m-th array element reflected wave process, R1 (Hi) is the m array element distance corresponding to the m-th array element and the ground reflection points, R2 (m) target with the m-th array element corresponding to the surface reflection point distance,
Figure CN102288944AC00035
hby(m)分别为第m个阵元对应地面反射点的水平坐标和垂直坐标,hax(m)为第m个阵元的水平坐标。 HBY (m) respectively corresponding to the m-th array element surface reflection point of the horizontal and vertical coordinates, hax ​​(m) is the horizontal coordinate of the m-th array element.
5.根据权利要求1所述的米波雷达超分辨测高方法,其中步骤(6)所述计算相应的直达导向矢量和多径导向矢量,是通过如下公式进行: VHF radar as claimed in claim 1 ultra high resolution measuring method, wherein step (6) of the calculated steering vector corresponding direct and multipath steering vector, is performed by the following formula:
Figure CN102288944AC00036
其中:Ad(9)为直达导向矢量,Ai(Q)为多径导向矢量,θ为搜索仰角 Wherein: Ad (9) for the direct steering vector, Ai (Q) multipath steering vector, θ is an elevation angle search
Figure CN102288944AC00037
m表示第m个阵元,Rd(m)为第m个阵元的直达波波程, Ri(Hi)为第m个阵元的反射波波程,Γ为地面反射系数,上标T表示转置。 m represents the m-th array element, Rd (m) is the m-th array element straight away Da Bobo, Ri (Hi) is the m-th array element drive reflected wave, the reflection coefficient Gamma] is the ground, the superscript T denotes Transpose.
6.根据权利要求2所述的米波雷达超分辨测高方法,其中步骤(8)所述计算投影矩阵, 是通过如下公式进行: VHF radar according to claim 2, wherein said ultra-high resolution measuring method, wherein step (8) of the projection matrix calculation is performed by the following formula:
Figure CN102288944AC00038
其中:Ρ( θ )为投影矩阵,θ为搜索仰角,As( θ)为合成导向矢量,上标H表示共轭转置,上标-1表示矩阵求逆。 Wherein: Ρ (θ) is the projection matrix, the elevation angle [theta] for the search, As (θ) is the steering vector synthesis, the superscript H denotes the conjugate transpose and the superscript -1 represents matrix inversion.
7.根据权利要求1所述的米波雷达超分辨测高方法,其中步骤(9)所述计算最大似然估计,是通过如下公式进行: VHF radar according to claim 1, wherein said ultra-high resolution measuring method, wherein step (9) calculates the maximum likelihood estimation, is performed by the following formula:
Figure CN102288944AC00039
其中:θ为目标精确仰角,arg max为寻找具有最大评分的参量,tr为矩阵求迹,Ρ( θ ) 为投影矩阵,R为对消后信号的协方差矩阵。 Wherein: θ precise target elevation, arg max to find parameter having the maximum score, tr is the trace matrix, Ρ (θ) is the projection matrix, R is the covariance matrix of the signal after cancellation.
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