CN102288944B - Super-resolution height measuring method based on topographic matching for digital array meter wave radar - Google Patents

Abstract

The invention discloses a digital array meter-wave radar super-resolution height measurement method based on terrain matching, which mainly solves the problem of relatively large height measurement error for undulating positions in the prior art. Its implementation steps: perform clutter cancellation and interference cancellation processing on the target signal received by the radar to obtain the target signal after cancellation; use the beamforming method to roughly measure the target elevation angle; determine the maximum likelihood search range according to the rough measurement elevation angle, And search within the search range; according to the search elevation angle, calculate the ground reflection point coordinates corresponding to each array element and the direct wave path and reflected wave path of the target relative to each array element; use the direct wave path and reflected wave path to calculate Corresponding direct steering vectors and multipath steering vectors; constructing synthetic steering vectors and calculating their projection matrix; finally performing maximum likelihood estimation to obtain the precise elevation angle of the target. The invention introduces the altitude parameter of the radar position and the synthetic guide vector into the super-resolution altimetry, improves the high-precision measurement, and can be used for target tracking.

Description

Digital Array Meter Wave Radar Super-resolution Altimetry Method Based on Terrain Matching

technical field

The invention belongs to the technical field of radar signal processing, and relates to meter-wave radar height measurement. Specifically, it proposes a terrain-matching-based super-resolution height measurement method for digital array meter-wave radar, which can be used for target tracking.

Background technique

According to the elevation angle beam forming method and scanning method, three-coordinate 3D radar can be divided into stacked beam radar, frequency scanning radar, phase scanning radar and digital beam forming radar.

The stacked beam radar stacks the received beams formed at the same time vertically in elevation and scans mechanically in azimuth to realize the measurement of the search target and the three coordinates of the target. For example, the land-based S-band three-coordinate AN/TPS-43 radar in the United States covers an elevation range of 20° with six elevation beams. The L-band three-coordinate S713Martello radar covers an elevation range of 20° with 8 stacked beams.

The frequency scanning radar produces different phase change gradients on the aperture surface by controlling the frequency change, so that the beam can be directed to the required elevation angle by means of electronic control, for example, the S-band shipboard three-coordinate AN/SPS-39, AN/SPS -48 radar.

Phased array three-coordinate radar uses phase shifters to scan in elevation or control pencil-shaped narrow beam scanning. For example, the L-band long-range three-coordinate AN/TPS-59 tactical mobile radar.

It can be seen that the current three-coordinate radar mainly works in microwave bands such as S-band and L-band. In the meter wave band, the beam is wider, and the beam is split due to ground and sea reflections. Therefore, the meter wave radars in the past were all two-coordinate radars, and the two-coordinate radars could not meet the requirements of modern warfare.

Domestic and foreign radar circles generally believe that meter wave radar has anti-stealth capabilities. However, meter-wave radar is limited by factors such as long wavelength, limited antenna size and height, wide antenna beam width, low angular resolution, and more importantly, it is difficult to detect due to the so-called "multipath" problem caused by ground and sea reflections. Low-altitude targets, and it is difficult to measure height in a multipath environment, so the height measurement problem of meter wave radar has always been a problem that has not been well solved in the radar field.

In order to better solve the problem of meter-wave altimetry, the most important technical approach is to increase the aperture of the antenna in the height dimension to reduce the beam width of the vertical plane of the antenna. For low-altitude targets, even if the aperture of the antenna in the height dimension is increased, the "multipath" problem cannot be avoided. There are three main types of technologies to solve the altimetry problem:

(1) The crossing beam method, that is, the single-frequency lobe splitting method, uses the change of the echo amplitude when the target crosses the beam to estimate the height. This method requires a long time and can only estimate the height but not measure the height.

(2) Multi-frequency lobe split altimetry method. Utilize multiple operating frequencies to work in time division, but require a wide operating bandwidth of multiple frequencies. This method is feasible in theory, but the actual system is more complicated, and there is no such practical system at present.

(3) Meter wave radar altimetry method based on lobe splitting. The phase relationship of different antenna split lobes is used to determine the elevation angle interval of the target, and the received signal is processed to extract the normalized error signal, and finally the height of the target is obtained by looking up the normalized error signal and the elevation angle interval. In 2006, Chen Boxiao et al. introduced the "meter-wave radar altimetry method based on lobe splitting" at the "Acta Electronics" and the Radar Annual Conference. This is a low-elevation altimetry method with a meter-wave radar that only needs 3 antennas in the vertical dimension. This method is only suitable for flat positions, and has high requirements for the flatness of the ground, and the measurement accuracy can only reach 1% of the distance, which is difficult to meet the actual use requirements of some high precision.

(4) Array super-resolution processing altimetry. The super-resolution technology in array signal processing is applied to distinguish direct wave signal and multipath signal. Because the direct wave signal and the multipath signal are coherent, this type of algorithm is mainly a super-resolution algorithm for estimating the DOA of the coherent source wave. Firstly, the spatial smoothing and Topelitz transform are used to solve the coherence, and then the signal subspace and noise subspace are used to solve the coherence. Space and subarray rotation invariance, etc. to measure angles. For example, in February 2009, Zhao Guanghui et al. published the paper "Meter Wave Radar Low Elevation Angle Processing Algorithm Based on Differential Preprocessing" in "Journal of Electronics and Information Technology" and in August 2009, Hu Tiejun et al. "The paper "Array Interpolation Beam Domain ML Meter-Wave Radar Altimetry Method" and the paper "Research on Multi-path Model of Meter-Wave Radar Altimetry" published by Hu Xiaoqin et al. Signal synthesis model of meter-wave radar array considering multipath delay difference. This method is based on the flat position model, and there is a bottleneck at the same time, that is, to distinguish the coherent, spatially close targets.

The above-mentioned altimetry methods are only applicable to the flat position model, that is, the wave path difference between the direct wave received by each antenna and the ground reflected wave satisfies an approximate linear relationship. However, for complex radar positions, the ground emission points of each antenna in a large array fluctuate greatly, and the direct multipath path difference of each antenna does not satisfy the approximate linear relationship. Large error, no longer applicable.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the above-mentioned prior art, propose a super-resolution altimetry method based on terrain matching, eliminate the influence of non-linear direct multipath wave path difference on angle measurement, and improve the angle measurement under complex position model Accuracy and position adaptability of the radar.

In order to achieve the above purpose, the present invention calculates the direct wave path and the ground reflected wave path of different array elements through the two-dimensional coordinates of the ground reflection points of each array element, and then uses the direct wave path and the reflected wave path to construct a synthetic guide Vector super-resolution processing, the specific steps include the following:

(1) Extract the target signal from the radar echo, and perform clutter cancellation and interference cancellation processing on the target signal to obtain the target signal after cancellation;

(2) Use the beamforming method to roughly measure the elevation angle of the target signal after cancellation, and obtain the rough elevation angle of the target signal

确定最大似然的搜索范围，当

小于ψ/2时，搜索范围为0～ψ，否则搜索范围为

其中ψ表示半功率波束宽度；(3) According to the roughly measured elevation angle of the target signal

Determine the maximum likelihood search range, when

When it is less than ψ/2, the search range is 0～ψ, otherwise the search range is

where ψ denotes the half-power beamwidth;

(4) Search within the search range determined in step (3), and determine the coordinates of the ground reflection points corresponding to each array element according to the search elevation angle:

(4a) The ground altitude of the reflection area is layered according to the interval of 1 meter, and the reflection points of the array elements on each layer are calculated according to the search elevation angle;

(4b) Find the nearest reflection points on the upper and lower sides of the elevation map of the radar position, denoted as a and b;

(4c) Vertically project points a and b to the elevation map of the radar position to obtain projected points c and d, use the position elevation data between points c and d to do curve fitting, and obtain the curve cd;

(4d) Take the intersection point of the straight line ab and the curve cd as the reflection point of the array element on the undulating ground;

(5) According to the ground reflection point, calculate the direct wave path and reflected wave path of the target relative to each array element;

(6) Using the direct wave path and the reflected wave path, calculate the corresponding direct steering vector and multipath steering vector;

(7) Calculate the synthetic steering vector A _s using the direct steering vector and the multipath steering vector:

A _s =A _d +A _i ,

Where: A _d is the direct steering vector, A _i is the multipath steering vector;

(8) calculate the projection matrix of the composite steering vector A _s ;

(9) According to the projection matrix and the covariance matrix of the canceled target signal, the maximum likelihood estimation is performed to obtain the precise elevation angle of the target.

Compared with the prior art, the present invention has the following advantages:

(1) The present invention is owing to use direct wave wave path and reflected wave wave path to construct synthesis steering vector, carries out angle measurement processing by synthesis steering vector, thereby has eliminated the influence of non-linear direct multipath wave path difference on angle measurement, has improved Angle measurement accuracy;

(2) The present invention introduces the radar position altitude parameter into the angle measurement algorithm due to the use of the radar position altitude map, thereby improving the position adaptability of the radar;

(3) Since the present invention calculates the reflection points by adopting the method of altitude layering and curve fitting in the reflection area, it simplifies the calculation process of the emission points of each array element on the undulating ground and reduces the calculation amount of the algorithm.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a radar receiving signal model figure among the present invention;

Fig. 3 is a schematic diagram of calculation of ground reflection points in the present invention;

Fig. 4 is the elevation map of the radar position used in the simulation of the present invention;

Fig. 5 is the path difference diagram of each array element direct wave and ground reflected wave simulated under the ideal position model by the present invention;

Fig. 6 is the path difference diagram of each array element direct wave and ground reflected wave simulated under the model of Fig. 4 with the present invention;

Fig. 7 is a simulation diagram of the angle measurement accuracy of the high elevation angle target with the change of signal-to-noise ratio under the model of Fig. 4 by different methods;

Fig. 8 is a simulation diagram of the angle measurement accuracy of the low elevation angle target with the change of signal-to-noise ratio under the model of Fig. 4 by different methods;

FIG. 9 is a graph of processing results for measured data.

Detailed ways

The content and effects of the present invention will be described in detail below in conjunction with the accompanying drawings.

With reference to Fig. 1, the present invention comprises the steps:

Step 1: Perform clutter cancellation and interference cancellation processing on the target signal received by the radar to obtain the target signal after cancellation.

The model of radar receiving target signal in the present invention is shown in Fig. 2 . In Figure 2, a far-field narrow-band signal is incident on a uniform linear array composed of M array elements. The tilt angle of the antenna is θ _a , the height of the antenna is h _a0 , and the interval between array elements is d. Assuming the first antenna is at sea level The projection point is the coordinate origin, point D is the ground projection point of the mth array element, point E is the ground projection point of the target, a _e is the equivalent earth radius, R _t is the target distance, θ is the search elevation angle, and point C is The center of the earth, point A is the mth array element, the horizontal and vertical coordinates of point A are h _ax (m) and _hay (m) respectively, point T is the target, and the horizontal and vertical coordinates of point T are h _tx and h _ty , G(m) represents the horizontal distance between point D and point E, where:

h _ax (m)=-d(m-1)cosθ _a , m=1, 2L, M

h _ay (m)=h _a0 +d(m-1)sinθ _a , m=1, 2L, M

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; tx</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; [</span>\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ty</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="R\; t"\; filenames="HDA0000060847400000042.png,HDA0000060847400000051.png"\; state="\{\{state\}\}">R</figure-callout></span><figure-callout\; id="2"\; label="R\; t"\; filenames="HDA0000060847400000042.png,HDA0000060847400000051.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">t</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ty</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ]</span>$

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ty</span>}}<span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}$

G(m)=h _tx -h _ax (m);

Point B is the ground reflection point of the target corresponding to the mth array element. The horizontal coordinates and vertical coordinates of point B are h _bx (m) and h _by (m) respectively. The wave lengths are R _d (m) and R _i (m) respectively, R _i (m) = R ₁ (m) + R ₂ (m), R ₁ (m) and R ₂ (m) are points B and The distance from point A and the distance from point B to point T.

From the signal model in Figure 2, the target signal x(m) received by the mth array element is obtained

x(m)= _xd (m)+ _xi (m)+c(m)+g(m)+n(m), m=1, 2L, M

x_i(m)为目标反射波信号，

c(m)为杂波信号，g(m)为干扰信号，n(m)为均值为零、方差为σ²的高斯白噪声，s为雷达发射信号，к为波数，Γ为地面反射系数。Among them: x _d (m) is the target direct wave signal,

x _i (m) is the target reflected wave signal,

c(m) is clutter signal, g(m) is interference signal, n(m) is Gaussian white noise with zero mean and variance ^σ2 , s is radar transmission signal, к is wave number, Γ is ground reflection coefficient .

The clutter and interference are canceled by adaptive filtering for x(m), and the target signal after cancellation is obtained

The target signal after cancellation is represented by vector X as:

Among them: the superscript T means transpose.

Step 2: Use the beamforming method to roughly measure the elevation angle of the target signal after cancellation, and obtain the rough elevation angle of the target signal

Among them: arg max is to find the parameter with the maximum score, abs is the modulo operation,

к表示波数，M表示阵元个数，R为对消后信号的协方差矩阵，R＝XX^H，上标T表示转置，上标H表示共轭转置，X为对消后目标信号矢量。

к indicates the wave number, M indicates the number of array elements, R is the covariance matrix of the signal after cancellation, R=XX ^H , superscript T indicates transpose, superscript H indicates conjugate transpose, X is the target signal after cancellation vector.

确定最大似然的搜索范围，当

小于ψ/2时，搜索范围为0～ψ，否则搜索范围为

其中ψ表示半功率波束宽度。Step 3: According to the rough measurement of the elevation angle of the target signal

Determine the maximum likelihood search range, when

When it is less than ψ/2, the search range is 0～ψ, otherwise the search range is

where ψ denotes the half-power beamwidth.

Step 4: Search within the search range determined in step (3), and determine the coordinates of the ground reflection points corresponding to each array element according to the search elevation angle.

Since the reflection point is located on the altitude map of the position, and the altitude map of the position is difficult to use mathematical expressions, the coordinates of the reflection point are not easy to solve directly. Here, the method of altitude layering and curve fitting is used to solve it. The solution steps refer to Figure 3. Including the following:

(4a) The ground elevation of the reflection area is layered at intervals of 1 meter, and the horizontal coordinate h _x (m, n) and vertical coordinate h _y (m, n) of the reflection point of the array element on each layer are calculated according to the search elevation angle, as shown in Fig. In 3, the horizontal axis represents the horizontal distance from the radar position, the vertical axis represents the altitude, the shadow represents the altitude of the radar position, the horizontal dotted line represents the altitude layer, and + represents the reflection point of the array element on each layer:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\frac{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ax</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}$

h _y (m, n)=n-1, m=1, 2, L, M, n=1, 2, L, N

a_e为等效地球半径，h_ay(m)为第m个阵元的垂直坐标，h_ty为目标的垂直坐标；Among them: m represents the mth array element, M represents the number of array elements, n represents the nth layer of the reflection area altitude stratification, N is the ground altitude fluctuation height of the reflection area, h _x (m, n) and h _y (m , n) are the horizontal and vertical coordinates of the reflection point of the mth array element on the nth layer respectively, G(m) is the ground horizontal distance between the target and the mth array element, h _ax (m) is the mth array The horizontal coordinate of the element, p is a temporary variable, ξ is a temporary variable,

a _e is the equivalent earth radius, h _ay (m) is the vertical coordinate of the mth array element, h _ty is the vertical coordinate of the target;

(4b) Find the nearest reflection points on the upper and lower sides of the elevation map of the radar position, denoted as a and b;

(4c) Vertically project point a and point b onto the elevation map of the radar position to obtain projected points c and d. The vertical dotted line in Fig. 3 represents the vertical projection, and use the position elevation data between point c and point d for curve fitting. get the curve cd;

(4d) The intersection of the straight line ab and the curve cd is used as the reflection point of the array element on the undulating ground.

Step 5: According to the ground reflection point, calculate the direct wave path R _d (m) and reflected wave path R _i (m) from the target to each array element by the following trigonometric formula:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ty</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ty</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}$

R _i (m) = R ₁ (m) + R ₂ (m), m = 1, 2, L, M

Where: m represents the mth array element, M represents the number of array elements, R _d (m) is the direct wave path from the target to the mth array element, _hay (m) is the vertical coordinate of the mth array element , a _e is the equivalent earth radius, h _ty is the vertical coordinate of the target, G(m) is the ground horizontal distance between the target and the mth array element, R _i (m) is the reflected wave from the target to the mth array element Wavelength, R ₁ (m) is the distance between the m-th array element and the ground reflection point corresponding to the m-th array element, R ₂ (m) is the distance between the target and the m-th array element corresponding to the ground reflection point,

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; by</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; by</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ax</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; by</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ty</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; by</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ty</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ax</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$

h _bx (m) and h _by (m) are the horizontal and vertical coordinates of the mth array element corresponding to the ground reflection point, and h _ax (m) is the horizontal coordinate of the mth array element.

Step 6: Using the direct wave path R _d (m) and the reflected wave path R _i (m), calculate the corresponding direct steering vector A _d (θ) and multipath steering vector A _i (θ):

A _d (θ) = [a _d (1), a _d (2), L, a _d (M)] ^T

A _i (θ) = [a _i (1), a _i (2), L, a _i (M)] ^T

m＝1，2，L，M，m表示第m个阵元，M表示阵元个数，к表示波数，Γ为地面反射系数，上标T表示转置。in:

m=1, 2, L, M, m represents the mth array element, M represents the number of array elements, к represents the wave number, Γ represents the ground reflection coefficient, and the superscript T represents transposition.

Step 7 _: Calculate the composite steering vector A s (θ) using the direct steering vector A _d (θ) and the multipath steering vector A _i (θ):

A _s (θ)＝A _d (θ)+A _i (θ)

Where: θ is the search elevation angle.

Step 8: Compute the projection matrix P(θ) of the synthetic steering vector using the synthetic steering vector A _s (θ):

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>$

Where: θ is the search elevation angle, superscript H means conjugate transpose, and superscript -1 means matrix inversion.

Step 9: Perform maximum likelihood estimation according to the projection matrix and the covariance matrix of the canceled target signal to obtain the precise elevation angle of the target:

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; tr</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; ]</span>$

Among them: θ is the precise elevation angle of the target, arg max is to find the parameter with the maximum score, tr is the matrix trace, P(θ) is the projection matrix, and R is the covariance matrix of the signal after cancellation.

The effects of the present invention can be further illustrated by the following simulation results and measured data processing results.

1. Simulation environment and conditions

The simulation environment uses the elevation map of the radar position shown in Figure 4. The horizontal axis represents the horizontal distance from the radar position, the vertical axis represents the altitude, and the shade represents the altitude of the radar position. The radar position is undulating terrain within 450 meters horizontally, and sea level beyond 450 meters horizontally.

The simulation conditions are the following radar parameters: the height of the antenna is 6 meters, the inclination angle is 6°, the number of array elements is 22, the interval between array elements is half a wavelength, and the number of snapshots is 10.

2. Simulation content

Simulation 1, using the present invention to simulate the path difference between the direct wave and ground reflected wave of each array element under the ideal position model, the simulation result is shown in Figure 5. The horizontal axis represents the change of target altitude from 1000 meters to 15000 meters, and the vertical axis represents the wave path difference between the direct wave and the ground reflected wave. Figure 5 shows the distance between the target and the radar at a horizontal distance of 50 km, and the altitude of the target varies along the horizontal axis. From Figure 5, it can be concluded that under the ideal position model, the wave path difference between the direct wave and the ground reflected wave of each array element satisfies a linear change.

Simulation 2, using the present invention to simulate the path difference between the direct wave and the ground reflected wave of each array element under the model shown in Fig. 4, and the simulation result is shown in Fig. 6 . The horizontal axis represents the change of target altitude from 1000 meters to 15000 meters, and the vertical axis represents the wave path difference between the direct wave and the ground reflected wave. Figure 6 shows the distance between the target and the radar at a horizontal distance of 50 km, and the altitude of the target varies along the horizontal axis, and the wave path difference between the direct wave and the ground reflected wave of the 1st, 6th, 11th, 16th and 22nd array elements. From Figure 6, it can be concluded that under the undulating position model, the wave path difference between the direct wave and the ground reflected wave of each array element does not satisfy the linear change.

In simulation 3, using the existing beamforming algorithm, forward-backward spatial smoothing MUSIC algorithm and the present invention to simulate the angle measurement accuracy of the high elevation target under the model in Figure 4, the simulation results are shown in Figure 7. The horizontal axis represents the change of the signal-to-noise ratio from -5 decibels to 15 decibels, and the vertical axis represents the angle measurement error. The target parameters selected for simulation: the target elevation angle is 4 degrees, the distance between the target and the radar is 50 kilometers, and the number of Monte Carlo experiments is 100 times. In Fig. 7, DBF represents the angular measurement error of the beamforming algorithm when the signal-to-noise ratio varies according to the horizontal axis, SSMUSIC represents the angular measurement error of the forward-backward spatial smoothing MUSIC algorithm when the signal-to-noise ratio varies according to the horizontal axis, and GSVML represents the angular measurement error of the present invention when the signal-to-noise ratio varies according to the horizontal axis. Angular error as the noise ratio varies along the horizontal axis. It can be concluded from Fig. 7 that the angle measurement error of the existing beamforming algorithm and the forward-backward spatial smoothing MUSIC algorithm for high elevation targets is relatively large, while the angle measurement error of the present invention is the smallest.

In simulation 4, using the existing beamforming algorithm, forward-backward spatial smoothing MUSIC algorithm and the present invention to simulate the angle measurement accuracy of the low-elevation-angle target under the model shown in Figure 4, the simulation results are shown in Figure 8. The horizontal axis represents the change of the signal-to-noise ratio from -5 decibels to 15 decibels, and the vertical axis represents the angle measurement error. The target parameters selected for simulation: the target elevation angle is 1 degree, the distance between the target and the radar is 200 kilometers, and the number of Monte Carlo experiments is 100 times. In Fig. 8, DBF represents the angular measurement error of the beamforming algorithm when the signal-to-noise ratio varies according to the horizontal axis, SSMUSIC represents the angular measurement error of the forward-backward spatial smoothing MUSIC algorithm when the signal-to-noise ratio varies according to the horizontal axis, and GSVML represents the angle measurement error of the present invention when the signal-to-noise ratio varies according to the horizontal axis. Angular error as the noise ratio varies along the horizontal axis. It can be concluded from Fig. 8 that the angle measurement error of the existing beamforming algorithm and the forward-backward spatial smoothing MUSIC algorithm for low-elevation targets is relatively large, while the angle measurement error of the present invention is the smallest.

3. The angle measurement results of the measured data of a warning radar

The altitude map of the warning radar position is shown in Figure 9(a), where the horizontal axis represents the horizontal distance from the radar position, the vertical axis represents the altitude, and the solid line represents the altitude of the radar position. The level of the radar position is within 6 kilometers. Terrain, 6 kilometers away from the horizon is sea level.

Use the existing beamforming algorithm, the forward and backward spatial smoothing MUSIC algorithm and the present invention to measure the angle of the warning radar measured data, the angle measurement processing results are shown in Figure 9 (b), where the horizontal axis represents the distance between the target and the position , the vertical axis represents the angle measurement error when the distance varies with the horizontal axis. In Figure 9(b), DBF represents the angle measurement error of the beamforming algorithm, SSMUSIC represents the angle measurement error of the forward-backward spatial smoothing MUSIC algorithm, and GSVML represents the angle measurement error of the present invention. It can be concluded from Fig. 9(b) that the angle measurement error of the existing beamforming algorithm and the forward-backward spatial smoothing MUSIC algorithm is relatively large, while the angle measurement error of the present invention is the smallest.

Claims (6)

1. the digital array metre wave radar super-resolution based on terrain match is surveyed high method, may further comprise the steps:

(1) from radar return, extracts echo signal, and this echo signal is carried out clutter the slake interference cancellation is handled, obtain offseting the back echo signal;

(2) use the wave beam forming method to carry out elevation angle bigness scale to offseting the back echo signal, obtain the bigness scale elevation angle of echo signal

(3) according to the bigness scale elevation angle of echo signal

Determine the hunting zone of maximum likelihood, when

Less than ψ/2 o'clock, the hunting zone is 0～ψ, otherwise the hunting zone is Wherein ψ represents half-power beam width;

(4) search in the hunting zone that step (3) is determined, according to the search elevation angle, determine the ground return point coordinate of each array element correspondence:

(4a) with ground, echo area height above sea level according to 1 meter at interval layering, according to the search elevation angle, calculate the reflection spot of array element on each layer, be to be undertaken by following formula:

$h_x(m,n)=\frac{G\left(m\right)}{2}-p\sin \frac{\mathrm{\&xi;}}{3}+h_{\mathrm{ax}}\left(m\right),$ m＝1,2,...,M,n＝1,2,...,N

h _y(m,n)＝n-1,m＝1,2,...,M,n＝1,2,...,N

Wherein: m represents m array element, and M represents element number of array, and n represents the n layer of echo area height above sea level layering, and N is that ground, echo area height above sea level rises and falls highly h _x(m, n) and h _y(m n) is respectively m array element at horizontal coordinate and the vertical coordinate of n layer reflection spot, and G (m) is the horizontal range of target and m array element, G (m)=h _Tx-h _Ax(m), p is temporary variable, $p=\frac{2}{\sqrt{3}}\sqrt{a_e(h_{\mathrm{ay}}\left(m\right)+h_{\mathrm{ty}}-2n+2)+{(G\left(m\right)/2)}^2},$ ξ is temporary variable,

h _Ax(m) be the horizontal coordinate of m array element, h _TxBe the horizontal coordinate of target, $h_{\mathrm{tx}}=a_e\arccos \left[\frac{{(h_{\mathrm{ty}}+a_e)}^2+{(h_{\mathrm{ay}}\left(1\right)+a_e)}^2-R_t^2}{2(h_{\mathrm{ty}}+a_e)(h_{\mathrm{ay}}\left(1\right)+a_e)}\right],$ a _eBe equivalent earth's radius, h _Ay(m) be the vertical coordinate of m array element, h _TyBe the vertical coordinate of target,

$h_{\mathrm{ty}}=\sqrt{{(h_{\mathrm{ay}}\left(1\right)+a_e)}^2+R_t^2-2(h_{\mathrm{ay}}\left(1\right)+a_e)R_t\cos (\mathrm{\&pi;}/2+\mathrm{\&theta;})}{-a}_e,$ R _tBe target range, θ is the search elevation angle;

(4b) search the radar site height above sea level figure nearest reflection spot in both sides up and down, be designated as a and b;

(4c) a point and b point vertical projection are arrived radar site height above sea level figure, obtain subpoint c and d, utilize the position elevation data between c point and the d point to do the curve match, obtain curve cd;

(4d) with the intersection point of straight line ab and curve cd as the reflection spot of array element on rolling ground;

(5) according to the ground reflection spot, calculate target direct wave wave-path and the reflection wave wave-path of each array element relatively;

(6) utilize direct wave wave-path and reflection wave wave-path, calculate corresponding through steering vector and multipath steering vector;

(7) use through steering vector and multipath steering vector to calculate synthetic steering vector A _s:

A _s＝A _d+A _i，

Wherein: A _dBe through steering vector, A _iBe the multipath steering vector;

(8) calculate synthetic steering vector A _sProjection matrix;

(9) carry out maximal possibility estimation according to projection matrix and the covariance matrix that offsets the back echo signal, obtain the accurate elevation angle of target.

2. metre wave radar super-resolution according to claim 1 is surveyed high method, and wherein the described use wave beam of step (2) forming method carries out elevation angle bigness scale to offseting the back echo signal, is to be undertaken by following formula:

Wherein:

Be the target bigness scale elevation angle, arg max is for seeking the parameter with maximum scores, and abs is for asking modular arithmetic,

κ represents wave number, and M represents element number of array, and subscript T represents transposition, and subscript H represents conjugate transpose, and R is the covariance matrix that offsets the back signal.

3. metre wave radar super-resolution according to claim 1 is surveyed high method, and relatively direct wave wave-path and the reflection wave wave-path of each array element of the described calculating target of step (5) wherein is to be undertaken by following triangle formula:

$R_d\left(m\right)=\sqrt{{(h_{\mathrm{ay}}\left(m\right)+a_e)}^2+{(h_{\mathrm{ty}}+a_e)}^2-2(h_{\mathrm{ay}}\left(m\right)+a_e)(h_{\mathrm{ty}}+a_e)\cos (G\left(m\right)/a_e)},$ m＝1,2,...,M

R _i(m)＝R ₁(m)+R ₂(m),m＝1,2,...,M

Wherein: m represents m array element, and M represents element number of array, R _d(m) be the direct wave wave-path of m array element, h _Ay(m) be the vertical coordinate of m array element, a _eBe equivalent earth's radius, h _TyBe the vertical coordinate of target, G (m) is the horizontal range of target and m array element, R _i(m) be the reflection wave wave-path of m array element, R ₁(m) be the distance of m array element and m array element corresponding ground reflection spot, R ₂(m) be the distance of target and m array element corresponding ground reflection spot,

$R_1\left(m\right)=\sqrt{{(a_e+h_{\mathrm{by}}\left(m\right))}^2+{(a_e+h_{\mathrm{ay}}\left(m\right))}^2-2(a_e+h_{\mathrm{by}}\left(m\right))(a_e+h_{\mathrm{ay}}\left(m\right))\cos ((h_{\mathrm{bx}}\left(m\right)-h_{\mathrm{ax}}\left(m\right))/a_e)},$

$R_2\left(m\right)=\sqrt{{(a_e+h_{\mathrm{by}}\left(m\right))}^2+{(a_e+h_{\mathrm{ty}})}^2-2(a_e+h_{\mathrm{by}}\left(m\right))(a_e+h_{\mathrm{ty}})\cos ((G\left(m\right)-h_{\mathrm{bx}}\left(m\right)+h_{\mathrm{ax}}\left(m\right))/a_e)},$ h _Bx(m) and h _By(m) be respectively horizontal coordinate and the vertical coordinate of m array element corresponding ground reflection spot, h _Ax(m) be the horizontal coordinate of m array element.

4. metre wave radar super-resolution according to claim 1 is surveyed high method, and the described calculating of step (6) through steering vector and multipath steering vector accordingly wherein is to be undertaken by following formula:

A _d(θ)＝[a _d(1),a _d(2),...,a _d(M)] ^T

A _i(θ)＝[a _i(1),a _i(2),...,a _i(M)] ^T

Wherein: A _d(θ) be through steering vector, A _i(θ) be the multipath steering vector, θ is the search elevation angle,

M represents m array element, R _d(m) be the direct wave wave-path of m array element, R _i(m) be the reflection wave wave-path of m array element, Γ is ground reflection coefficent, and subscript T represents transposition, and κ is wave number.

5. metre wave radar super-resolution according to claim 2 is surveyed high method, and the described calculating projection matrix of step (8) wherein is to be undertaken by following formula:

$P\left(\mathrm{\&theta;}\right)=A_s\left(\mathrm{\&theta;}\right){\left[A_s^H\left(\mathrm{\&theta;}\right)A_s\left(\mathrm{\&theta;}\right)\right]}^{-1}{A}_s^H\left(\mathrm{\&theta;}\right)$

Wherein: P (θ) is projection matrix, and θ is the search elevation angle, A _s(θ) be synthetic steering vector, subscript H represents conjugate transpose, and subscript-1 representing matrix is inverted.

6. metre wave radar super-resolution according to claim 1 is surveyed high method, and the described calculating maximal possibility estimation of step (9) wherein is to be undertaken by following formula:

$\mathrm{\&theta;}=\arg \underset{\mathrm{\&theta;}}{\max }\mathrm{tr}\left[P\left(\mathrm{\&theta;}\right)R\right]$

Wherein: θ is the accurate elevation angle of target, and arg max is for seeking the parameter with maximum scores, and tr is that matrix is asked mark, and P (θ) is projection matrix, and R is the covariance matrix that offsets the back signal.

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