基于迭代子空间投影的低海拔VHF雷达目标高度测量提升技术

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本文探讨了一种创新的低海拔目标高度测量方法，名为基于迭代子空间投影的时空通用MUSIC算法（TS-GMUSIC）。在传统的时空处理基础上，研究者采用了交替投影（AP）理论，与常规的将方向矢量逐次投影来估算角度不同，该方法将接收的回波映射到不同的信号子空间，从而实现对目标仰角的精确估计。这种方法的一大优点是能够简化多目标的常规方向搜索，将它们归结为单一目标参数的联合估计，提高了效率。针对低海拔目标的特性，特别是多径效应，研究者特别考虑到了直接波和镜面波的特性。在VHF雷达系统中，由于宽波束在地面反射时通常会被分裂，反射波与直达波会同时存在于目标回波中。通过利用不同高度天线之间的相位关系，可以确定目标所在的仰角区域。利用不同天线接收的回波幅度比较，结合标准化误差信号，可以直接查找误差信号表获取目标的高度信息。论文进一步分析了粗糙地形对高度测量精度的影响，指出该方法对于平坦和斜坡地形的数据处理结果表明其有效性。通过蒙特卡洛仿真，TS-GMUSIC相较于现有时空算法在低海拔高度测量方面的性能得到了显著提升。这对于VHF雷达在实际应用中的高度精确测量具有重要意义，尤其是在需要处理复杂环境和多目标情况下，该方法展现出了其独特的优势和实用性。总结来说，本文的研究不仅提供了一个新颖的信号处理技术，还展示了如何在VHF雷达系统中有效地解决低海拔目标高度测量的问题，具有很高的工程价值和理论贡献。通过结合子空间投影和多元波束技术，TS-GMUSIC方法有望提高雷达系统的定位精度和鲁棒性，为未来的无线通信和导航领域带来新的突破。

Fig. 2. Elevation pattern of direct wave.

Fig. 3. Beam patterns of antennas.

target and ¯

¼ ¯, (4) can be written as

(¯)=F(¯)

1 ¡ exp

¡j

4¼

sin¯

¶¸

= F(¯) ¢ 2sin

2¼

sin¯

jÁ

(5)

(¯)j = F(¯) ¢ 2

sin

2¼

sin¯

(6)

where Á

= ¼=2 ¡ (2¼=¸)H

sin¯. We can find from (5)

and (6) the following.

1) When (2¼=¸)H

sin¯ = n¼ (n is an integer),

(¯)j = 0, and the beam splits; when (2¼=¸)H

sin¯ =

((2n +1)=2)¼, F

(¯) reaches its maximum, and it

is obvious that F

(¯) is related to the height of the

antenna and the wavelength.

2) When the phase 2¼ ¢ H

sin¯=¸ is within the

range [2n¼,(2n +1)¼] or [(2n +1)¼,(2n +2)¼], which

means sin ¯ is within the range of (n¸=H

,(2n +1)¸=

)or((2n +1)¸=2H

,(n +1)¸=H

), the phase of

(¯)isÁ

or ¼ + Á

respecti vely, which we call the

“180 deg out-of-phase” relationship between the

adjacent split beams. Such a relationship is shown

in Fig. 3, where the heights of the antennas are 4 m,

7 m, and 12 m, respectively. Here the symbols “+”

and “¡” are used to express the two phases which

have the out-of-phase relationship. It is obvious that

the wave crest and the wave trough of each beam have

been staggered.

III. METHOD FOR ALTITUDE MEASUREMENT BASED

ON BEAM SPLIT IN VHF RADAR

Assume that the height difference between

antennas is far smaller than the range resolution, the

baseband signal model for the combined direct and

reflected beam in the far field is

(¯) = [exp(¡jkR

0,i

)+¡ exp(¡jkR

1,i

)]F(¯)

¼ exp(¡jk¢ R) ¢ F(¯)[1 ¡ exp(¡j2k ¢ H

sin(¯))]

= F(¯) ¢ 2sin(k ¢ H

sin(¯))exp(jÁ

)(7)

where k =2¼=¸ is the wave number and

¡ k ¢ H

sin¯ ¡ k ¢ R: (8)

If 0 <k¢ H

sin¯<¼, i.e., 0 < sin ¯<¸=2H

,the

phase difference between two receiving antennas is

1,2

= ©[U

(¯)] ¡ ©[U

(¯)] ¼ k(H

¡ H

)sin¯ (9)

where ©[x] denotes the phase of x.From(9)wesee

that the phase difference can be used to determine

ele vation ¯. But in the case of ¸ =1:7m,H

=12m,

and ¯<4 deg, it is difficult to measure the angle

directly because the elevation range is limited.

To measure the altitude of the target efficiently,

we should first estimate which split beam or altitude

range the target is in. From (7) and (8) we find that

the phase of the receiving antennas are Á

or ¼ + Á

so the phase difference Á

1,2

between two antennas is

1,2

or §¼ + Á

1,2

.ThevariableÁ

1,2

is multivalued and

cannot be used to measure the elevation of the target

directly; however, we can determine the approximate

range that Á

1,2

is in. Then we can get

1,2

= sign[cos(Á

1,2

)] =

1, cos(Á

1,2

) ¸ 0

0, cos(Á

1,2

) < 0

(10)

Similarly, we can get the phase sign between

antennas (1,3) denoted as C

1,3

, and that between

antennas (2,3) as C

2,3

. The combination of C

1,2

, C

1,3

and C

2,3

can be regarded as an elevation code, denoted

as C

1,3

1,2

2,3

for example. When the heights of the

antennas are 4 m, 7 m, 12 m, respectively, and the

carrier frequency is 180 MHz, we can calculate the

elevation code using (5) and (10), and the results are

showninTableI.For¯>11:5deg,theelevation

code becomes multivalued, a case called “subarea

ambiguity.” We mainly discuss the measurement of

low altitude targets in this paper.

CHEN ET AL.: ALTITUDE MEASUREMENT BASED ON BEAM SPLIT AND FREQUENCY DIVERSITY IN VHF RADAR 5

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