Altitude Measurement Based on Beam Split and Frequency Diversity in VHF Radar-jTB.pdf

I. INTRODUCTION

Altitude Measurement Based

on Beam Split and Frequency

Diversity in VHF Radar

With the rapid development of concealment and

ARM (antiradiation missile) technology, current radar

often experiences difficulties in tracking low-flying

targets, i.e., targets that are within a beamwidth of

the horizon. The difficulty is due to the reflections

from the surface of the Earth. In general, the

reflected energy consists of the specular and diffuse

components. The specular component is usually more

difficult to deal with since it is by far the stronger

of the two; it is highly correlated with the direct

component, and it also lies within the beamwidth

of the receiving antenna. Thus, detecting the target

of low altitude and avoiding the influence of the

multipath are becoming more challenging. Nakatsuka

[1] and Zoltowski [2] introduce multiple beams to

separate the paths respectively. Recently Boman [3]

presents a new low-angle target-tracking method

with comprehensive target models. Considering

the complex reflection over the sea, E. Bosse [4]

investigates the Swerling fluctuating targets tracking.

Recently array signal processing has been used in this

field, and much effort has been spent in developing

high-resolution techniques for direction-of-arrival

(DOA) estimation of multiple signals [5—7]. These

methods, such as the multiple signal classification

(MUSIC) [8] algorithm, min-norm [9] algorithm, are

based on the subspace, which can provide an excellent

performance at high signal-to-noise ratio (SNR), long

data records, and in a spatially uncorrelated sources

field. However, when some of the signals are fully

coherent, e.g., when the target flies at a low altitude,

the echo received contains multipath signals, and

these techniques encounter serious difficulties. The

maximum likelihood (ML) [10] method, which is

based on analyzing the joint probability distribution

of received data, can be used in the case of coherent

signals with better statistical performance than

MUSIC. However, more computation is required,

which restricts the ML algorithm from practical

applications. Motivated by computational efficiency

and the need for real-time tracking, a number of ML

estimation schemes have been proposed for low-angle

radar tracking [11]. Some other methods based on

multifrequency tracking are also underdeveloped

[4, 12]. In this paper, we propose a new method for

altitude measurement based on beam split.

In 1939, an American made the first radar, CXAM,

that could estimate the altitude of a target by using

the multipath signals. The performance of this radar is

greatly affected by many aspects such as the condition

of the sea, the reflection of the atmosphere, and the

SCR of the target. During World War II, a new set of

radar called CH was built in England which measures

the altitude of a target by comparing the amplitude

of the main beams of two receiving antennas. By

switching in aerials mounted at different heights above

BAIXIAO CHEN

GUANGHUI ZHAO

SHOUHONG ZHANG

Xidian University

China

A new beam split altitude interferometry based on altitude

diversity and frequency diversity for very high frequency (VHF)

radar is proposed in this paper. As opposed to microwave radar,

VHF radar has a wide beam which is usually split when ground

reflection occurs. The reflected wave which is coherent with the

direct wave will always be contained in the target echo. In this

paper, several antennas of different heights are utilized. Owing to

the certain relationship among the phases of the split beams, the

elevation region where the targets are located can be determined

using the phases of echoes. Using “amplitude-comparison”

of echoes from various antennas to get the normalized error

signals, the elevation of the target can be obtained by looking

it up in the error signal table. The effect of roughness on the

altitude measurement accuracy is also analyzed. The real data

processing on flat and slope terrains testifies to the validity of the

proposed method. The altitude measurement precision, especially

in low-elevation regions, is greatly improved by using frequency

diversity.

Manuscript received September 17, 2006; revised August 2, 2007,

January 26, May 27, and July 11, 2008; released for publication

July 18, 2008.

IEEE Log No. T-AES/46/1/935925.

Refereeing of this contribution was handled by P. Lombardo.

This work was supported by the National Science Foundation of

China under Grant 60772068 and the Program for New Century

Excellent Talents in University under Grant NCET-06-0856.

Authors’ addresses: B. Chen and S. Zhang, National Lab for Radar

Signal Processing, Xidian University, Xi’an, Shaanxi, China; G.

Zhao, Intelligent Perception and Image Understanding Key Lab of

Ministry of Education, Xidian University, Xi’an, Shannxi 710071,

China, E-mail: (ghzhao@mail.xidian.edu.cn).

0018-9251/10/$26.00 ° 2010 IEEE

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in with only one receive antenna. Here three sets of

antennas located in high, medium, and low positions

are used to measure altitude. As shown in Fig. 1, O 1 ,

O 2 ,and O 3 are the three receiving antennas whose

heights are H 1 , H 2 ,and H 3 , respectively, while the

transmit antenna is placed next to O 2 . Suppose that

the height of the target is H T , the elevation is ¯ ,and

the horizontal distance from the target to the antenna

is R 0 . We can then obtain H T = R 0 tan ¯ ÀH i and

R 2 = R 0 + H T . According to geometry,

R 0, i =

R 0 +( H T ¡H i ) 2 =

R 0 + H T + H i ¡ 2 H T H i

Fig. 1. Multipath geometry for low-altitude target in flat plane.

1+ H i ¡ 2 H T H i

R 2

= R

the ground, the angle of elevation of the echo signal

is assessed, and when combined (automatically by

an electrical calculator) with the measured range,

the aircraft’s height is calculated [13]. However, the

method is inapplicable when the target flies low in the

far field.

Because of its long wavelength, very high

frequency (VHF) radar has particular advantages

in anticoncealment and anti-ARM. Recently much

attention has again been paid to the development of

VHF radar [14] systems all over the world. However,

thewidebeamofVHFradarwillbesplitdueto

the ground reflection, so this kind of radar can only

be used to estimate altitude roughly. It has been a

challenge to enhance the capability of VHF radar to

measure altitude accurately.

Many methods have been developed to avoid the

effect of multipath, an effect which, on the contrary,

is employed here. Because antennas at different

heights have different split beams that are related

to one another in phase, we adopt what we call a

“phase and amplitude comparison” [15] method to

measure the altitude. This paper presents the principle

of this method in detail, and analyzes its performance

and the influence of surface roughness. Finally both

simulation and experimental results are presented.

The paper is organized as follows. In Section II

we present the beam split phenomenon. In Section III

we propose the method for altitude measurement

based on beam split in VHF radar. In Section IV we

analyze the performance of the method. In Section V

we present the influence of SNR on the accuracy of

altitude measurement. In Section VI the experimental

results are given. And in Section VII a brief summary

is made.

1+ H i ¡ 2 H T H i

2 R 2

¼R

( *H i ¿H T )

1 ¡H i H T

¼R

R 2

= R¡H i sin ¯ , i =1—3 (1)

R 1, i =

R 0 +( H T + H i ) 2 =

R 0 + H T + H i +2 H T H i

= R

1+ H i +2 H T H i

R 2

1+ H i +2 H T H i

2 R 2

¼R

( *H i ¿H T )

H T

R 2

¼R

1+ H i

= R + H i sin ¯ , i =1—3 (2)

where R 0, i denotes the direct path and R 1, i ( i =1,2,3)

the multipath.

The difference between R 0, i and R 1, i is

d R , i = R 1, i ¡R 0, i ¼ 2 H i sin ¯:

(3)

Taking the influence of the reflected wave into

consideration, the pattern with respect to elevation ¯

¡j 4 ¼

F i ( ¯ )= F ( ¯ 0 )+ ¡F ( ¯ i )exp

¸ H i sin ¯

(4)

where ¸ is the wavelength and ¡ = ½ r exp( jÁ r )isthe

reflectance of ground. For horizontal polarization

and flat ground, ¡ = ¡ 1, ½ r =1, Á r = ¼ ; F ( ¯ )isthe

elevation pattern function without considering the

influence of the reflected wave, and the antenna is

composed of 8 log periodic dipole antenna elements

of horizontal polarization. Fig. 2 is the elevation

pattern of direct wave of one of the antennas, where

the longest element length is 1.5 m, the shortest

element length is 0.5 m, the scaling factor ¿ is 0.86,

andthespacingfactor ¾ is 0.1. ¯ 0 and ¯ 1 are the

direction of the direct wave and the reflected wave,

respectively. For wide beam, the gain is approximately

constant, i.e., F ( ¯ 0 ) ¼F ( ¯ 1 ), in the vicinity of zero

degree. In far field, if the antenna is far lower than the

II. BEAM SPLIT PHENOMENON

A beam must be sensitive to elevation when it is

used to measure altitude. It is possible for VHF radar

to measure altitude because beam split makes each

beam narrow. More than one antenna should be used

because we cannot decide which beam the echo is

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F i ( ¯ )is Á i or ¼ + Á i respectively, 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

Fig. 2. Elevation pattern of direct wave.

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

U i ( ¯ )=[exp( ¡jkR 0, i )+ ¡ exp( ¡jkR 1, i )] F ( ¯ )

¼ exp( ¡jk¢R ) ¢F ( ¯ )[1 ¡ exp( ¡j 2 k¢H i sin( ¯ ))]

= F ( ¯ ) ¢ 2sin( k¢H i sin( ¯ ))exp( jÁ i )

( 7 )

where k =2 ¼=¸ is the wave number and

Á i = ¼

(8)

Fig. 3. Beam patterns of antennas.

If 0 <k¢H i sin ¯<¼ , i.e., 0 < sin ¯<¸= 2 H i ,the

phase difference between two receiving antennas is

Á 1,2 = © [ U 1 ( ¯ )] ¡© [ U 2 ( ¯ )] ¼k ( H 2 ¡H 1 )sin ¯ (9)

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

that the phase difference can be used to determine

elevation ¯ . But in the case of ¸ =1 : 7m, H i =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 i or ¼ + Á i ,

so the phase difference Á 0 1,2 between two antennas is

Á 1,2 or §¼ + Á 1,2 .Thevariable Á 0 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 0 1,2 is in. Then we can get

target and ¯ 0 ¼¯ , (4) can be written as

¶¸

¡j 4 ¼

F i ( ¯ )= F ( ¯ )

1 ¡ exp

¸ H i sin ¯

2 ¼

¸ H i sin ¯

= F ( ¯ ) ¢ 2sin

e jÁ i

(5)

1, cos( Á 0 1,2 ) ¸ 0

0, cos( Á 0 1,2 ) < 0 :

¯ ¯ ¯ ¯

2 ¼

¸ H i sin ¯

¶¯ ¯ ¯ ¯

C 1,2 =sign[cos( Á 0 1,2 )]=

jF i ( ¯ ) j = F ( ¯ ) ¢ 2

sin

(6)

(10)

where Á i = ¼= 2 ¡ (2 ¼=¸ ) H i sin ¯ . We can find from (5)

and (6) the following.

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 C 1,2 C 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.

1) When (2 ¼=¸ ) H i sin ¯ = n¼ ( n is an integer),

jF i ( ¯ ) j =0, and the beam splits; when (2 ¼=¸ ) H i sin ¯ =

((2 n +1) = 2) ¼ , F i ( ¯ ) reaches its maximum, and it

is obvious that F i ( ¯ ) is related to the height of the

antenna and the wavelength.

2) When the phase 2 ¼¢H i sin ¯=¸ is within the

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

means sin ¯ is within the range of ( n¸=H i ,(2 n +1) ¸=

2 H i )or((2 n +1) ¸= 2 H i ,( n +1) ¸=H i ), the phase of

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2 ¡k¢H i sin ¯¡k¢R:

TABLE I

Elevation Code

C 1,2 C 1,3 C 2,3

Elevation

111

0 : 5 deg—4 deg

1 0 0

4 deg—6 : 6deg

001

6 : 6 deg—8 deg

0 1 0

8 deg—11 : 5deg

jU 1 ( ¯ ) j 2 + jU 2 ( ¯ ) j 2 : (11)

Substituting (7) into (11) we get

E 12 ( ¯ )= sin 2 ( Μ 1 ) ¡ sin 2 ( Μ 2 )

Fig. 4. Error curves.

sin 2 ( Μ 1 )+sin 2 ( Μ 2 )

the elevation ¯ is around 4 deg, because the error

E 13 peaks at about 4 : 3degandthesensitivityistoo

low. In different intervals, we should select the error

curves with higher gradient with which to measure

elevation. Sometimes we can combine two or even

three curves together to improve the precision of the

altitude measurement.

The method presented above is feasible on

condition that:

sin( k ( H 1 + H 2 )sin ¯ )sin( k ( H 1 ¡H 2 )sin ¯ )

1 ¡ cos( k ( H 1 + H 2 )sin ¯ )cos( k ( H 1 ¡H 2 )sin ¯ )

(12)

where Μ 1 = k¢H 1 sin ¯ , Μ 2 = k¢H 2 sin ¯ .

Similarly, we can get error signals E 13 ( ¯ )and

E 23 ( ¯ ). Before we estimate the altitude of the target,

an error curve plot should be first generated according

to the wavelength, the heights of the antennas and

the range of the elevation (0 : 5deg <¯< 11 : 5deg).

Then the amplitudes of every two antennas should be

computed. From (12) we get the error curve, and then

the elevation of the target can be obtained by selecting

the appropriate curve. Fig. 4 shows the error curves

E 12 ( ¯ ), E 13 ( ¯ ), and E 23 ( ¯ ), respectively. As error

signal is unique in each elevation interval, we should

decide which one or two error curves and which parts

of them can be used according to elevation code. For

example, if ¯< 4 deg, error signal E 13 can be used.

However, E 12 rather than E 13 should be used when

1) all antennas have the same radiation pattern

F ( ¯ ),

2) all receive channels are identical,

3) the terrain where the radar is set is flat, and the

reflected point and the radar are in the same plane.

As discussed above, the flow for altitude

measurement based on reflected wave of several

antennas is shown in Fig. 5, where the front-end

processing includes receiving, analog to digital

converter (ADC), and coherent integration. The

detailed signal processing is as follows.

Fig. 5. Flow chart of altitude measurement.

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After determining the elevation code, we propose

to compare the amplitudes of signals from different

antennas. By using (11) we get an error signal

E 12 ( ¯ )= jU 1 ( ¯ ) j 2 ¡jU 2 ( ¯ ) j 2

Fig. 6. Reflectance of rough surface and deviation of elevation measurement. (a) Relation between roughness and reflectance.

(b) Error of measurement by ground fluctuation.

1) Equation (12) is used to create an elevation

error curve plot according to operating frequency of

radar, heights of antennas, and terrain conditions.

2) The channels are equalized by inputting test

signal to the three channels when the radar is at rest.

3) Equation (10) is used to calculate the elevation

code C 13 , C 12 ,and C 23 andthentoestimatewhich

elevation intervals the target is in.

4) The amplitude responses of every two channels

are compared, and (11) is used to get the error signals.

5) The elevation of the target is obtained by

looking up the elevation error curve.

6) Considering the curvature radius of the Earth,

the altitude of the target is

H ¼R 0 ¢ sin ¯ + H a + R 0

where ½ 0 is the reflectance of smooth ground and

½ 0 =1, Ã is the graze angle, k =2 ¼=¸ ,and I 0 ( x )is

the zero-th order modified Bessel function. Defining

roughness as D =( ¾ h sin Ã ) =¸ , the relationship

between roughness and ground reflectance is shown

in Fig. 6(a). The corresponding error curve is

E 12 ( ¯ )

2 ½ r sin( k ( H 1 + H 2 )sin ¯ )sin( k ( H 1 ¡H 2 )sin ¯ )

1+ ½ r ¡ 2 ½ r cos( k ( H 1 + H 2 )sin ¯ )cos( k ( H 1 ¡H 2 )sin ¯ ) :

(15)

The reflected wave, regarded as the integral of

echo signal in the area irradiated by sidelobe, is

known as

(13)

2 R e

U i ( ¯ )=exp( ¡jkR 0, i )+

¡ exp( ¡jk¢R 1, i ) d−:

where R e is the radius of the Earth, H a is the height

of the antenna, and R 0 is the horizontal distance from

target to antenna.

−

(16)

The error of elevation measurement caused by

ground fluctuation is shown in Fig. 6(b), where

abscissa is the rms error ¾ h . It is obvious that the

deviation in elevation can reach 0 : 15 deg when surface

roughness is 2 m. In order to assure the accuracy of

altitude measurement, the radar should be placed on a

flat floor. For cases of 3) and 4), the radar is located

in a slope position which is shown in Fig. 7. In Fig. 7,

Μ denotes the tilt angle of the slope relative to the

horizontal level; the heights of antennas are H i ;the

altitude of the center of the ground reflection is d ,

which is far smaller than H T ; the horizontal distance

from antenna location to the reflect center is R B ;

and the graze angle is Ã . According to geometrical

relation, we get

tan Ã = H i ¡d

R B

IV. PERFORMANCE ANALYSIS FOR ALTITUDE

MEASUREMENT

Altitude measurement method based on ground

reflection is influenced greatly by the ground features.

Four cases are discussed here: 1) surface roughness

is rather small in flat ground; 2) surface roughness

is rather great in flat ground; 3) surface roughness

is rather small in sloped ground; and 4) surface

roughness is rather great in sloped ground. For 1) and

2) the centers where the primary lobes of antennas

are reflected lie in the same horizontal level; only the

roughness where the sidelobes irradiate is different.

Assuming that the mean of ground level h is zero and

the rms value of ground level is ¾ h , we can get the

mean ground reflectance of rough surface [16, 17]:

= H t + H i

R 0

¼ tan ¯

(17)

R B ¼ H i ¡d

½ r = ½ 0 exp( ¡ 2 k 2 ¾ h sin 2 Ã ) ¢I 0 ( k 2 ¾ h sin 2 Ã ) (14)

tan ¯

(18)

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