TARGET-REFLECTION CHARACTERISTICS ANO ANGULAR ACCURACY 30 · 41

TRACKING RADAR

5.5 TARGET-REFLECTION CHARACTERISTICS ANO ANGULAR ACCURACY 30 · 41

·Q5

The angular accuracy of tracking radar will be influenced by such factors as the mechanical properties of the radar antenna and pedestal, the method by which the angular position of the antenna is measured, the quality of the s~a systeQ1, the stability of the electronic circuits, the noise level of the receiver, the antenna beamwidth, atmospheric fluctuations, and the reflection characteristics of the target. These factors can degrade the tracking accuracy by causing the antenna beam to fluctuate in a random manner about the true target path. These noiselike fluctuations are sometimes called tracking noise, or jitter.

A simple radar target such as a smooth sphere will not cause degradation of the angular- tracking accuracy. The radar cross section of a sphere is independent of the aspect at which it is viewed: consequently, its echo will not fluctuate with time. The same is true, in general, of a radar beacon if its antenna pattern is omnidirectional. However, most radar targets are of a more complex nature than the sphere. The amplitude of the echo signal from a complex target may vary over wide limits as the aspect changes with respeci to the radar. In addition, the effective center of radar reflection may also change. Both of these effects-amplitude fluctua- tions and wandering of the radar center of reflection-as well as the limitation imposed by receiver noise can limit the tracking accuracy. These effects are discussed below.

Amplitude fluctuations. A complex target such as an aircraft or a ship may be considered as a number of independent scattering elements. The echo signal can be represented as the vector addition of the contributions from the individual scatterers. If the target aspect changes with respect lo the radar-as might occur because of motion of the target, or turbulence in the case of aircraft targets-the relative phase and amplitude relationships of the contributions from the individual scatterers also change. Consequently, the vector sum, and therefore the ampli- tude. change with changing target aspect.

Amplitude fluctuations of the echo signal are important in the design of the lobe- switching radar and the conical-scan radar but are of little consequence to the monopulse tracker. Both the conical-scan tracker and the lobe-switching tracker require a finite time to obtain a measurement of the angle error. This time corresponds in the conical-scan tracker to at least one revolution of the antenna beam. With lobe switching, the minimum time is that necessary lo obtain echoes at the four successive angular positions. In either case four pulse- repetition periods are required to make a measurement; in practice, many more than four are often used. If the target cross section were to vary during this observation time, the change might he erroneously interpreted as an angular-error signal. The monopulse radar, on the other hand. determines thc_ang.ular . .cr-i:OLon_the_.ba.sl~ of a single pulse. Its accuracy will therefore not be affected by changes in amplitude with time.

To reduce the effect of amplitude noise on tracking, the conical-scan frequency should be chosen to correspond toa-low·vafoe·ofamplitude noise. If considerable amplitude fluctuation noise were to appear at the conical-scan or lobe-switching frequencies, it could not he readily eliminated with filters or AGC. A typical scan frequency might be of the order of 30 Hz.

Higher frequencies might also be used since target amplitude noise generally decreases with increasing frequency. However, this may not always be true. Propeller-driven aircraft produce modulation components at the blade frequency and harmonics thereof and can cause a sub- stantial increase in the spectral energy density at certain frequencies. It has been found ex per- imentally that the tracking accuracy of radars operating with pulse repetition frequencies from

1000 to 4000 Hz and a lobing or scan rate one-quarter of the prf are not limited by echo amplitude fluctuations. ²⁹

The percentage modulation of the echo signal due to cross-section amplitude tluctuations is independent of range if AGC is used. Consequently, the angular error as a result of ampli- tude fluctuations will also be independent of range.

Angle fluctuations. ²⁹•3

°

Changes in the target aspect with respect to the radar can cause the apparent center of radar reflections to wander from one point to another. (The apparent centa of radar reflection is the direction of the antenna when the error signal is zero.) In general, the apparent center of reflection might not correspond to the target center. In fact,

it

need not he confined to the physical extent of the target and may be off the target a significant fraction of the time. The random wandering of the apparent radar reflecting center gives rise to noisy or jittered angle tracking. This form of tracking noise is called angle noise, angle scitztillations, angle fluctuations, or target glint. The angular fluctuations produced by small targets at long range may be of little consequence in most instances. However, at short range or with rela- tively large targets (as might be seen by a radar seeker on a homing missile), angular lluct ua- tions may be the chief factor limiting tracking accuracy. Angle fluctuations affect all tracking radars whether conical-scan, sequential-lobing, or monopulse.

Consider a rather simplified model of a complex radar target consisting of two indepen- dent isotropic scatterers separated by an angular distance Ou, as measured from the radar.

Although such a target may be fictitious and used for reasons of mathematical simplicity, it might approximate a target such as a small fighter aircraft with wing-tip tanks or two aircraft targets flying in formation and located within the same radar resolution cell. It is also a close approximation to the low-angle tracking problem in which the radar sees the target plus its image reflected from the surface. The qualitative effects of target glint may be assessed from this model. The relative amplitude of the two scatterers is assumed to be a, and the relative phase difference is a. Differences in phase might be due to differences in range or to rclkcting properties. The ratio

a

is defined as a number less than unity. The angular error l\O as measured from the larger of the two targets is³¹

fi() a²

+

a cos a

0 0

=

1

+

^a2

+

2a cos a.

(5.2)

This is plotted in Fig. 5.13. The position of the larger of the two scatterers corresponds to ti0/0₀

=

0, while the smaller-scatterer position is at ti0/00

= +

I. Positive values of MJ corn!- spond to an apparent radar center which lies between the two scatterers; negative values lie outside the target. When the echp signals from both scatterers are in phase (a

=

0), the error reduces to a/(a

+

1 ), which corresponds to the so-called "center of gravity" of the two scat- terers (not to be confused with the mechanical center of gravity).

Angle fluctuations are due to random changes in the relative distance from radar to the scatterers, that is, varying values of a. These changes may result from turbulenct in the aircraft

0.5 0.4 · 0.2

0 ^{a ==} 0

t::.B

Bo· -- 0.2

-

·-04 -- 0.6 '-

- 0.8 - -1.0

0 ?O <'10 60 80 100 120 140 160 180

Phase difference Cl'.'

Figure 5. IJ Plot of Eq. (5.2). Apparent radar center t10 of two isotropic scatterers of relative amplitude a and 1elativc phase shirt rx, separated by an angular extent Ov.

flight path or from the changing aspect caused by target motion. In essence, angle fluctuations are a distortion of the phase front of the echo signal reflected from a complex target and may be visualized as the apparent tilt of this phase front as it arrives at the tracking system.

Equation (5.2) indicates that the tracking error 6.0 due to glint for the two-scatterer target is directly proportional to the angular extent of the target 0_{0 .} This is probably a reasonable approximation to the behavior of real targets, provided the angular extent of the target is not too large compared with the antenna beamwidth. Since 0₀ varies inversely with distance for a fixed target size, the tracking error due to glint also varies inversely with distance.

I\ slightly more complex model than the two-scatterer target considered above is one consisting or many individual scatterers, each of the same cross section, arranged uniformly along a line or length L perpendicular to the line of sight from the radar. The resultant cross section from such a target is assumed to behave according to the Rayleigh probability distribu- tion. The prohahility or the apparent radar center lying outside the angular region of L/R radians (in dne tracking plane) is 0.134, where R is the distance to the target. ³² Thus 13.4 per- cent of the time the radar will not be directed to a point on the target. Similar results for a two-dimensional model consisting or equal-cross-section scatterers uniformly spaced over a circular area indicate that the probability that the apparent radar center lies outside this target

is 0.20.

Angle fluctuations in a tracking radar are reduced by increasing the time constant of the AGC system (reducing the bandwidth).^29·33·34 However, this reduction in angle fluctuation is accompanied by a new component of noise caused by the amplitude fluctuations associated with the echo signal; that is, narrowing the /\GC bandwidth generates additional noise in the vicinity of zero frequency, and poorer tracking results. Amplitude noise modulates the tracking-error signals and produces a new noise component, proportional to true tracking errors. that is enhanced with a slow AGC. Under practical tracking conditions it seems that a wide-bandwidth (short-time constant) AGC should be used to minimize the overall tracking noise. However, the servo bandwidth should be kept to a minimum consistent with tactical requirements in order to minimize the noise.

Receiver and servo noise. Another limitation on tracking accuracy is the receiver noise power.

The accuracy of the angle measurement is inversely proportional to the ·square root of th~

signal-to-noise power ratio. ² Since the signal-to-noise ratio is proportional to l/ R⁴ (from the radar equation), the angular error due to receiver noise is proportional to the square of the target distance.

Servo noise is the hunting action of the tracking servomechanism which results from backlash and compliance in the gears, shafts, and structures of the mount. The magnitude of

servo noise is essentially independent of the target echo and will therefore be independent of range.

Summary of errors. The contributions of the various factors affecting the tracking error are summarized in Fig. 5.14. Angle-fluctuation noise varies inversely with range; receiver noise varies as the square of the range; and amplitude fluctuations and servo noise are independent of range. This is a qualitative plot showing the gross effects of each of the factors.

Two different resultant curves are shown. Curve A is the sum of all effects and is representative of conical-scan and sequential-lobing tracking radars. Curve B does not include the amplitude fluctuations and is therefore representative of monopulse radars. In Fig. 5.1 the amplitude fluctuations are assumed to be larger than servo noise. If not, the improvement of monopulse tracking over conical scan will be negligible. In general, the tracking accuracy deteriorates at r~,both short and long target ranges, with the best tracking occurring at some intermediate range.

\ .JFrequency agility and glint reduction. ³⁵-4o,ss The angular error due to glint, which affects all tracking radars, results from the radar receiving the vector sum of the echoes contributed by the individual scattering centers of a complex target, and processing

it

as

if it

were the return from a single scattering center. If the frequency is changed, the relative phases of the individual

c..

e ...

~ 0.1

C

:.ii:

u

e

-

^c..

.E ::>

C CJ' 0

"'

E c..

~0.01 :;:

.E

(I)

a:::

I I

/ 4Receiver noise

( monopulse)

10 100

Relative radar ronge ^1,000

Figure 5.14 Relative contributions to angle tracking error due to amplitude fluctuations, angle Huctua- tions, receiver noise, and servo noise as a function or range. (A) Composite error for a conical-scan or sequential-lobing radar; (B) composite error for monopulse.

scatterers will change and a new resultant is obtained as well as a new angular measurement.

Measurements are independent if the frequency is changed by an amount³⁶

C

!!.:fc = "ii5 ^(5.3)

where c = velocity of propagation and D

=

target depth. The glint error can be reduced by averaging the independent measurements obtained with frequency agility. (The depth D as seen by the radar might be less than the geometrical measurement of target depth if the extremities of the target result in small backscatter.)

The improvement I in the tracking accuracy when the frequency is changed pulse-to-pulse is approximately³⁷

(5.4)

where B fa= the frequency agility bandwidth, D

=

target depth, c

=

velocity of propagation, B₁₁

=

glint bandwidth, and

J,.

pulse repetition frequency. (The approximation holds for large prf's and for the usual glint bandwidths which are of the order of a few hertz to several tens of hertz.)³⁶ For example. with a target depth D of 7 m and a frequency-agile bandwidth of JOO MHz, the glint error is reduced by a factor of 2.6. According to the above, the improve- m~nt in trackin~curacy is proportional to the square root of the frequency agility band- width. or I "'

,J

^{B fa .}

A different glint model, based on the assumption that the angular motion of a complex target can be described by a gaussian random yaw motion of zero mean, yields the result that the reduction in angle error due to frequency agility asymptotically approaches a value of 3.l with increasing agility bandwidth.³⁸ The model also gives the variance of the inherent glint lor a frequency-agile radar as

var= 0.142y5

(5.5)

where

ro

is the lateral radius of gyration of the collection of scatterers comprising the target.

The value of }'o for a "typical" twin-jet aircraft in level flight at near head-on or near tail-on aspect is said³⁸ to be equal to half the separation of the jet engines. For a ship at broadside,

,o

is approximately 0.15 times the ship length.

When angle errors due to glint are large, the received signals are small; that is, the received signal amplitude and the glint error are negatively correlated. Thus, by transmitting a number of frequencies and using the angle error corresponding to that frequency with the largest signal, it is possible to eliminate the large angle ~rrors associated with glint. ³⁹.4° Those returns of low amplitude and, hence, of high error, are excluded in this technique. Instead or selecting only the largest signal for processing, the indicated position of the target at each frequency can be weighted according to the amplitude of the return.⁴⁰ Only a small number of frequencies is needed to reduce substantially the glint error. The reduction in rms tracking error by processing only that signal (frequency) with the largest amplitude is approximately⁴⁰

a"

<1 rms ~ ---N 1

s

N

s

⁴

(5.6)

where ^<T₁ is the single-frequency glint error and N is the number of frequencies. The tracking error will not decrease significantly for more than four pulses. Each of the frequencies must be separated by at least

lif~,

as given by Eq. (5.3).

Frequency agility, as described here for the reduction of glint, applies to the monopulse tracking radar. It also reduces the glint in a conical scan or a sequentia.1-)obing radar. but the

changing frequency can result in amplitude fluctuations which can affect the angle tracking accuracy if the spectrum -of the fluctuations at the conical scan or the lobing frequencies is increased. Thus, frequency agility might cause an increase in the angle error due to amplitude lluctuations in these systems while decreasing the error due to glint. The ovc.:rall effect of frequency agility in conical scan or sequential lobing systems is therefore more complicakd to analyze than monopulse systems which are unaffected by amplitude fluctuations.

It has also been suggested⁵⁴ that polarization agility can reduce the glint error. Since the individual echoes from the various scattering centers that make up a complex target are likely to be sensitive to the polarization of the incident radar signal, a change in the polarization can possibly result in an independent measure of the apparent target direction. By observing the target with a variable polarization producing independent measurements, the angle error due to glint is averaged and the effect of the large glint errors is reduced. Experimental measure- ments with an X-band, conical-scan, pulse doppler radar tracking an M-48 Hink at approxi- mately 500 m range reduced the angular tracking error by about one-half. In these tests, the hest results were obtained when the plane of polarization was switched in small increments (5.6 to 22.5°) at a rate greater than 500 steps per second, which is more than an order of magnitude greater than the 40 Hz conical-scan rate.

~-angle tracking.^{41 53}•90

- 94 A radar that tracks a target at a low elevation angle, near the surface of the earth, can receive two echo signals from the target, Fig. 5.15. One signal is retkcted directly from the target, and the other arrives via the earth's surface. (This is similar to the description of surface reflections and its effect on the elevation coverage, as in Sec. 12.2.) The direct and the surface-reflected signals combine at the radar to .J'kld_an angle measure-

ment that differs from the true measurement that would have been made with a single target in the absence of surface reflections. The result is an error in the measurement of elevation. The surface-reflected signal may be thought of as originating from the image of the target mirrored by the earth's surface. Thus, the effect on tracking is similar to the two-target model used to describe glint, as discussed previously. The surface-reflected signal is sometimes called a multipath signal.

An example of the elevation angle error at low angles is shown in Fig. 5.16 for a target at constant height.⁴³ At close range the target elevation angle is large and the antenna beam does not illuminate the surface; hence the tracking is smooth. At intermediate range, where the elevation angle is from 0.8 to as much as six beamwidths, the surface-reflected signal enters the radar by means of the antenna near-in sidelobes. The surface-reflected signal is small so that the antenna makes small oscillations about some mean position. At greater ranges (eleva- tion angles less than about 0.8 beamwidth), where the an"tenna main beam illuminates the s~rface, the interference between the direct and the reflected signals can result in large errors in elevation angle. The angular excursions can be up (into the air) or down (into the ground). The peak errors are severe and can be many times the angular separation between the target and its

Antenna beam

path

---

_{- - ~:~:~ Image}

Figure S.15 Low-angle tracking illustrating the surface-reflected signal path and the target image.

1.6 1.4 1.2 ^:

QB

"' ^0.6

IA.I uJ a: 0.4

"'

uJ

0 0.2 '

a: 0

a: _Q

a:

""

z _-0.2

0 ~

;,- -0.4

..,

..J

""

^-0.6

-a.a

·!.O -1.2 .::1.4

-1.6 -1.8

-2.0

TRACK TIME (MINUTES)

Figure 5.16 Example of the measured elevation tracking error using a phased-array radar with 2._7~- beam width. Aircraft target flew out in range at a nearly constant altitude. The numbers along the zero error Iine,indicate the track time in minutes. (From Linde.⁴⁶⁾