OTHER TOPICS

TRACKING RADAR

5.8 OTHER TOPICS

Servo system. The automatic tracking of the target coordinates in angle, range, and doppler frequency is usually accomplished with a so-called Type I I servo system.1.2·³•67

•68 It is also referred to as a zero velocity error system since in theory no steady-state error exists for a constant velocity input. A steady-state error exists, however, for a step-acceleration input.

Thus, the accelerations the system must handle need to be specified in order to select a suitable Type II system. The tracking bandwidth of the servo system is defined as the frequency ·where its open-loop filter transfer function is of unity gain. It represents the transition from closed loop to open loop operation. One of the functions of the servo system is to reduce the

fluctuations of the input signal by filtering or smoothing. Therefore, the tracking bandwidth should be narrow to reduce the effects of noise or jitter, reject unwanted spectral components such as the conical-scan frequency or engine modulation, and to provide a smoothed output of the measurement. On the other hand, a wide tracking bandwidth is required to accurately follow, with minimum lag, rapid changes in the target trajectory or in the vehicle carrying the radar antenna. That is, a wide bandwidth is required for following changes in the target trajectory and a narrow bandwidth for sensitivity. A compromise must generally be made between these conllicting requirements. A target at long range has low angular rates and

a

low signal-to-noise ratio. A narrow tracking bandwidth is indicated in such

a

case to increase sensitivity and yet follow the target with minimum lag. At short range, however, the angular rates are likely to be large so that a wide tracking bandwidth is needed in order to follow the target properly. The loss in sensitivity due to the greater bandwidth .is offset by the greater target signal at the shorter ranges. The bandwidth should be no wider than necessary in order to keep the angle errors due to target scintillation, or glint, from becoming excessive. The tracking bandwidth in some systems might be made variable or even adaptive to conform automatically to the target conditions.

Another restriction on the tracking bandwidth is that it should be small compared to the lowest natural resonant frequency of the antenna and servo system including the structure foundation, in order to prevent the system from oscillating at the resonant frequency. The shaded region in Fig. 5.19 describes the measured bounds of the lowest servo resonant frequency as a function of antenna size achieved with actual tracking radars.

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Antenna diameter - ft

Figure 5.19 Lowest servo resonant-frequency as a function of antenna diameter for hemispherical scan- ning raraboloid reflector antennas. (Based 011 measurements compiled by D. D. Pidhayny of the Aerospace Corporation.)

Precision "on-axis" tracking.^62-65 Some of the most precise tracking radars are those asso- ciated with the instrumentation used at missile-testing ranges.⁶² One such class of precision tracking radar has been called on-axis tracking.⁶³ The output of a conventional sl!rvo system lags its input. The result of the lag is a tracking error. The on-axis tracker accounts for this lag, as well as for other factors that can contribute to tracking error, so as to keep the target being tracked in the center of the beam or on the null axis of the difference pattern. On-axis tracking, as compared with trackers with a target lag, improves the accuracy by reducing the coupling between the azimuth and elevation angle-tracking channels, by minimizing the generation of cross polarization and by reducing the effects of system nonlinearities.

The processes that constitute on-axis tracking include ( 1) the use of adaptive tracking whose output updates a stored prediction of the target trajectory rather than control the antenna servo directly, (2) the removal by prior calibration of static and dynamic system biases and errors, and (3) the use of appropriate coordinate systems for filteriqg (smoothing) the target data.

The radar's angle-error signals are smoothed and compared to a predicted measurement based on a target-trajectory model updated by ·the results of previous measurements. (Prior knowledge of the characteristics of the trajectory can be incorporated in the model, as, ror example, when the trajectory is known to be ballistic.) If the difkrence between the prediction and the measurement is zero, no adjustment is made and the antenna mount is pointed according to the stored prediction. If they do not agree, the target trajectory prediction is changed until they do. Thus, the pointing of the antenna is made open-loop based on the stored target-trajectory prediction updated by the radar measurements. The servo loop that points the antenna is made relatively wideband (high data rate) to permit a fast tracking response against targets with high angular acceleration. The process of adjusting the predicted position based on the measured position is performed with a narrow bandwidth. This error- signal bandwidth is adaptive and can be made very narrow to obtain good signal-to-noise ratio, yet the system will continue to point open-loop based on the stored target-trajectory prediction and the wide tracking-bandwidth of the antenna-pointing servos. For convenience the range, azimuth, and elevation (r, 0, </>) coordinates of the radar output are converted to rectilinear (x, y, z) target coordinates to perform the data smoothing and comparison with prediction. In radar coordinates, the track of a target on a straight-line trajectory is curvilinear and can generate apparent accelerations. This does not happen when tracking in rectilint.:ar coordinates. The rectilinear coordinates of the updated target prediction are converted back to

radar coordinates to drive the antenna.

Systematic errors are determined by prior measurement and are used to adjust the encoded antenna position to provide the correct target position. Systematic errors include (l) error in the zero reference of the encoders that indicate the orientation of the radar axes, (2) misalignment of the elevation axis with respect to the azimuth axis (nonorthogonality), (3) droop or flexing of the antenna and mount caused by gravity, (4) misalignment of the radar with respect to the elevation axis (skew"), (5) noncoincidence of the azimuth plane of the mount to the local reference plane (mislevel), (6) dynamic lag in the servo system, (7) finite transit time that results in the target being at a different position by the time the echo is received by the radar, and (8) bending and additional time delay of the propagation path due to atmo- spheric refraction.

A boresight telescope mounted on the radar antenna permits calibration of the mechani- cal axis of the antenna with respect to a star field. This calibration accounts for bias in azimuth and elevation, mislevel, skew, droop, and nonorthogonality. Tracking a visible satel- lite with the radar permits the position of the RF axis relative to the mechanical (optical) axis to be determined. The difference between the position measured by the optics and that

measured hy tile radar is ohlained artcr correction is made for the <liffcre11ce in atmospheric refraction ror optical and RF propagation. This type of dynamic calibration requires the radar to be large enough to track satellites.

There is nothing unique about any of the individual processes that enter into on-axis tracking. They can each he applied individually, if desired, to any tracking radar to improve the accuracy of track.

High-range-resolution monopulse.⁶⁶ lt has been noted previously in this chapter that the presence of multiple scatterers within the range-resolution cell of the radar results in scintilla- tion. or glint. which can introduce a significant error. The use of a radar with high range-