# Chapter 5 Automatic Tracking Systems

Automatic Tracking Systems

Introduction

In any fire control system, target tracking is the means by which target parameters are measured with respect to the tracking station. These parameters, azimuth, elevation, range, and relative target velocity are ultimately employed to predict the collision point between the target and whatever weapon is launched against it. Before any computation or launching can be accomplished, however, the critical targets parameters must be continuously and accurately measured. This process of continuous measurement is not exact and some error is always present.

The line-of-sight (LOS) between the sensor and target, along which radiant energy from the target is received by the sensor, is used to track the target. If the tracking element were at all times pointed directly along this line-of-sight, tracking would be perfect and no error would exist. In reality, however, error is always present, and therefore a second line, the tracking line, is defined as the line that forms the axis of symmetry of the radiated energy, commonly called the antenna boresight axis. When error exists, the line-of-sight and the tracking line are not coincident; usually the tracking line lags the line-of-sight by some small amount, due to the general inability of mechanical tracking systems to anticipate target movements. This error defines the central problem of any tracking system: How can the error between the line-of-sight and the tracking line be reduced to an acceptable minimum average value?

This problem of minimizing the error between the LOS and the tracking line is further complicated by the fact that weapon platforms are not generally stable. The combined effects of weapon platform roll, pitch, and yaw produce a disturbance in the tracking system that is not related to target motion. These rotational motions not only affect the tracking element's ability to hold the target, but also generate erroneous output data. Since the basis of relative target velocity computation is an accurate measurement of target Position over time, the uncompensated rotational motions of the weapon platform would result in erroneous target velocities being generated. As will be seen in a later chapter in this text, target velocity data is a major input for the computation of the weapon launch lead angle.

Tracking radars require separate components for range and angle tracking of a specific target. These functions were performed manually in early radars by operators watching target video, then positioning handwheels to maintain markers over the desired target blip on each scope. The handwheels positioned potentiometers, which adjusted voltages analogous to target azimuth, elevation, or range that were supplied to fire control computers and lead-computing gun sights. As target speeds and operator workloads increased, automatic tracking circuitry was developed that maintained tracking efficiency over sustained periods and made possible the later development of unmanned homing weapons.

Angle-tracking Servo System

Once a target position error signal has been extracted from the returning energy, it forces input to the azimuth and elevation-drive servo systems. These systems keep the antenna pointing at the target; i.e., they serve to minimize the error between the LOS and the tracking line.

In general, all angle-tracking servo systems function conceptually in the same manner. In this regard, practical tracking servo systems accomplish the following functions:

(1) They sense position error magnitude and direction.

(2) They provide for position feedback.

(3) They provide for data smoothing/stabilization.

(4) They provide for velocity feedback to aid in achieving a smooth track.

(5) They provide a power driving device.

It must be emphasized that the concepts discussed here are applicable to the following diverse systems:

- Shipboard fire control mono-track systems (single target capability)

- Homing missiles

- Acoustic homing torpedoes

- Aviation fire control tracking systems (single target capability)

This discussion will be developed from a viewpoint of how the servo system illustrated in figure 5-2 satisfies each of the functions (1) through (5) above.

Position error magnitude and direction. This function is performed by the radar itself in conjunction with circuitry that has been designed specially for the type of radar employed. From the study of sensor subsystems, recall that generally the output of a sensor is target position data, and that this data is available only when the sensor is pointing at the target. Since target position data should be available to the weapon control system at all times, some means of detecting target motion is required if the sensor is to follow the target. Recall also that target information enters the sensor from a beam of energy, with the energy concentrated along the axis of the beam. For example, using a radar sensor, target information is available when the target is within the radar's beam of energy and is strongest when the target is on the beam axis. As

the target moves to the periphery of the beam, the return signal level begins to diminish. The amount of signal reduction can therefore be used as a measure of how far the target is away from the beam axis and ultimately can be employed to position the radar antenna back on the target automatically. However, the return signal level will diminish by the same amount regardless of which direction the target takes with respect to the beam axis. For this reason a means of sensing direction is required in addition to that of sensing magnitude. If the target is not exactly in the center of the radar beam, then an error exists between the direction that the radar antenna is pointing and the true line-of-sight to the target. Several methods of determining position error are presented below.

(1) Sequential lobing--One of the first tracking methods developed was lobe switching or sequential lobing, which is still in use today in some countries. Recall from chapter 2 that direction (in one axis) can be determined by a double lobe system very rapidly. If the angular error in the orthogonal coordinate is desired simultaneously, the beam could be stepped in a minimum of three (usually four) positions for signal comparisons in a process called sequential lobing. The stepping process is limited by the PRF of the system in that beam position must be stopped long enough for at least one transmission and received echo, and probably more prior to switching to the next position. Four separate antennas or four separate feed horns are required in addition to very complex waveguide plumbing and switching techniques. Because three horns or antennas are shorted at an one time, considerable scanning losses occur, and the data rate is extremely low unless sophisticated electronic lobing systems are used.

(2) Conical Scan--The natural extension of this beam-stepping process in four positions is to rotate the beam continuously in a circular fashion. The error between the tracking axis and the line-of-sight can then be sensed in magnitude and direction by causing the radar beam to be rotated rapidly about the axis of the antenna, thus producing a narrow cone of energy in space. This is generally accomplished mechanically by nutating the feed point (rotating the feed horn) in a small circle around the focal point of a fixed paraboloid; thus, the antenna beam will lie along the axis of the reflector. If the feed point is moved transversely slightly away from the focus, the beam will be at an angle with the axis. If the feed point is oscillated back and forth, the beam will swing from side to side. If the feed point is moved (nutated) in a circle about the axis, a conical scan will result.

Now examine figure 5-6. In this case the antenna axis is pointed directly at the target, so no matter where the transmitted lobe is in the nutation cycle, the echo received by the radar is always of the same amplitude. Although maximum possible energy return is never received, the resulting echoes are all equally strong, and target tracking is very accurate. In actuality, a pulsed radar is employed with a PRT less than the nutation period.

The rate of beam rotation must be such that several pulses of radiated energy are exchanged with the target during each period of beam rotation. In actual practice, the ratio PRF/Fs is approximately 40 to 1, where fs is the scan frequency and PRF is the pulse repetition frequency of the radar.

When the LOS and the tracking line are coincident--i.e., the target is exactly on the tracking line--successive target echoes received by the system will be of equal amplitude since the beam center is at all times equidistant from the target during each scan period. However, if the target is not exactly on the antenna axis, an error exists between the line-of-sight and the tracking line. This error is immediately detectable because as the beam rotates, the return pulses are amplitude modulated due to the varying proximity of the target and the beam center. The frequency of modulation is the scan frequency of the system fs.

This concept of amplitude modulating the sensor input signal is not limited in application to active radar systems. Any system whose function it is to track an energy source can be made to do so by employing the conical scan concept, i.e., laser, infrared, and sonic sensors.

Using the error signal generated from the amplitude modulated input signal in figure 5-7, the radar will be repositioned to cause the returning input signal to again equalize as in figure 5-6.

For a system using conical scan techniques, the actual movement of the beam through space is easily detected by the target. Since the error signal is computed directly from the varying amplitude of the return energy, it is possible for the target to use a transponder, which samples the incoming energy and then rebroadcasts it. When the target senses maximum incoming energy, the transponder rebroadcasts an amount equal to or slightly greater than is sensed. As the energy falls off in amplitude due to the major axis of the beam moving away, the transponder will broadcast a signal with proportionally greater amplitude (dotted line in figure 5-8).

When the incoming energy increases with the approach of the main beam axis, the transponder will broadcast a signal with less and less enhancement, until at maximum it is again equal to or slightly greater than the radar echoes. As a result, the radar's tracking system drives the radar away from the target. This technique is referred to as inverse conical scan and is a common means of deceiving conical scan tracking systems.

(3) COSRO--As a means of achieving a degree of immunity to deception from inverse conical scan ECM, a system known as COSRO was developed. COSRO, meaning Conical Scan on Received Only, employs a non-scanning transmit beam and a rotary (nutating) scanner in the waveguide between the duplexer and the receiver to extract elevation and azimuth angle error. A receiver in a target being tracked by the COSRO radar would detect a steady, non-scanning, pulse radar beam that would provide no information that would assist in determining deception techniques beyond the radar performance parameters listed in chapter 2.

During the rest time between pulses, the duplexer switches the antenna to the COSRO scanner (figure 5-9 and 5-10) and receiver. The COSRO scanner has the effect of shifting the axis of greatest sensitivity to echo reception similar to the slight change in the direction of the transmitted beam of a conical scan radar caused by nutation of the feed horn. One could imagine a receive "beam," similar in shape to a transmitted beam, being nutated about the radar boresight axis. The COSRO scanner determines the distribution of signal strength in the received energy by use of an RF signal detector rotated by a motor tachometer. The location of the greatest amount of returned energy is determined, and signals are sent to the elevation and azimuth power drives to reposition the antenna on the center of the target. When the target is centered, the COSRO scanner will sense equal signal strength throughout the rotation of the RF signal detector. This concept can be employed with sequential lobing radars to produce a Lobe on Receiver

Only or LORO radar. While there are techniques to deceive these types of radars, as presented in chapter 11, much more sophistication, complexity, and expense are involved.

(4) Monopulse--Conical scanning and sequential lobing techniques determine the target's position relative to the radar's main beam axis. If the target is on axis, its amplitude for the return pulse is maximized. If the target is off axis, the return pulse's amplitude is less. The amount of decrease is dependent on how far off axis the target is. Using this idea and moving the beam through space, the radar amplitude modulated a train of pulses coming aback to the receiver. An error signal is extracted from the

train of pulses and is used to position the radar. Serious tracking errors can be generated in such a system if the return of any one pulse is markedly increased or decreased in amplitude as compared to the next pulse in the train. Such a fluctuation could easily occur if there were a sudden change in the target's radar cross section (or any number of other reasons). To avoid these errors, a tracking system determines the amplitude modulation using only one pulse instead of a train of pulses. To accomplish this, the target must be located in two or more beams simultaneously--and a comparison made between the return pulse in each beam. This technique is known as simultaneous lobing, or since the tracking error signal is derived from a single pulse, it is also called monopulse. The comparison of the return echo in each beam can be done either in amplitude or phase. We will concentrate on amplitude comparison.

Let's look at two beam systems. These beams can be generated simultaneously in space by a single reflector, and two adjacent feed horns fed by one transmitter. Figure 5-11 shows these beams slightly overlapped.

If an observer were to actually move across the beam paths in figure 5-11 with a power meter, the meter would sense the algebraic sum of the electromagnetic energy produced by the two beams. If the power meter is moved about to various positions in front of the reflector and the measured power levels graphed, a plot as depicted in figure 5-12 would be produced. Notice that the radiation pattern appears as one lobe, though it is really the sum of two separate lobes.

The monopulse radar is designed so that each beam can be identified separately by employing different polarization or some other tagging process. For this reason the beams can be examined together (sum) as depicted in figure 5-12 or separately. By summing the beams, the monopulse radar will receive a large return from a target centered between the two beams just as if it were tracking with the center of a strong single beam. This aspect is employed by the monopulse radar for target detection and range determination. For angle tracking, the radar receiver will invert the value of the energy from one beam, thus

changing the sign (figure 5-13), and sum that negative value with the positive value from the other beam. It can be shown that if the target is on the boresight axis of the reflector, there will be equal reflected energy in the two beams. Thus, their algebraic sum would be zero. If the target were to the right of the boresight axis, the sum would be positive, and if it were to the left, the sum would be negative. A graph of the algebraic sum or difference of energy from the two beams is depicted in figure 5-14.

This is how the monopulse radar determines the amount and direction of angular error in one axis. For example, any target to the left of center would have a negative amplitude, and any target to the right of centerline a positive amplitude. The farther from centerline, the greater the magnitude of the signal. This can easily be used as an error signal to drive a servomotor to keep the antenna pointed at the target, thereby reducing the error to a very small value. Figure 5-15 depicts a simplified block diagram of a monopulse system.

This diagram depicts the microwave comparator circuit shown in figure 5-16. The microwave comparator circuit is composed of waveguide and hybrid junctions called "magic tees." The hybrid junctions have two inputs and two outputs. One output is the sum of the inputs, and one is the difference of the inputs. Four hybrids can be connected as shown in figure 5-15 to provide azimuth and elevation error. In this case a cluster of four feed horns producing four beams, indicated by the letters A, B, C, and D, are used. To determine azimuth, the sum of the C and D horn outputs are subtracted from that of the A and B horns. If the result is positive, then the target is to the right of the boresight axis, assuming the horns at the top of the diagram are facing the reader. If the result is negative, then the target is to the left of the boresight. Elevation error is determined by subtracting the sum of the outputs of the B and D horns from the sum of the outputs of the A and C horns, a positive value indicating that the target is above the boresight and a negative value indicating that the target is below the boresight. The tracking circuit and power drives will attempt to equalize the amplitude of the target echo in all four horns, which would result when the target was on the boresight axis.

The signal-to-noise ratio for a monopulse tracker would generally be higher than that of a conical scan system, since the target is tracked on the axis of summation of the beams rather than on the edge. The target would not be able to sense whether it was being tracked by a monopulse or a COSRO radar, thus making ECM techniques complicated. It is very difficult to deceive a monopulse radar in angle, but it is as easy (or hard) to deceive it in range as with any other radar. The disadvantages of increased complexity and cost of monopulse over that of other techniques are being reduced by advances in technology, so that most of today's tracking and homing systems incorporate some variation of this system.

Position feedback. When an error signal is developed and the system is caused to drive in response to it, the system must know when it has reduced the error toward zero. The position feedback is accomplished as an intrinsic part of the error signal generation from the radar. As the system moves in response to the original error, the result is to position the tracking line in coincidence with the LOS. This action by the system reduces the position error signal toward zero, thus providing an indication that the system has responded correctly to the error initially measured by the radar. This process is essentially

instantaneous and continuous throughout the entire time that the sensor is providing target information to the system. The equilibrium state of the tracking system then is a null composite error signal input to the phase sensitive demodulator (E(t) = 0)), resulting in zero DC output to the drive system. It must be understood that the true equilibrium state is never achieved while the system is actually tracking, but that if operating properly, the system will always tend toward this state.

Data Smoothing and Stabilization

Stabilization. It should be understood that no single method of compensation for rotational movement exists. Nevertheless, all systems incorporate gyroscopic devices in one way or another. With reference to stabilization, tracking systems can be grouped into three major classes:

(1) Unstabilized--The tracking subsystem operates in a totally unstable environment, and therefore its output contains rotational motion components. Gyroscopic compensation is external to the tracking subsystem.

(2) Partially stabilized--The tracking member is stabilized along one axis (cross level), and the output contains rotational disturbances associated only with the uncompensated axis. The remainder of compensation is external to the tracking subsystem.

(3) Fully stabilized--The tracking member is gimbal-mounted and remains totally unaffected by rotational movement. Its output is completely free of rotational disturbances, and therefore no further compensation need be done prior to computation.

The reference gyro can be dedicated to a specific weapons system, or all weapons and sensors could be served by a single gyro reference. The usefulness of a gyro as a stable reference is due to its tendency to remain in a fixed plane in space if no force is applied to it, and its tendency to turn at right angles to the direction of an outside force applied to it.

Inertia. Gyroscopic inertia enables a gyro to remain at an apparently fixed orientation in space. This property allows it to be used as a directional reference or a vertical reference because it generally remains in the same plane while the vehicle or platform carrying it undergoes roll, pitch, and yaw. This apparent rigidity in space has been used to resist roll in ships; however, this means of direct stabilization required from one to three rotors weighing up to 120 tons each. Modern methods of stabilizing ships, aircraft, and weapons employ very small gyros as vertical and directional references for some type of autopilot. The autopilot senses movement of the gyro, then calculates error and generates a control signal that causes a hydraulic or electrical device to rotate a Control Surface that supplies the force to correct the orientation of the ship or aircraft in space or to alter its direction of motion. In each case the gyro (called a free gyro) is permitted to remain fixed in space, thereby moving an attached variable resistor or similar device as the platform rotates under it. In some ships and aircraft, an electrical signal is produced and distributed where needed from a single master gyro for use in navigation, weapons, and sensors, or command and control systems.

Precession. A gyro's spin axis has a tendency to turn at right angles to the direction of a force applied to it (figure 5-18). This precession causes the flight path of spin-stabilized gun projectiles to curve in the horizontal plane (chapter 19). As depicted in figure 5-19, when a downward force is applied by the weight on the end of the gyro spindle, a torque (D) results in precession in a counterclockwise direction. Thus, with a force applied in the vertical plane, the gyro precesses in the horizontal plane. A rate gyro or integrating gyro is fixed in one axis, and the torque of precession is converted to an electrical signal that is

used to compute displacement or as a means of controlling gain in an antenna or launcher positioning system.

The integrating gyro. Stabilization and data smoothing can be accomplished with the same equipment. Inputs include roll or pitch angle and target position angle error, which are converted to a single output. The major input is the angle error signal that the gyro smooths to prevent the system from attempting to follow the instantaneous changes in the error signal. The position-error voltage derived from the radar is generally not a smoothly changing signal. If the drive system were to attempt to follow this signal, the result would be a series of jumps and a relatively rough positioning of the tracking element. The key to this smoothing process is the fact that the gyro cannot respond instantaneously to the changing input signal. This results in an averaging of the small incremental input changes. Figure 5-21 illustrates this electrical input/output relationship.

The governing equation for a gyro device is:

T = I dA/dt

where

T is torque

is the angular velocity of spin

I is the moment of inertia about the spin axis

d /dt is the angular velocity of precession

The input to the gyro itself is torque caused by the error signal being fed to small coils about the torque axis shaft. When a torque is applied, the response of the gyro is precession, and a signal proportional to the amount of precession is produced by a signal generator mounted on the precession axis shaft. The ability to follow an input signal accurately is governed by the rate of precession.

d /dt = T/I (5-1)

Equation (5-1) illustrates that the rate of precession, and ultimately the response of the gyro, are essentially governed by the spin velocity. The slower the spin, the greater will be the response to a given input torque. To achieve a smoothing function, the rate of spin, , should be relatively high to prevent the gyro from reacting to all the small changes in the input error signal.

The stabilization process results from the fact that the gyro is mounted in the housing of the tracking element. When the weapon platform pitches and rolls, the gyro reacts to this movement and generates a

signal that results in positioning the tracking element in the opposite direction to the rotational motion of the weapon platform.

Limitations. A gyro spinning on earth will appear to tilt with the passage of time without any force applied. In reality the gyro is remaining in its original orientation, and the tile due to the rotation of the earth on its axis. Because the gyro does not rotate on frictionless bearings, there is some reaction force that causes the gyro to drift. Both of these phenomena must be taken into account when the gyros are employed.

Velocity feedback. The primary purpose of velocity feedback is to aid in the prevention of a dynamic overshoot. The velocity feedback signal is employed in a degenerative manner; i.e., the feedback voltage is subtracted form the output drive signal of the gyro. This subtraction serves to limit the speed of the output motors at an equilibrium level. This equilibrium level is governed by the ratio of the feedback voltage to the input drive voltage.

Power driving devices. Naval weapons systems generally employ two broad categories of motive devices: electric motors and electrically controlled hydraulic motors. These devices are used to actually move the driven element of the system. The use of two types of motors usually depends upon the physical size of the load to be driven. Smaller loads, such as missile-steering control surfaces and small fire control directors, are driven by electric motors. Electrohydraulic motors are used to position heavy loads such as missile launchers and gun mounts.

Range Tracking

Automatic range tracking has been an objective since the early days of radar. The first range-tracking units, developed during World War II, were electromechanical devices such as the Mechan Range Unit. As target closing speeds increased, electronic analog, digital, and hybrid rangers replaced mechanical units to respond to the threat.

The purpose of the range unit is to follow the target in range and provide continuous distance information or slant range to the target. Timing pulses are sent to the receiver and display unit to provide range gating and allow the angle tracking system to look at only one specific range interval (really a time interval) where the desired target echo pulse will be received. The location of the range gate and that of the target are examined, the amount and direction of error between the center of the gate and the target is determined, error voltages are generated, and circuitry responds by moving the gate to center it on the target. This operation is carried out by a closed-loop feedback system similar to the angle tracking servo system discussed previously.

There are several methods of sensing range-tracking error; however, all implementations involve some method of incrementing the distance to maximum range of the radar such that specific portions of range interval can be examined. One type of range gating system is described below.

(1) Early and late gate--The main range gate is split into early and late gates, each charging a separate capacitor. When target video enters that portion of the gate, each capacitor charges to a voltage proportional to the amount of target video in that half of the gate, such that if the video is centered, each capacitor will have an equal, though opposite, charge. Summing the charges on the two capacitors Will result in a positive or negative error voltage, or in a zero error voltage if the target is centered.

Summary

This chapter has presented an analysis of automatic tracking systems. The tracking function was traced from the generation of position error magnitude and direction to the load-driving device. Two methods of generating position error were investigated in detail, conical scan and monopulse. Conical scan produces an error signal by causing the beam of sensor energy to be rotated rapidly about the sensor (antenna) axis. Monopulse systems achieve the same result by electronically dividing the radiated energy into four separate parts, which form the beam. The relative amplitudes of the returning energy in the four parts are compared, and an error results when there is an imbalance in signal strength.

A typical tracking servo system was discussed, with emphasis placed on the following characteristics:

(1) Position error magnitude and direction

(2) Position feedback

(3) Data smoothing and stabilization

(4) Velocity feedback

(5) Power driving device

References

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