The track of a target can be determined with a surveillan~ radar from the coordinates of the target as measured from scan to scan. The quality of such a track will depend on the time between observations, the location accuracy or each observation, and the number of extra- neous targets that might he present in the vicinity of the tracked target. A surveillance radar that develops tracks on targets it has detected is sometimes called a track-while-scan (TWS) radar.
One method of obtaining tracks with a surveillance radar is to have an operator manually mark with gr~ase pencil on the face of the cathode-ray tube the location of the target on each scan. The simplicity of such a procedure is offset by the poor accuracy of the track. The accuracy of track can be improved by using a computer to determine the trajectory from inputs supplied by an operator. A human operator, however, cannot update target tracks at a rate greater than about once per two seconds.69 Thus, a single operator cannot handle more than about six target tracks when the radar has a twelve-second scan rate (5 rpm antenna rotation rate). Furthermore an operator's effectiveness in detecting new targets decreases rapidly after about a half hour of operation. The radar operator's trarfic handling limitation and the effects of fatigue can be mitigated by automating the target detection and tracking process with data processing called automatic detection and tracking (ADT). The availability of digital data processing technology has made ADT economically feasible. An ADT system performs the functions of target detection, track initiation, track association, track update, track smoothing (filtering) and track termination.
The automatic detector part or the ADT quantizes the range into intervals equal to the range resolution. /\teach range interval the detector integrates n pulses, where n is the number
of pulses expected to be returned from a target as the antenna scans past. The integrated pulses are compared with a threshold to indicate the presence or absence of a target. An exam pk is the commonly used moving window detector which examines continuously the
Ji!~iJ}
~mples within each quantized range interval and announces the presence of a target if m out of n of these samples cross a preset threshoid. (This and other automatic detectors are described in Sec. 10.7 and in Ref. 70.) By locating the center of the n puls_es, an estimate of the target'sangular direction can be obtained. This is called beani sp/itti11g.
If there is but one target present within the radar's coverage, then detections on two scans are all that is needed to establish a target track and to estimate its velocity. However, there are usually other targets as well as clutter echoes present, so that three or more detections are needed to reliably establish a track without the generation of false or spurious tracks.
Although a computer can be programmed to recognize and reject false tracks, too many false tracks can overload the computer and result in poor information. It is for this.t,ame reason of avoiding computer overload that the radar used with A I_?.T should be designed to exclude unwanted signals, as from clutter and interference. A good ADT system therefore requires a radar with a good_MTLand._ag.ood CEAR_.(.c_onstant false alarm rate) receiver. A clutter map, generated by the radar, is sometimes used lo reduce the load on the tracking computer hy blanking clutter areas and removing detections associated with large point clutter sources not rejected by the MTI. Slowly moving echoes that are not of interest can also he removed hy the clutter map. The availability of some distinctive target characteristic, such as its altitude, might also prove of help when performing track association.71 Thus, the quality of the ADT will depend significantly on the ability of the radar to reject unwanted signals.
When a new detection is received, an attempt is made to associate it with existing tracks.96 This is aided by establishing for each track a small search region, or gate, within which a new detection 1s predicted based on the estimate of the target speed and direction. It is desired to make the gate as small as possible so as to avoid having more than one echo fall within it when the traffic density is high or when two tracks are close to one another. However, a large gate area is required if the tracker is to follow target turns or maneuvers. More than one size gate might therefore be used to overcome this dilemma. The size of the small gate would be determined by the accuracy of the track. When a target does not appear in the small gate, a larger gate would be used whose search area is determined by the maximum accelera- tion expected of the target during turns.
On the basis of the past detections the track-while-scan radar must make a smoothed estimate of a target's present position and velocity, as well as a predicted position and velocity.
One method for computing this information is the so-called
a-fJ
tracker (also called the g-h tracker84), which computes the present smoothed target position\x"
and velocityI
hy thefollowing equations 72 '
Smoothed position: Xn = Xpn
+
a(xn - Xpn) Smoothed velocity: Xn = Xn -1+ ~
(xn - X pn)(5.8) (5.9)
where xP"=
predicted position of the target at the nth scan, x,,=
measured position at the nth scan, a = position smoothing parameter,fJ
= velocity smoothing parameter, andTs
= time between observations. The predicted position at the n+
1st scan isx,, + x" Ts.
(When accelera- tion is important a third equation can be added to describe ana.-fJ-y
tracker, where y = acceleration smoothing parameter.)73 Fora.
=p
= 0, the tracker uses no current informa- tion, only the smoothed data of prior observations. If a =p
= 1, no smoothing is included at all.The classical
a-fJ
filter is designed to minimize the mean square error in the smoothed (filtered)position and velocity, assuming small velocity changes between observations, or data samples.
Benedict72 suggests that to minimize the output noise variance at steady state and the tran- sient response to a maneuvering target as modeled by a ramp function, the
cx.-P
coefficients are related byf1
= cx.2/(2 - a). The particular choice of ex. within the range of zero to one depends upon the system application, in particular the tracking bandwidth. A compromise usually must be made between good smoothing of the random measurement errors (requiring narrow handwidth) and rapid response to maneuvering targets (requiring wide bandwidth). Another criterion for selecting thecx.-fJ
coefficients is based on the best linear track fitted to the radar data in a least squares sense. This gives the values of a andf3
as 742(211 - 1) a=---
11(11
+ 1)
6
/3=
n(n+ 1)
where II is the number of the scan or target observation (n > 2).The standard
a-/1
tracker docs not handle the maneuvering target. However, an adaptive'Y.-/1
tracker is one which varies the two smoothing parameters to achieve a variable bandwidth so as to follow maneuvers. The value of ex. can be set by observing the measurement error x" - x,,". At the start of tracking the bandwidth is made wide and then it narrows down if the target moves in a straight-line trajectory. As the target maneuvers or turns, the bandwidth is widened to keep the tracking error small.The Kalman filter 78 is similar to the classical
cx.-{3
tracker except that it inherently pro- vides for the dynamical or maneuvering target. In the Kalman filter a model for the measure- ment error has to be assumed, as well as a model of the target trajectory and the disturbance or uncertainty of the trajectory. 81 Such disturbances in the trajectory might be due to neglect of higher-order derivatives in the model of the dynamics, random motions due to atmospheric turbulence, and deliberate target maneuvers. The Kalman filter can, in principle, utilize a wide variety of models for measurement noise and trajectory disturbance; however, it is often assumed that these are described by white noise with zero mean.75 A maneuvering target does not always fit such an ideal model, since it is quite likely to produce correlated observations.The proper inclusion of realistic dynamical models increases the complexity of the calcula- tions. Also, it is difficult to describe a priori the precise nature of the trajectory disturbances.
Some form of adaptation to maneuvers is required.76 The Kalman filter is sophisticated and accurate, but is more costly to implement than the several other methods commonly used for the smoothing and prediction of tracking data. 77 Its chief advantage over the classical
a-fi
tracker is its inherent ability lo take account of maneuver statistics. If, however, the Kalman
..
filter were restricted to modeling the target trajectory as a straight line and if the measurement noise and the trajectory disturbance noise were modeled as white, gaussian noise with zero mean, the Kalman filter equations reduce to the
rx-P
filter equations with the parameters ex. and {1 computed sequentially by the Kalman filter procedure.The classical
a-P
tracking filter is relatively easy to implement. To handle the maneuver- ing target, some means may be included to detect maneuvers and change the values of a. andP
accordingly. In some radar systems, the -data rate might also be increased during target maneuvers. As the means for choosing a and
P
become more sophisticated, the optimalcx.-P
tracker becomes equivalent to a Kalman filter even for a target trajectory model with error. In this sense, the optimal
rx-P
tracking filter is one in which the values of a. andP
requireknowledge of the statistics of the measurement errors and the prediction errors, and in which a and
p
are determined in a recursive manner in that they depend on previous estimates of the mean square error in the smoothed position and velocity.79(The above discussion has been in terms of a sampled-data system tracking targets detected by a surveillance radar. The concept of the
cx.-P
tracker or the Kalman filter also canbe applied to a continuous, single-target tracking radar when the error signal is processed digitally rather than analog. Indeed, the equations describing the
a-P
tracker are equivalent to the type II servo system widely used to model the continuous tracker.)If, for some reason, the track-while-scan radar does not receive target information on a particular scan, the smoothing and prediction operation can be continued by properly accounting for the missed data.80 However, when data to update a track. is missing for a sufficient number of consecutive scans, the track is terminated. Although the criterion for terminating a track depends on the application, one example suggests that when three target reports are used to establish a track, five consecutive misses is a suitable criterion for termination. 8 2
One of the corollary advantages of ADT is that it effects a bandwidth reduction in the output of a radar so as to allow the radar data to be transmi!ted to another location via narrowband phone lines rather than wideband microwave links. This makes it .. more conve- nient to operate the radar at a remote site, and permits the outputs from many radars to be communicated economically to a central control" point.
It should be noted that the adaptive thresholding of the automatic detector can cause a worsening of the range-resolution._B.y analggy_~o the angular.J1!~9Jµti~n the angk coordinate88 it wo~ seem a priori that tw_o_t;!rgets might be resolved in range if their separation is abou~)>fthe pulse width. However, it has-been shown;:::,,-::: ...
_____ -
89 tha(--;ith automatic detection the probability of resolvmg targets in range does not rise above 0.9 until they are separated by 2.5 pulse widths. To achieve this resolution a log-video receiver should be used and the threshold should be proportional to the smaller of the two means calculated from a number of reference cells on either side of the test cell. It also assumes that the shape of the return pulse is not known. If it is, it should be possible with the proper processing to resolve targets within a pulse width:When more than one radar, covering approximately the same volume in space, are located within the vicinity of each other, it is sometimes desirable to combine their outputs to form a single track file rather than form ~eparate tracks.83•97
-s.:1 Such an automatic detection and integrated tracking system (ADIT) has the advantage of a greater data rate than any single radar operating independently. The development of a single track file by use of the total available data from all radars reduces the likelihood of a loss of target detections as might be caused by antenna lobing, fading, interference, and clutter since integrated processing permits the favorable weighting of the better data and lesser weighting of the poorer data.
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