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H.Szu and J. P. Garcia
simulation processing two radar pulses we have demonstrated
the ability to detect target signals over 20dB down from the
Indexing terms: Radar, Signal processing
The effectiveness of moving target indicator (MTI) processing
degrades substantially in- the presence of even moderate
phase jitter or phase noise. A technique originally developed
for processing images viewed through turbulent media is
applied to correct for phase jitter in MY1 radar processing.
Introduction: The well known moving target indicator (MTI)
processing technique takes advantage o r the fact that the
phase of the radar clutter signal is constant while the phase of
the target signal varies. This permits clutter to be subtracted
over multiple radar pulses while preserving the target signal.
The main requirement for MTI processing is a stable phase of
the radar signal. This requirement, however, is not always
realisable [I]. Some types of clutter exhibit phase variation
over time. In addition to this environmental source of phase
jitter there is also system-based phase jitter. Very high power
amplifiers exhibit nondeterministic phase instabilities. When
these cases apply, the result is seriously degraded clutter cancellation (Fig. I). Adaptive MTI has been successful in dealing
with some cases of phase noise but may not be suflicient when
the phase is changing within a subpulse.
Fig. 2 Steps in SRMFIMTI processing
a Centroiding
b Calculation of master subpulse
c Sectioning of master subpulse
d Registration w.r.1. maste; subpulse
Fig. 1 T w o radar pulses (jour subpulses per pulse) representing clutter
return, and diflerence showing how phase jitter degrades M T l cancellation
a Two radar pulses
b Difference
An image processing technique known as the self-reference
matched filter [2] (SRMF) can compensate for image distortion of an object viewed through a turbulent medium. In a
sense this technique is a two dimensional analogue of processing a time series signal subject to nondeterministic phase
jitter. In a simple elegant manner, a variation of the SRMF is
used to implement MTI processing on two or more jittered
radar pulses over consecutive scans. Just as in conventional
MTI, the SRMF-based MTI processing is performed after the
radar signals have been mixed down to the video frequency.
All the subpulses from both pulses are processed together.
This technique involves seven steps:
(i) centroiding the subpulses (Fig. 2a)
The length of a section is defined as a predetermined count
of zero crossings. The count starts at the first zero amplitude
point on the first positive to negative transition. Then for
every subsequent positive to negative transition encountered,
the counter is incremented until it attains some predetermined
value. The distance along the waveforms from the initial zero
crossing to the final zero crossing determines the length of the
section. Implicit to this approach is that every section begins
and ends at a common phase on the waveform. In the final
step of the processing, subpulses comprising the second pulse
are weighted by -1 so that once both pulses are phase
matched, the second pulse will effectively cancel out the first
pulse. The intensity of the residue when no signal is present
will depend on the spectrum of the phase jitter such that
higher frequency phase shifts will cause higher intensity residues.
Simulation: A computer simulation was written to demonstrate the above theory. The phase jitter as a function of frequency X u ) was modelled with the real part having a llf
form [4] where
(ii) shifting the subpulses so that their centroids coincide
(iii) summing the shifted subpulses to produce a master subpulse (Fig. 2b)
(iv) dividing the master subpulse into sections and then centroiding these sections (Fig. 2c)
(v) repeating this procedure with the individual subpulses
(vii) performing a weighted summation of the processed subpulses in which subpulses from half of the pulses are weighted
by -1.
Fig. 2d represents the shifting of the subpulse sections so that
their centroids are coincident with the centroids of the analogous sections on the master pulse. From an SRMF/MTI
ELECTRONlCS LETTERS 10th June 1993 Vol. 29 No. 12
The phase as a function of frequency was chosen to be a
uniform random distribution between -n/2 and n/2. Subsequent to computing Im {Xu)} from the phase, Xu) was
transformed to the time domain bv a comulex DFT. Fie. 3
f (t)
= k, A@)exp [ - i(w, t
+ 4)l
+ k, 4)exp C - i(w, t + 4 + 431
where k, is the weighting coefficient for the clutter (k, is arbitrarily set to unity), k , is the weighting coeficient for the
target, A(t) is the square weighting function, w, is the radar
video frequency, 4 is the phase term, and 4, is the target
phase. Two phase jitter functions were numerically generated
presently existing radar systems could be inexpensively
upgraded to MTI systems with only minor modifications to
their signal processing electronics and software.
Acknowledgments: This work was supported in part by the
NSWC Dalgren Division Independent Research Program.
Fig. 3 Randomly generated phase jitter function
and subsequently used in generating two radar square modulated pulse signals by letting 4 = x(t) for each pulse. Each
pulse consists of four subpulses like the pulses shown in Fig. 1.
The frequency of the pulses corresponds to the video frequency of the radar. This was selected to be 30 MHz, and the
R F frequency and the pulse width were chosen to be 3 G H z
and l o p , respectively. For the simulation, each subpulse was
divided into 10 sections in which the section length was
defined by four zero counts. Fig. 4a and b show the average of
0IEE 1993
13th April I993
H. Szu and J. P. Garcia (Naual Surface Warfare Center, Code R44,
I0901 New Hampshire Ave., Silver Spring, M D 20903-5000, U S A )
‘Introduction to radar systems’ (McGraw-Hill, New
York, 1980). pp. 129-138
2 SZU, H. H., and BLODOETT, 1. A.: ‘Self reference spatiotemporal
image-restoration technique’, J. Opt. Soc. Am., 1982, 12, (12), pp.
3 szu, H. H., BMDOETT, I. A., and SICA, L.: ‘Local instances of good
seeing’, Opt. Commun., December 1980, JS, (3). pp. 317-322
4 OOLDMAN, s. 1.: ‘Phase noise analysis in radar systems using personal computers’ (John Wiley & Sons, New York, 1989), Chaps.
L. Y. X. Ma, T. S.Low and S. K. Tso
Fig. 4 Radar simulation
a Average subpulse of first pulse
b Average subpulse of second pulse
c Output ofSRMF/MTI processing
d Difference of first and second average subpulse
Indexing terms: Algorithms, Control systems, Controllers
the four subpulses in the two radar pulses. Fig. 4c is the
output of the SRMF/MTI processing over the two pulses with
no target (k, = 0). Fig. 4d is the difference of the two average
subpulses without processing. As can be seen, the SRMF/MTI
greatly enhances the effectiveness with which the pulses cancel
each other. Next the above SRMF processing was repeated
with an artificial target inserted into the radar signals. The
phase of the artificial target is of the form bt = bo + k , t ,
represents some constant phase shift and k , t represents the linear time dependent phase shift where k, is the
target velocity divided by the carrier wavelength. A target was
chosen to be travelling with a head-on velocity component of
IOOOm/s that translates to a phase shift of 2rr x 10000rad/s in
the radar signal. Fig. 5 shows the result of an artificial target
Fig. S Radar simulation with target - 2 0 d B downfrom clutter
a Average subpulse of first pulse
b Average subpulse of second pulse
c Output of SRMF/MTI processing
d Differenceo f first and second average subpulse
having k, = 1/100th the magnitude of k,. The integration of
the SRMF/MTI output residue for the 1/100th (-20dB)
target is over twice that of the output with no target. This
indicates that for the above phase jitter, the target signal just
exceeds the threshold of detectability based on the criteria of a
signal-to-noise ratio of unity. This simulation demonstrates
the potential of the above technique. Using the SRMF, certain
An effective discrete learning control method is proposed for
improving the tracking performance of linear systems repeating the task from cycle to cycle. With this method, the
current cycle data are intentionally introduced into the learning control law. Analysis of the convergence is conducted
completely in the discrete-time domain. The fast convergence
performance is further substantiated by simulation results.
Introduction: Iterative learning control was originally proposed for robot applications [l], which enables us to find the
control torque that makes the robot follow the desired trajectory exactly over a finite time interval through the repetition
of trials. The usefulness of this kind of scheme has already
been illustrated by experiments for manipulator trajectory
control [2, 31. Recently, this new type of control scheme has
received much attention [4-61 for application in dynamic
systems whose operations are required to repeat from cycle to
cycle with unchanged reference commands.
It is noted that the existing learning control algorithms [l,
2, 4-61 have mostly been developed and analysed in the
continuous-time domain. However, from an implementation
point of view, it would be more reasonable to discuss an
iterative learning control scheme fully in the discrete-time
domain because the storage of the past data in digital memory
is definitely required for any practical learning control implementation. It is well known that many control algorithms in
continuous time are still available in discrete time provided
that the sampled theorem is guaranteed. Conceptually, there
certainly exists some restriction such as the sampled theorem
to determine the sample period in the learning control system
so that the scheme is still effective, or the convergence is also
guaranteed in the discrete time domain. Unfortunately, these
issues are seldom discussed in the literature.
Another weakness of existing learning schemes is that the
current cycle information does not enter into consideration in
the design of the scheme. Obviously, a feedback path of information in the current cycle will definitely play an important
role in learning, even though past cycle information is to be
used. In this Letter, the learning control algorithm is developed realistically in the discrete-time domain and the current
cycle information is directly introduced into the proposed iterative learning controller. The convergent analysis is also completely based on a discrete system so that we can obtain a
10th June 1993
Vol. 29
No. 12
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