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Full text of "A brief survey of adaptive control systems"

UBRAKY 

tkchn;cal report sac 

HAVA1 rOSTGHADUATE 
UCWOBSY. CAJUFOaMU 



NPS62-78-003 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




A 


BRIEF 


SURVEY 


OF ADAPTIVE 


CONTROL 


SYSTEMS 










Donald A. 


Stentz 
















March 


1978 








Final 


Rep 


ort 


for Peric 


d May 


1977 - 


March 


1978 



Approved for public release ; distribution unlimited 

Prepared for: 

search and Engineering Department 
FEDDOCS /a l Torpedo Station 

D 208.14/2:NPS-62-78-003 fport, Washington 98345 



NAVAL POSTGRADUATE SCHOOL 
Monterey, California 93940 

Rear Admiral T. F. Dedman Jack R. Borsting 

Superintendent Provost 

The work reported herein was supported by funds provided 
by the Naval Torpedo Station, Keyport, Washington. 



Reproduction of all or part of this report is authorized 



This report was prepared by: /\ 



UNCLASSIFIED 



SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) 



REPORT DOCUMENTATION PAGE 



1. REPORT NUMBER 

NPS62-78-003 



2. GOVT ACCESSION NO 



READ INSTRUCTIONS 
BEFORE COMPLETING FORM 



3. RECIPIENT'S CATALOG NUMBER 



4. TITLE (and Subtitle) 



A BRIEF SURVEY OF ADAPTIVE CONTROL 
SYSTEMS 



5. TYPE OF REPORT a PERIOD COVERED 

"inal for Period 

May 1977 - March 1978 



6. PERFORMING ORG. REPORT NUMBER 



7. AUTHORfsJ 



8. CONTRACT OR GRANT NUMBERfaJ 



Donald A. Stentz 



9. PERFORMING ORGANIZATION NAME AND ADDRESS 

Naval Postgraduate School 
Monterey, California 93940 



10. PROGRAM ELEMENT, PROJECT, TASK 
AREA 4 WORK UNIT NUMBERS 

N0025378WR00002 



11. CONTROLLING OFFICE NAME AND ADDRESS 



Research Projects Division 
Research and Engineering Department 
Naval Torpedo Station, Keyport, WA 98345 



12. REPORT DATE 

March 1978 



13. NUMBER OF PAGES 



14. MONITORING AGENCY NAME & ADDRESSf/f dltterent from Controlling Office) 



15. SECURITY CLASS, (of thla report) 



Unclassified 



I5a. DECLASSIFI CATION/ DOWN GRADING 
SCHEDULE 



16. DISTRIBUTION STATEMENT (ol this Report) 



Approved for public release; distribution unlimited 



17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, It different from Report) 



18. SUPPLEMENTARY NOTES 



19. KEY WORDS (Continue on reverse aide If necessary and Identity by block number) 



Adaptive control systems 
Adaptive arrays 
Adaptive filters 
Index of performance 



20. ABSTRACT (Continue on reverse aide It necessary and Identify by block number) 



This document summarizes the principles of adaptive control 
systems and suggests a number of possible uses of this new 
technology on acoustic tracking ranges. A bibliography of 
recent literature is included. 



DD 1 JAN 73 1473 EDITION OF 1 NOV 65 IS OBSOLETE 

S/N 0102-014- 6601 | 



UNCLASSIFIED 



SECURITY CLASSIFICATION OF THIS PAGE (When Data Sntarmd) 



TABLE OF CONTENTS 

INTRODUCTION 4 

ADAPTIVE CONTROL SYSTEMS DEFINED 5 

INDEX OF PERFORMANCE 6 

POSSIBLE USES IN ACOUSTIC TRACKING RANGES 9 

BENEFITS OF ADAPTIVE SYSTEMS 11 

ESSENTIAL PROCESSES OF ADAPTIVE CONTROL 12 

ADAPTIVE CONTROL LOOP WITH TWO INPUTS 13 

BLOCK DIAGRAM OF TWO SENSOR ADAPTIVE CONTROL SYSTEM ... 14 

RECENT RESEARCH ACCOMPLISHMENTS 16 

CONCLUSIONS 18 

REFERENCE LIST 19 

APPENDIX A. REFERENCES 20 

INITIAL DISTRIBUTION LIST 30 



INTRODUCTION 

Historically, targets tracked on acoustic tracking ranges 
have been accomplished in an artificially quiet environment. 
All except essential ship movement is stopped, the desired 
tracking signal is made as strong as possible, arrays are tuned 
for the desired sound in both frequency and direction, and all 
transmissions and receptions are kept synchronized. 

When it is desired to determine how the target or weapon 
reacts when operating in a noisy or interfering environment, the 
above described methods are not satisfactory. For example: If 
a torpedo is being tested for its tracking and detection ability 
when being countermeasured intentionally or is being operated in 
an environment of heavy shipping, the test range should be able 
to track the torpedo in that environment accurately. If a track- 
ing system could be designed that would ignore all CM, spectral 
ship noise, and even broadband background noise, much more infor- 
mation about the torpedo characteristics could be obtained. 
Recent developments, including high density solid state circuitry, 
may make this a very real possibility. This new technology is 
called "adaptive control" and by making use of it could result 
in accurate and highly sensitive adaptive range tracking systems. 

The following paragraphs indicate the progress made since 
about 1966. Parameters used to obtain control in the adaptive 
process are defined, and the three processes generally used to 
improve the control characteristics over a reasonable period of 
time are described. 



ADAPTIVE CONTROL SYSTEMS DEFINED 

Some systems can be operated in an optimal manner because 
the controller parameter /s can be preprogrammed to adapt to the 
system's environment. In order to achieve optimum control, the 
control parameters are automatically set relative to instanta- 
neous environmental conditions encountered at each point in time. 
Obviously, the changing environment may be so complicated or 
unknown that a reasonable model is difficult to estimate and 
evaluate. When no compromise between the design objectives is 
possible that will result in an acceptable fixed-parameter sys- 
tem, and where preprogrammed adjustments cannot be made due to 
a lack of information regarding the system performance with time, 
the use of an adaptive control system may be indicated [1]. 

Eveleigh [1] points out that adaptive control provides a 

possible solution to control problems of the following general 

form: 

"The system to be controlled is normally exposed to a 
time-varying environment either in the form of changing 
system parameters, input signals and disturbances with 
time-varying statistical characteristics, or changing 
performance objectives." 

Thus an adaptive system is one which measures its performance 

relative to some performance characteristic called an Index of 

Performance , or IP, and modifies its parameters to achieve 

optimum operation. 



INDEX OF PERFORMANCE 

When designing an adaptive system, it is necessary to 
establish uniquely the optimum solutions. Eveleigh suggests 
that the concept of an index of performance, or IP, be utilized 
and goes on to define some of the more generally accepted IP's. 

a. Phase margin (9 ) - the angle between the negative real 
axis and the straight line connecting the origin and the point 
of intersection of the Nyquist plot and the unit circle. 

b. Gain margin (G ) - 1/G , where G is the open-loop trans- 
a — mo o r r 

fer function magnitude at the frequency when phase lag is 180° . 
G is a direct measure of the ratio by which loop gain may 
increase before instability occurs. Other factors remain con- 
stant of course. 

c. Control-loop bandwidth (BW) - this bandwidth may have 
to be constrained by making use of filters. 

d. Peak frequency (M ) - the maximum magnitude of the closed- 
loop system transfer function. 

e. Percent overshoot - ratio of peak response minus final 
value to final value. 

f. Rise time (T ) - time axis projection of a line tangent 
to the response curve at its steepest point. 

g. Delay time (T^) - time it takes the output to rise to 
half its final value. 

h. Settling time (T ) - time necessary for the output to 
settle and remain within ± five percent of the final value. 



i. Steady-state error (E ) - for a unit step input this IP 
is a common constraint and is zero for a type-n system, n >_ 1; 
and it is (1/K + 1) when K is the open loop gain for a type-zero 
system. 

j . Mean- square error - perhaps the most used IP is the mean- 
square error. It is defined as: 

T 



ms 



lim 
T->-o° 



i 



1/21 e 2 (t)dt 



This IP is generally identified as the (LMS) algorithm. e(t) is 
the closed-loop control system error. 

Each of the above IP's listed have advantages and disadvan- 
tages depending on the particular system being adapted and to 
what extent optimization is to be obtained. Other IP's that 
will not be defined and should be considered when designing an 
adaptive system are mentioned below. A complete discussion of 
these IP's may be found in reference [1]. 

a. Integral Squared-Error Criterion, ISE 

Integral of Time Multiplied by Squared-Error, ITSE 
Integral of Squared-Time Multiplied by Squared-Error, 



b 
c 

ISTSE 
d 
e 

ITAE 
f 

g 



Integral of Absolute Value of Error, IAE 

Integral of Time Multiplied by Absolute Value of Error, 



Integral of Exponentially Weighted Squared-Error, IExSE 
Integral of Modified Exponentially Weighted Squared- 
Error, IMExSE 

A Eveleigh points out, "It is apparent that an 'optimum 
system" is a very subjective term ... in one application fast 



initial response or rise time for a step input may be all impor- 
tant ... in other cases rapid response may be equally undesir- 
able . . . the optimum system is highly dependent upon applica- 
tion." When n > 1 parameters are available as choice variables, 
a unique solution is only possible when an IP exhibiting an 
extreme value at the desired optimum point is used. 

If no useful fixed-parameter controller provides acceptable 
response of the system's operational envelope, then some means 
must be found for adjusting controller parameters that are 
sensitive to short-term conditions. If an IP can be selected 
which dictates the system's instantaneous or short-term average 
performance quality, and if a control-loop can be designed to 
optimize the IP automatically by adjusting its parameters, then 
the new configuration is called an adaptive control loop. This 
adaptive system is actually an effort to extend the basic optimum- 
control concept to time-varying systems. It is easily seen then 
that the optimum parameter value is not generally determined by 
a single set of measurements, but rather it is approached 
gradually by a succession of identification, decision, and modi- 
fication procedures. This suggests that there is a "learning 
curve" associated with each system as a function of time. The 
usefulness of a particular system may depend heavily upon the 
shape of this learning curve; it could, for instance, preclude 
real time processing. 



POSSIBLE USES IN ACOUSTIC TRACKING RANGES 

The literature concerning adaptive systems cites many 
examples for use in missiles, radar antennas, and communications 
systems. These examples include control of flight pattern, 
turning a "deaf ear" to noise and interference, tracking, and 
processing signals in the presence of noise. Very little will 
be found concerning how this relatively new technology can be 
used on an acoustic tracking range whether one similar to Dabob 
Bay or on an at sea range designed for fleet exercises. How- 
ever, it seems logical that most of the literature concerning 
the above mentioned uses is directly applicable to the under- 
water acoustic tracking range. Due to the slowness of sound 
velocity in water, the speed of some targets, and ranges desired, 
some adjustments would have to be made. It does seem likely that 
the basic principles, the IP's, and advantages would apply even 
though the parameters may vary widely. It is also quite likely 
that the water environment as a propagation medium, sources of 
interference, ambient noise level, and other constraints may 
prove to be a more difficult medium in which to work when 
compared to the radio frequency case most often described. It 
would also seem likely that the use of adaptive systems in this 
more complicated environment may actually make it unnecessary 
to model the environment over a long time period, but only for 
the short time required for a single adaptation to be performed. 
This is related to the learning curve mentioned earlier. A 
measurement (sample) is taken, and on the basis of that value 

9 



or when compared with an earlier sample or the desired signal, 
a decision is made and the adaptive system parameter/ s varied 
to produce a new point on the optimization or learning curve. 
We, so to speak, gradually sneak up on the optimum operating 
point as we learn what is happening from one sample to the 
next. This is important because it may ultimately relieve 
some of the hard to achieve requirements of the preprogrammed 
approach to optimization. 



10 



BENEFITS OF ADAPTIVE SYSTEMS 

What then are the benefits of using adaptive control on the 
acoustic tracking range? The most obvious one is to improve the 
signal-to-noise ratio of the output of the tracking receiver by 
making the adaptive system ignore noise, multipath, or other 
interference coming from directions and sources other than that 
of the desired target. This is to say improve the S/N ratio by 
decreasing noise and interference. For Dabob Bay, this technique 
is appealing because by attempting to obtain improvement through 
stronger signal sources may result in multipath interference, 
reverberation, and detection of unwanted distant target signals. 
All this may ultimately leave the S/N ratio unchanged or even 
reduced. By holding signal power down and effectively decreasing 
noise power, a beneficial effect can be obtained without the 
above interference problems arising. It is possible that some 
improvement could be achieved by adapting the bandwidth of the 
tracking receiver to the desired signal spectrum while the beam 
portion is being adapted as well. 



11 



ESSENTIAL PROCESSES OF ADAPTIVE CONTROL 

Figure 1 shows a block diagram of a system and its adaptive 
controller. Since the diagram does not identify the system 
itself, no mention is made of the type of IP used. It could be 
any of the IP's defined or listed earlier. Of great importance 
is the sequence of events during a single adaptive event. These 
are: identification, decision, and modification. Essentially, 
the controller design depends upon the choice of IP, controller 
topology, the adjustable parameters of the system, and the 
characteristics of the means of response. It may be a replica 
of the desired signal. The output response should eventually 
match the desired response depending upon the time characteristics 
of the system's learning curve. 



Input, desired 
response or 
replica 



i Error 
/~S, O-MS) 



Modification 
controller 
parameter 
"^t settings 



7K 



Environmental effects causing 
significant change in transfer 
function of system 



Control Systems to be 



input 



Parameters adjusted 
to assure optimum 
performance 



■^ 



optimized 



jJl 



Decision 



logic 

7TT- 



vj IP Measurement 
Identification 



Output 
respons 



(Should 
eventuall 
match desr 
response 
a c cor dingo 
learning 
curve. ) 



FIGURE 1. CONTROL SYSTEM WITH AN ADAPTIVE CONTROLLER 



12 



ADAPTIVE CONTROL LOOP WITH TWO SENSOR INPUTS 

From such a block diagram as shown in Figure 1, it is 

difficult to imagine how it would be used in a given system. 

Figure 2 shows how the operations could be used to adapt an 

underwater array composed of two hydrophones so that the array 

and associated adaptive system would optimize the output. B. 

and B~ represent beam-steering signals that command the main 

beam to "look" or steer in a desired direction, 8 . At the 

s 

same instant that the beam is steered in the direction desired, 
an in terf erring noise occurs in the direction, 9 . Ordinarily, 
a side lobe (not shown) would pick up the noise and introduce 
it into the processor along with the desired signal, thus 
reducing the S/N ratio. The adaptive process will cause the side 
lobe in the direction of the noise source to reduce to a null, 
thus blocking the noise and resulting in a S/N improvement. 
Again, the three essential processes are indicated: identifica- 
tion, decision, and modification. For each new sensor added to 
the array, an additional adaptive control loop must be added. 
It is thus easily seen why solid state circuitry and digital 
electronics are used rather than the more involved analog 
technology. If it is assumed that B, , the input beam steering 
command for hydrophone 1, is a fixed parameter, this signal 
weights E-, in such a manner that in conjunction with the signal 
from the second hydrophone, E~, amplifier, hard limiter, corre- 
lator mixer and integrator, with added weighting given by B 2 
will modify the E ? W~ value and ultimately optimize the 

13 



Desired 
Signal 
Wavefront 



Hydrophone 

1 



Input bean 
steering 

command 
signal 



Interfering 
Noise Signal 
Wavefront 



formed at 
§ by adaptive 

controller chang- 
ing weighting 
values 




Hydrophone 2 
Preamp 



Hard 
Limiter 



Correlation 
Mixer 

l f OUTPUT 

(W^ + W^) 



IDENTIFICATION 



g Output of hard 
limiter freq, 
(phase) and 
time dependent 
only 



FIGURE 2. TWO SENSOR ADAPTIVE CONTROL SYSTEM 



14 



uncorrelated noise or interference signals arriving from the 
direction 9 . The same pattern is used if there are signals 
arriving from more than two hydrophones . Each control loop would 
eventually be added in the summer just prior to the output. The 
output would then consist of the sum of the weighted signal 
from each sensor in the array. The performance factor of 
ultimate interest in an adaptive array is the improvement in the 
output SNR as compared to a conventional array subjected to the 
same interference conditions [2]. 



15 



RECENT RESEARCH ACCOMPLISHMENTS 

Gabriel [2] defines an adaptive array as a system consisting 
of an array of sensor elements and a real time adaptive receiver 
processor. When given a beam-steering command, it samples the 
current environment and automatically proceeds to adjust the 
element control weights to optimize (determine by the choice 
of IP) the output SNR in accordance with a selected algorithm. 
He says that array systems of this type are sometimes referred 
to as "smart" arrays. This term is appropriate since the adap- 
tive system uses far more of the available information in the 
array aperture than does a conventional array. 

Widrow [3], [6] describes an adaptive noise canceller con- 
figured as a notch filter and realized by an adaptive noise 
canceller. Advantages of this method are that it offers easy 
control of bandwidth, an infinite null, and the capability of 
adaptively tracking the exact frequency of the interference. 
This appears to be of value for tracking ranges as it sometimes 
becomes necessary to track "keep track of" the unwanted source 
of the interference in addition to reducing its effect on the 
desired signal. For example: If a countermeasure is attached 
to a vehicle, and a null is formed in the direction of the CM, 
then it would not be possible to track signals from the CM vehicle 
tracking the null would provide the necessary information about 
the activities of the CM vehicle while the CM is nulled in the 
array aperture. Widrow points out various applications for 
using this principle of adaptive noise cancelling among which 

16 



he includes noise in speech signals, antenna side lobe inter- 
ference, and periodic or broadband interference for which there 
is no external reference source. Adaptive noise cancelling is 
a method of optimal filtering that can be applied whenever a 
suitable reference input is available. Widrow and his coworkers 
established the least mean square (LMS) algorithm based on the 
method of steepest decent. Griffiths [5]. 

The sensitivity of an array of sensors to interfering noise 
sources can be applied whenever a suitable processing scheme 
of the outputs of the individual array elements can be found 
[4]. The particular combination of array and processing performs 
as a filter in both space and frequency. Using the LMS criterion, 
Widrow shows the sharpening of the null in the direction of the 
noise source as each sample is taken and the learning curve is 
forced toward the optimum condition. Tracking a particular tar- 
get from among multiple targets seems quite possible when using 
adaptive technology. The tracking array positively listens for 
the desired target and determines through time of arrival by 
taking into consideration the environmental condition and the 
last or predicted position of the target. 



17 



CONCLUSIONS 

This report has described the adaptive control system by 
defining the most commonly used Index of Performances, IP's, and 
discussing the three essential processes, identification, 
decision, and modification, that are involved in all such sys- 
tems. A block diagram of a system composed of two sensors is 
included. A number of possible applications of adaptive systems 
that could find use on an acoustic tracking range are discussed. 
One of the purposes of this report was to acquaint the reader 
with the research being carried on in the field of adaptive 
control systems. To help provide a measure of this activity, 
several reference lists are included. 

It seems quite possible that many of the possible approaches 
of adaptive processing may be applicable to the acoustic track- 
ing range. These would include tracking improvement, keeping 
track of noise and interference sources, reduction of signal 
strength thereby reducing multipath and reverberation problems, 
communications, and various other signal processing applications 
associated with the range operation. 



18 



REFERENCES 



1. Eveleigh, Adaptive Control and Optimization Techniques , 
McGraw-Hill, 1967. 

2. Gabriel, "Adaptive Arrays - An Introduction," Proc. IEEE, 
Vol 64, No 2, Feb 1976, pp 139. 

3. Widrow, B., "Adaptive Filters" in Aspects of Network and 
System Theory, R. E. Kalman and N. DeClaris , Editors, 
New York: Holt, Rinehart and Winston, 1971. 

4. Widrow, B., P. E. Montey, L. J. Griffiths, and B. B. Goode, 
"Adaptive Antenna Systems," Proc. IEEE Vol 55, pp 2143-2159, 
Dec 1967. 

5. Griffiths, L. J., "A Simple Adaptive Algorithm for Real- 
Time Processing in Antenna Arrays," Proc. IEEE, Vol 57, 
pp 1697-1704, Oct 1969. 

6. Widrow, B., Glover, J. R. , J. M. McCool , etal., "Adaptive 
Noise Cancelling," Principles and Applications, Proc. IEEE, 
Vol 63, No 12, Dec 1975, pp 1692-1716. 



19 



APPENDIX A 
REFERENCES 

1. Adams, W. and P. Moulder, "Anatomy of Heart," in Encyclopedia 
Britannica, Vol. 11, pp. 219-229, 1971. 

2. Applebaum, S. P., "Adaptive Arrays," Syracuse University 
Res. Corp., Rep. SPL TR 66-1, August 1966. 

3. Bode, H. and C. Shannon, "A Simplified Derivation of Linear 
Least Squares Smoothing and Prediction Theory," Proc. IRE, 
Vol. 38, pp. 417-425, April 1950. 

4. Booker, A. H., C. Y. Ong , J. P. Burg and G. D. Hair, 
"Multiple-Constraint Adaptive Filtering," Texas Instruments, 
Science Services Division, Dallas, TX, April 1969. 

5. Brennan, L. E. and I. S. Reed, "Theory of Adaptive Radar," 
IEEE Trans. Aerospace Electron Systems, Vol. AES-9, pp. 
237-252, March 1973. 

6. Brennan, L. E. and I. S. Reed, "Effect of Envelope Limiting 
in Adaptive Array Control Loops," IEEE Trans. Aerospace 
Electron System, Vol. AES-7, pp. 698-700, July 1971. 

7. Brennan, L. E., E. L. Pugh and I. S. Reed, "Control Loop 
Noise in Adaptive Array Antennas," IEEE Trans. Aerospace 
Electron Systems, Vol. AES-7, pp. 254-262, March 1971. 

8. Brown, J. E., Ill, "Adaptive Estimation in Nonstationary 
Environments," Stanford Electron Labs, Stanford, CA Doc. 
SEL 70 056, Tech Rep. TR 6795-1, August 1970. 

9. Bryn, F. , "Optimum Signal Processing of Three-Dimensional 
Arrays Operating on Gaussian Signals and Noise," J. Acoust. 
Soc. Am., Vol. 34, pp. 289-297, March 1962. 

10. Bryson, A. E., Jr., and Y. C. Ho, "Applied Optimal Control," 
Waltham, MA, Blaisdell, 1969. 

11. Burg, J. P., "Three-Dimensional Filtering with an Array of 
Seismometers," Geophysics, Vol. 29, pp. 693-713, October 1964. 

12. Burg, J. P., "Maximum Entropy Spectral Analysis," presented 
at the 37th Annual Meeting, Soc. Exploration Geophysicists , 
Oklahoma City, OK, 1967. 

13. Buxton, J., I. Hsu and R. Barter, "Fetal Electrocardiography," 
J. A.M. A., Vol. 185, pp. 441-444, 10 August 1963. 

20 



14. Capon, J., R. J. Greenfield, and R. J. Kolker, "Multi- 
dimensional Maximum Likelihood Processing of a Large 
Aperture Seismic Array," Proc. IEEE, Vol. 55, pp. 192-211, 
February 1967. 

15. Chestnut, H. and R. W. Mayer, Servomechanisms and Regula- 
ti ng System Design , Vol. 1, 2nd Ed. (New York : Wiley) 
T959. 

16. Claerbout, J. F., "Detection of P Waves from Weak Sources 
at Great Distances," Geophysics, Vol. 29, pp. 197-211, 
April 1964. 

17. Compton, R. T. Jr., "Adaptive Arrays: On Power Equalization 
with Proportional Control," Ohio State University Electro- 
science Lab. Rep. 3234-1, Contract N00019-71-C-0219 , 
December 1971. 

18. Covingron, A. E. and N. W. Broten, "An Interferometer for 
Radio Astronomy with a Single-Lobed Radiation Pattern," 
IRE Trans. Antennas Propagation, Vol. AP-5, pp. 247-255, 
July 1957. 

19. Cox, J. R. Jr. and L. N. Medgyesi-Mitschang, "An Algorithmic 
Approach to Signal Estimation Useful in Fetal-Electrocardio- 
graphy," IEEE Trans. Biomedical Engineering, Vol. BMI-16, 

pp. 215-219, July 1969. 

20. Daniell, T. P., "Adaptive Estimation with Mutually Correlated 
Training Samples," Stanford Electronic Labs., Stanford, CA, 
Doc. SEL-68-083, Tech Rep. TR 6778-4, August 1968. 

21. Davies, D. E. N., "Independent Angular Steering of Each Zero 
of the Directional Pattern for a Linear Array," IEEE Trans. 
Antennas Propagation, (Commun.), Vol. AP-15, pp. 296-298, 
March 1967. 

22. Davisson, L. D. , "A Theory of Adaptive Filtering," IEEE 
Trans. Information Theory, Vol. IT-12, pp. 97-102, April 
1966. 

23. Dvoretzky, A., "On Stochastic Approximation," Proc. 3rd 
Berkeley Symposium on Mathematical Statistics and Probability, 
J. Neyman, Editor, pp. 39-55 (Berkeley, CA: University of 
California Press) 1956. 

24. Finkbeiner, D. T. II, Introduction to Matrices and Linear 
Transformations , (San Francisco, CA: Freeman) 1966. 

25. Fleming, W. H., Fu nctions of Several Variables , (Reading, MA: 
Addison-Wesley) 1965 . 



21 



26. Frost, 0. L. Ill, "Adaptive Least Squares Optimization Sub- 
ject to Linear Equality Constraints," Stanford Electronics 
Lab., Stanford, CA, Doc. SEL-70-055, Tech Rep. TR-6796-2, 
August 1970. 

27. Frost, 0. L. Ill, "An Algorithm for Linearly Constrained 
Adaptive Array Processing," Proc. IEEE, Vol. 60, pp. 926- 
935, August 1972. 

28. Gabor, D., W. P. L. Wilby, and R. Woodcock, "A Universal 
Nonlinear Filter Predictor and Simulator which Optimizes 
Itself by a Learning Process," Proc. Inst. Elec. Eng. , Vol. 
108B, July 1960. 

29. Gabriel, W. F. , Ed. Proceedings Adaptive Antenna Systems 
Workshop of March 11-13, 1974, Naval Research Laboratory, 
Washington, DC, NRL Rep. 7803, September 19 74. 

30. Glaser, E. M. , "Signal Detection by Adaptive Filters," 
IRE Trans. Information Theory, Vol. IT-7, pp. 87-98, April 
1961. 

31. Glover, J., "Adaptive Noise Cancelling of Sinusoidal Inter- 
ferences," Ph.D. dissertation, Stanford University, Stanford, 
CA, May 1975. 

32. Good, I. J. and K. Koog, "A Paradox Concerning Rate of 
Information," Information Control, Vol., 1, pp. 113-116, 
May 1958. 

33. Goode , B. B., "Synthesis of a Nonlinear Bayes Detector for 
Gaussian Signal and Noise Fields Using Wiener Filters," 
IEEE Trans. Information Theory (Correspondence), Vol. IT-13, 
pp. 116-118, January 1967. 

34. Gardner, M. F. and J. L. Barnes, Transients in Linear 
S ystems , Vol. 1 (New York: Wiley) 1942. 

35. Griffiths, L. J., "A Comparison of Multidimensional Wiener 
and Maximum Likelihood Filters for Antenna Arrays," Proc. 
IEEE (Letters), Vol. 55, pp. 2045-2047, November 1967. 

36. Griffiths, L. J., "Signal Extraction Using Real-Time 
Adaptation of a Linear Multichannel Filter," Stanford 
Electronics Lab., Stanford, CA Doc. SEL-60-017, Tech. Rep. 
TR 67881-1, February 1968. 

37. Griffiths, L. J., "A Simple Adaptive Algorithm for Real-Time 
Processing in Antenna Arrays," Proc. IEEE, Vol. 57, pp. 1696- 
1704, October 1969. 

38. Griffiths, L. J., "Comments on 'A Simple Adaptive Algorithm 
for Real-Time Processing in Antenna Arrays' (Author's 
Reply)," Proc. IEEE (Letter), Vol. 58, pp. 798, May 1970. 



22 



39. Griffiths, L. J., "Rapid Measurement of Instantaneous 
Frequency," IEEE Trans. Acoustics, Speech, and Signal 
Processing, Vol. ASSP-23, pp. 209-222, April 1975. 

40. Green, P. E. Jr., R. A. Frosch, and C. F. Romney, "Principles 
of an Experimental Large Aperture Seismic Array (LASA) , " 
Proc. IEEE, Vol. 53, pp. 1821-1833, December 1965. 

41. Harrington, R. F., Field Computation by Moment Methods , Ch . 10 
(New York: MacMillan) 1968. 

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28 



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