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REFERENCES
Anderson, B. D.O., and J. B. Moore (1979), Optimal Filtering (Prentice-Hall: Englewood Cliffs, NJ).
Apostol, A. (1974), Mathematical Analysis, 2nd Ed. (Addison-Wesley: Reading, MA).
Ash, R. B., and M. F. Gardner (1975), Topics in Stochastic Processes (Academic: New York).
Baker, C. R. (1969), "On the Deflection of a Quadratic Linear Test Statistic," IEEE Trans. Inform. Theory, vol. IT-15, pp. 16-21.
Bene~, V. E. (1981), "Exact Finite Dimensional Filters for Certain Diffusions with Nonlinear Drift," Stochastics, vol. 5, pp. 65-92.
Ben~, V. E. (1987), "Nonlinear Filtering: Problems, Examples, Applications," Chapter 1 in Advances in Statistical Signal Processing - Volume 1: Estimation, H. V. Poor, Ed. (JAI Press: Greenwich, CT).
Bierman, G. J. (1977), Factorization Methods for Discrete Sequential Estimation (Academic: New York).
Billingsley, P. (1979), Probability and Measure (Wiley: New York).
Boekee, D. E., and J. C. Ruitenbeck (1981), "A Class of Lower Bounds on the Bayesian Probability of Error," Inform. Sciences, vol. 25, pp. 21-25.
Breiman, L. (1968), Probability (Addison-Wesley: Reading, MA).
Brockett, R., and J. M. C. Clark (1980), "The Geometry of the Conditional Density Equation," in Analysis and Optimization of Stochastic Systems, O. L. R. Jacobs, Ed. (Academic: New York).
Carlyle, J. W. (1968), "Nonparametric Methods in Detection Theory," Chapter 8 in Communication Theory, A. V. Balakrishnan, Ed. (McGraw-Hill: New York).
DeBruijn, N. G. (1961), Asymptotic Methods in Analysis, 2nd Ed. (North-Holland: Amsterdam).
Desoer, C. R., (1970), Notes for a Second Course on Linear Systems (D. Van Nostrand: Princeton, NJ).
540
Doob, J. L. (1953), Stochastic Processes (Wiley: New York).
Duncan, T. E. (1968), "Evaluation of Likelihood Functions," Inform. Control, vol. 13, pp. 62-74.
Duncan, T. E. (1970), "Likelihood Functions for Stochastic Signals in White Noise," Inform. Control, vol. 16, pp. 303-310.
Dunford, N., and J. T. Schwartz (1958), Linear Operators-Part I (Wiley: New York).
Feldman, J. (1958), "Equivalence and Perpendicularity of Gaussian Process," Pacific J. Math., vol. 8, pp. 699-708.
Feldman, J. (1960), "Some Classes of Equivalent Gaussian Process on an Interval," Pacific J. Math., vol. 10, pp. 1211-1220.
Ferguson, T. S. (1967), Mathematical Statistics: A Decision Theoretic Approach (Academic: New York).
Girsanov, J. V. (1960), "On Transforming a Certain Class of Stochastic Process by Absolutely Continuous Substitution of Measures," Theory Prob. Appl., vol. 5, pp. 285-301.
Goodwin G. C., and K. S. Sin (1984), Adaptive Filtering, Prediction and Control (Prentice-Hall: Englewood Cliffs, NJ).
Grenander, U. (1981), Abstract Inference (Wiley: New York).
Hajek, J. (1958), "On a Property of Normal Distributions of Any Stochastic Process," Czech. Math. J., vol. 8, pp. 610-617.
Hajek, J., and Z. Sidak (1967), Theory of Rank Tests (Academic: New York).
Hampel, F. R., et al. (1986), Robust Statistics: The Approach Based on Influence Functions (Wiley: New York).
Hazewinkel. M., and S. Marcus (1982), "On Lie Algebras and Finite Dimensional Filtering," Stochastics, vol. 5, pp. 29-62.
Honig, M. L., and D. G. Messerschmidt (1984), Adaptive Filters: Structures, Algorithms, and Applications (K1uwer: Boston).
Huber, P. J. (1965), "A Robust Version of the Probability Ratio Test," Ann. Math. Stat., vol. 36, pp. 1753-1758.
Huber, P. J. (1981), Robust Statistics (Wiley: New York).
Huber, P. J., and V. Strassen (1973), "Minimax Tests and the Neyman-Pearson Lemma for Capacities," Ann. Statist., vol. 1, pp. 251-263.
541
Kailath, T. (1966), "Some Integral Equations with 'Nonrational' Kernels," IEEE Trans. Inform. Theory. vol. IT-12, pp. 442-447.
Kailath, T. (1969), "A General Likelihood Ratio Formula for Random Signals in Gaussian Noise," IEEE Trans. Inform. Theory., vol. IT-15, pp. 350-361.
Kailath, T. (1971), "The Structure of Radon Nikodym Derivatives with Respect to Wiener and Related Measures," Ann. Math. Stat., vol. 42, pp. 1054-1067.
Kailath, T. (1981), Lectures on Wiener and Kalman Filtering (Springer-Verlag: New York).
KasSam, S. A., and H. V. Poor (1985), "Robust Techniques for Signal Processing: A Survey," Proc. IEEE, vol. 73, pp. 433-481.
Kassam, S. A., and J. B. Thomas (1980), Nonparametric Detection: Theory and Applications (Dowden, Hutchinson & Ross: Stroudsburg, PA).
Kendall, M. G. (1948), Rank Correlation Methods (Griffin: London).
Kendall, M. G., and A. Stuart (1961), The Advanced Theory of Statistics-Vol. 2 (Hafner: New York).
Kobayashi, H., and J. B. Thomas (1967), "Distance Measures and Related Criteria," Proc. 5th Ann. Allerton Conf. Circuit and System Theory, Monticello, IL, pp. 491-500.
Kullback, S. (1959), Information Theory and Statistics (Wiley: New York).
Lehmann, E. L. (1983), Theory of Point Estimation (Wiley: New York).
Lehmann, E. L. (1986), Testing Statistical Hypotheses (Wiley: New York).
Lipster, R. S., and A. N. Shiryayev (1977), Statistics of Random Processes I: General Theory (Springer-Verlag: New York).
Ljung, L., and T. Soderstrom (1982), Theory and Practice of Recursive Identification (MIT Press: Cambridge, MA).
Lovitt, W. V. (1950), Linear Integral Equations (Dover: New York).
Lugannani, R., and S. Rice (1980), "Saddle Point Approximation for the Distribution of the Sum of Independent Random Variables," Adv. Appl. Prob., vol. 12, pp. 475-490.
542
Lukacs, E. (1960), Characteristic Functions (Hafner: New York).
Marcus, S. I. (1984), "Algebraic and GeometriC Methods in Nonlinear Filtering," SIAM J. Control Optimization, vol. 22, pp. 817-844.
Martin, R. D., and S. C. Schwartz (1971), "Robust Detection of a Known Signal in Nearly Gaussian Noise," IEEE Trans. Inform. Theory, vol. IT-17, pp. 50-56.
Mazo, J. E., and J. Salz (1965), "Probability of Error for Quadratic Detectors," Bell Syst. Tech. J., vol. 44, pp. 2165-2186.
Nevel'son, M. B., and R. Z. Has'minskii (1973), Stochastic Approximation and Recursive Estimation (American Mathematical Society: Providence, RI).
Noether, G. E. (1955), "On a Theorem of Pitman," Ann. Math. Stat., vol. 26, pp. 64-68.
Oppenheim, A. V., and R. W. Schafer (1975), Digital Signal Processing (Prentice-Hall: Englewood Cliffs, NJ).
Papoulis, A. (1986), Probability, Random Variables and Stochastic Processes (McGraw-Hill: New York).
Parzen, E. (1962), Stochastic Processes (Holden-Day: San Francisco).
Schweppe, F. C. (1965), "Evaluation of Likelihood Functions for Gaussian Signals," IEEE Trans. Inform. Theory, vol. IT-H, pp. 61-70.
Shepp, L. A. (1966), "Radon-Nikodym Derivatives of Gaussian Measures," Ann. Math. Stat., vol. 37, pp. 321-353.
Skorohod, A. V. (1974), Integration in Hilbert Space (Springer-Verlag: New York).
Slepian, D. (1958), "Some Comments on the Detection of Gaussian Signals in Gaussian Noise," IRE Trans. Inform. Theory, vol. IT -4, pp. 65-68.
Stranovich, R. L., and Yu. G. Sosulin (1965), "Optimal Detection of a Diffusion Process in White Noise," Radio Eng. Electron. Phys., vol. 10, pp. 704-713.
Tantaratana, S. (1986), "Sequential Detection of a Positive Signal," Chapter 7 in Communications and Networks: A Survey of Recent Advances, I. F. Blake and H. V. Poor, Eds. (SpringerVerlag: New York).
543
Thomas, J. B. (1971), An Introduction to Applied Probability and Random Processes (Wiley: New York).
Thomas, J. B. (1986), An Introduction to Applied Probability (Springer-Verlag; New York).
Trench, W. F. (964), "An Algorithm for the Inversion of Finite Toeplitz Matrices," J. SiAM, vol. 12, pp. 515-522.
Van Trees, H. L. (1968), Detection, Estimation and Modulation Theory-Part I (Wiley: New York).
Viterbi, A. (1968), Principles of Coherent Communications (Wiley: New York).
Wong, E. (1983), Introduction to Random Processes (Springer-Verlag: New York).
Wong, E., and B. Hajek (1985), Stochastic Process in engineering Systems (Springer-Verlag: New York).
Yao, K., and R. M. Tobin (1976), "Moment Space Upper and Lower Bounds for Digital Systems with Intersymbol Interference," IEEE Trans. Inform. Theory, vol. IT-22, pp. 65-74.
INDEX
a-fJ tracker. 305 OI-{3-y tracker. 308 a posteriori probabilities. 11 a priori probabilities. 9 Absolute continuity of
measures. 370 Acceptance region. 8 Affl-nity. 127 Alternative hypothesis. 8 Amplifier-limiter. 70 Arrival time. estimation of. 457 Asymptotic efficiency of an
estimate. 245 Asymptotic normality
of least-squares. 264. 267 of MLE·s. 255. 455
Asymptotic relative efficiency (ARE). 128
Autoregressive (AR) sequence. 349 prediction of. 352
Autoregressive/moving-average (ARMA) sequence. 349
Bayes ~timate. 197 Bayes risk. 9. 44. 197 Bayes rule. 9 Benes class of nonlinear
diffusions. 521 Berry-Eseen bound. 134 Bessel function. 49 Bhattacharyya bound. 127 Bias. 246 Binary channel. 12.29. 39 Binary integrator. 165
Cameron-Martin formuill. 404
Cauchy's criterion for mean-square convergence. 389
Cauchy noise. 73. 118 Cepstrum.345 Channel equalization. 217
Characteristic function. 105. 117 Chernoff bounds. 124 Cholesky decomposition. 84.
340 Coherent detection. 66. 399
locally optimum. 71 Completeness. 225
of a sufficient statistic. 227 for exponential families. 229
Conditional density in nonlinear filtering. 497 evolution equation. 497 unnormalized.516
Conditional-mean estimate. 199
Conditional-median estimate. 201
Conditional-mode estimate. 203
Conditional risk. 8. 44. 197 Consistency
in hypothesis testing. 129 of least-squares. 262. 267 of MLE·s. 252. 455
Constant-false-alarm-rate (CFAR) detection. 158
Correlation detector. 67 Correlator.67
bank. 391 nonlinear. 72
Correlator-limiter. 186 Costs
absolute error. 199 posterior. 12 squared error. 198 uniform. 11.201
Counting measure. 372 Covariance matrix. 74 Cubic sensor problem. 520 Cumulant generating
function. 121 Cramer-Rao bound. 238 Critical region. 8
Decision rule. 8 Bayes. 10. 44 minimax. 22 Neyman-Pearson. 34 randomized. 32 sequential. 137 terminal. 137
Deflection. 425 Detection probability. 32 Differential phase-shift
keying (DPSK). 190 Diffusions. 490
evolution of the densities. 492 evolution of the moments. 493
Dominated convergence theorem. 254
Drift. of a diffusion. 490 Dynamical system. 287
E-contaminated mixture. 179. 268
Efficacy of a test. 133 Eigenfunctions. 379 Eigenvalues
of a matrix. 82 of a covariance function. 379
Eigenvectors. 82 Empirical distribution
function. 174 Energy detector. 103. 169 Equivalence of measures. 376 Estimator-correlator
discrete time. 111 continuous time -
diffusion signals. 519 continuous time -
Gaussian signals. 425. 429 continuous time -
nonGaussian signals. 444 Exponential distribution.
204.244 Exponential family. 228 Extended Kalman filter. 524
phase-locked loop. 526
S4S
Factorization theorem. 221 False-alarm probability. 31 Filterin,g.290 Fisher's information. 238
continuous time signals. 453 matrix parameters. 258
Fisher-Yates test. 167 Fokker-Planck equation. 492 Fredholm determinant. 437 Fredholm integral equation.
407.488 Fredholm resolvent. 435. 466 Fundamental identity of
sequential analysis. 149
Gamma density. 105 Gamma function. 106
incomplete. 107 Gaussian noise. 66. 399 Gaussian random process. 382 Gaussian random vector. 74 Girsanov's theorem. 445 Grenander's dichotomy. 387 Grenander's theorem. 377
Hard limiter. 73 Hellinger integral. 127 Hypothesis testing
Bayesian. 7 composite. 43 locally optimum. 54 M-ary.7 minimax. 19 Neyman-Pearson. 31 nonparametric. 157 simple. 43 UMP.50
Homogeneity. tests of. 175
Information inequality. 235 for exponential families. 238 for vector parameters. 258
Innovations process continuous time. 441. 445 discrete time. 110.298 linear. 464 vector. 469
Innovation theorem Gaussian processes. 438 linear. 464 nonGaussian processes. 445
In-phase channel. 94 Ito correction term. 431 Ito differentiation rule. 502
vector version. 508 Ito processes. 504 Ito stochastic integral. 431.
444
J -divergence. 127 Jensen's inequality. 124
Kalman-Bucy filter as an approximate nonlinear
filter. 534 continuous time. 482 discrete time. 292. 323 measurement update. 297 time update. 297 with correlated state and
measurement noises. 361 with feedback. 361
Kalman gain matrix. 296. 483 Karhunen-Loeve expansion. 380 Kolmogorov-Smirnov tests. 174 Kolmogorov-Szego-Krein
formula. 341 Kolmogorov's forward
equation. 492 Kushner's equation. 498
Laplacian noise. 67 Least-favorable distribution
for detection. 179 for estimation. 270
Least-favorable priors. 22 Least-squares estimate
of signal parameters. 260 consistency of. 262. 267 asymptotic normality of. 264. 267
Lebesgue decomposition. 448 Lebesgue measure. 371 Lebesgue-Stieltjes integral.
370.444
546
Level of a test. 32 Levinson algorithm. 321 Levy-Doob theorem. 445 Lie algebra. 520 Likelihood equation. 243 Likelihood-ratio test. 10
generalized. 55 Linear detector. 104 Linear growth condition. 490 Linear MMSE estimation.
309.460 Linear observation model.
216.471 Lipschitz condition. 490 Locally most powerful
(LMP) testing. 54 Location testing. 15.27.36.51
M -estimate. 269 Martingale. 445 Matched filter. 67 Maximum a posteriori
probability (MAP) decision rule. 12
MAP estimation. 203 MAP equation. 204 Mann-Whitney test. 174 Marcum's Q -function. 98 Markov inequality. 121 Markov process. 490
transition densities. 491 Maximum-likelihood
estimates (MLE·s). 242 asymptotic normality of. 255.455 consistency of. 252. 455 of signal parameters. 259. 451 of vector parameters. 257
Maximum-likelihood test. 55 Mean-square continuity. 381 Mean-square integral. 378
Stieltjes. 379 Measurability. 367 Measure. 367
absolute continuity. 370 probability. 367 CT-finite. 369 singularity. 375
Median. 201 Mercer's theorem, 380 Minimal sufficiency. 220 Minim um-mean-absolute-error
(MMAE) estimation. 199 Minimum-mean-squared-error
(MMSE) estimation. 198. 309 Minimum-probability-of-error
decision rule. 11 Minimum-variance unbiased
estimate (MVUE). 218 Miss probability. 31 Moment-space bounds. 128
Neyman-Pearson criterion. 32
Neyman-Pearson lemma. 33 Noise blanker. 73 Noncoherent detection. 92. 407 Nonlinear filtering
approximations. 524. 530. 534 basic equation of. 506 conditional density. 498 evolution of the conditional
mean. 501 evolution of the conditional
variance. 502 unnormalized conditional
density. 516 Nonparametric test. 158 Normal scores test. 167 Null hypothesis. 8
547
On-off keying (OOK). 92 Orthogonality principle. 313.462 Outliers. 269
Paley-Wiener condition discrete time. 337 continuous time. 487
Parameter estimation Bayesian. 197 maximum-likelihood. 242 recursive. 271 robust. 268 signal parameters. 259 unbiased. 219 vector parameters. 212. 257
Partial correlation (PARCOR) coefficients. 321
Periodogram. 114 Phase-locked loop. 526 Pitcher's equation. 398 Pitcher's theorem. 395 Pitman-Noether theorem. 132 Poisson distribution. 275 Polarity coincidence correlator
(PCC).170 Power of a test. 32 Power function. 38 Power spectrum. 114.328 Prediction. 290. 471
Kalman-Bucy.292 Levinson. 319 Wiener-Kolmogorov.341
Prior probabilities. 9 least favorable. 22
Probability ratio test. 10 Projection
onto an eigenvector. 82 theorem. 314
Pseudosignal. 76. 398
Quadratic detector. 103. 125.424
Quadratic variation. 434. 510 Quadrature channel. 94 Quaternary phase-shift keying
(QPSK).189
Radar range estimation. 457 Radiometer. 103 Radon-Nikodym derivative. 371
on (Rn .En ). 372 on discrete sets. 373
Radon-Nikodym theorem. 371 Rao-Blackwell theorem. 223 Rank tests. 166 Receiver operating
characteristics (ROCs). 38 Recursive estimation
of fixed parameters. 271 of discrete-time signals. 292 of continuous-time signals. 482.499.524
Reflection coefficients. 321
Rejection region. 8 Relative efficiency. 129 Relative entropy. 127 Residual. 298 Resolvent kernel. 466 Riccati equation
discrete time. 305 continuous time. 483
Robust detection. 175 Robust estimation. 268
Saddle-point approximation. 120
Sample number of a sequential test. 145
Schwarz inequality. 135 Second-order filter. 528 Sequential detection. 136 Sequential probability ratio
test (SPRT). 143 truncated. 156
Shepp's theorem. 428 Signal-amplitude estimation
Bayesian. 209 maximum-likelihood. 246 minimum-variance unbiased. 230 robust. 268
Signal detection. 63 deterministic signals. 64. 384 nonparametric. 158 robust. 175 signals with random parameters. 90. 407 sequential. 136 stochastic signals. 101. 413
Signal estimation. 286 Kalman-Bucy filtering. 292. 470 Levinson filtering. 319 nonlinear filtering. 488 phase tracking. 524 Wiener-Kolmogorov filtering. 325.485
Signal-parameter estimation. 259 (See also. Signal-amplitude estimation)
548
arrival time. 457 continuous time. 451 robust. 268
Signal selection. 86 Signal-to-noise ratio (SNR).
81. 392 generalized. 425
Significance level. 32 Sign test. 162 Singular detection. 375.
390.395 for rational signals and noise. 427
Singularity of measures. 375 Gaussian measures. 426 with respect to Wiener measure. 428
Smoothing. 290.471 Soft limiter. 70 Spectral decomposition
of a covariance function. 380 of a matrix. 82
Spectral factorization continuous time. 486 discrete time. 337 of rational spectra. 345
Square root of a matrix. 84 State estimation. 290 Stochastic approximation. 273 Stochastic differential
equation. 489 Stochastic integral
Ito. 431. 444 mean-square. 378 Stratonovich.431
Stochastic system. 287 linear. 291. 471 state equation. 287. 471 measurement equation. 290. 471
Stopping rule. 13 7 Sufficiency. 220 System identification. 265
persistence of excitation in. 267 sufficient richness in. 267
t -test. 163 Thermal noise. 66.382
Toeplitz matrix. 320 Tracking. 286 Track-while-scan (TWS)
radar. 290. 303. 306 Transition densities of
a diffusion. 491 Two-channel tests. 168 Types I and II errors. 31
Unbiasedness asymptotic. 245 of a test. 53 of an estimate. 219
Uniformly most powerful (UMP) tests. 50
Unnormalized conditional density in nonlinear filtering. 516
Wald's approximations. 147 Wald's identity. 150 Wald-Wolfowitz theorem. 145 White noise
continuous time. 400. 419 discrete time. 85. 336
549
Whitening filter in detection. 85 in estimation. 299. 340 in continuous time. 417. 486
Wide-sense Markov model. 350
Wiener process. 401 properties. 414 representation. 416
Wiener-Hopf equation continuous time. 435. 485 general. 318 for causal filtering. 486 for noncausal filtering. 327. 486
Wiener-Kolmogorov filtering. 325.485 causal. 333. 344 noncausal. 326 MSE error in. 330. 332
Wilcoxon test. 166. 174
Yule-Walker equations. 320
Zakai equation. 517