Page 10 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

CONTENTS ix

9.1.3 Feature extraction 312
9.1.4 Feature selection 314
9.1.5 Complex classifiers 316
9.1.6 Conclusions 319
9.2 Time-of-flight estimation of an acoustic tone burst 319
9.2.1 Models of the observed waveform 321
9.2.2 Heuristic methods for determining the ToF 323
9.2.3 Curve fitting 324
9.2.4 Matched filtering 326
9.2.5 ML estimation using covariance models
for the reflections 327
9.2.6 Optimization and evaluation 332
9.3 Online level estimation in an hydraulic system 339
9.3.1 Linearized Kalman filtering 341
9.3.2 Extended Kalman filtering 343
9.3.3 Particle filtering 344
9.3.4 Discussion 350
9.4 References 352

Appendix A Topics Selected from Functional Analysis 353
A.1 Linear spaces 353
A.1.1 Normed linear spaces 355
A.1.2 Euclidean spaces or inner product spaces 357
A.2 Metric spaces 358
A.3 Orthonormal systems and Fourier series 360
A.4 Linear operators 362
A.5 References 366

Appendix B Topics Selected from Linear Algebra
and Matrix Theory 367
B.1 Vectors and matrices 367
B.2 Convolution 370
B.3 Trace and determinant 372
B.4 Differentiation of vector and matrix functions 373
B.5 Diagonalization of self-adjoint matrices 375
B.6 Singular value decomposition (SVD) 378
B.7 References 381

Appendix C Probability Theory 383
C.1 Probability theory and random variables 383
C.1.1 Moments 386