Discrete Stochastic Processes and Optimal Filtering

Index

A, B

adaptive filtering 197

algebra 3

analytical 187

autocorrelation function 96

autoregressive process 128

Bienaymé-Tchebychev inequality 143

Borel algebra 3

C

cancellation 199

Cauchy sequence 158

characteristic functions 4

coefficients 182

colinear 213

convergence 218

convergent 219

correlation coefficients 41

cost function 204

covariance 40

covariance function 107

covariance matrix 258

covariance matrix of the innovation process 248

covariance matrix of the prediction error 249

cross-correlation 184

D

deconvolution 199

degenerate Gausian 64

deterministic gradient 225

deterministic matrix 245

diffeomorphism 31

diphaser 209

E

eigenvalues 75 215

eigenvectors 75

ergodicity 98

ergodicity of expectation 100

ergodicity of the autocorrelation function 100

expectation 67

F, G

filtering 143, 247

Fubini's theorem 162

Gaussain vectors 13

Gradient algorithm 211

H, I

Hilbert spaces 145

Hilbert subspace 144

identification 199

IIR filter 186

impulse response 182

independence 13, 246

innovation 240

innovation process 172, 248

causal 187

orthogonal 192

K, L

Kalman gain 254

least mean square 184

linear observation space 168

linear space 104

LMS algorithm 222

lowest least mean square error 185

M, N

marginals 9

Markov process 101

matrix of measurements 246

measure 5

measurement noise 238

measurement noise vector 246

minimum phase 187

multivariate 245 250

multivariate processes 166

multivector 245

O

observations 245

orthogonal matrix 216

orthogonal projection 238

P

Paley-Wiener 187

prediction ...