Discrete Stochastic Processes and Optimal Filtering, 2nd Edition

Index

A, B

adaptive

algebra

autocorrelation

autoregressive process

Bienaymé-Tchebychev

Borel algebra

C

cancellation

Cauchy sequence

causal

characteristic functions

coefficients

correlation

collinear

convergence

convergent

cost function

covariance

function

matrix

matrix of the innovation process

matrix of the prediction error

crosscorrelation

D

deconvolution

degenerate

deterministic

gradient

diffeomorphism

diphaser

E

eigenvalues

eigenvectors

ergodicity

of expectation

of autocorrelation function

expectation

F, G

filtering

Fubini’s theorem

gradient algorithm

H

Hilbert

spaces

subspace

I

identification

IIR

impulse response

independence

independents

innovation

process

K, L

Kalman’s gain

least mean square

linear

observation space

space

lowest least mean square error

M

marginals

Markov process

matrix of measurements

measure

measurement noise

vector

multivariate

processes

multivector

O

observations

orthogonal

matrix

projection

P

Paley-Wiener

prediction

error

predictor

pre-whitening

principle axes

probability distribution function

process noise vector

projection

Q, R

quadratic form

random

variables

vector

vector with a density function

regression plane

Riccati’s equation

S

Schwarz inequality

second order

stationarity

stationary processes

singular

smoothing

spectral density

stability

stable

matrix

stationary processes

stochastic

gradient

process

system noise

T

Toeplitz

trace

trajectory

transfer function

transition

equation

matrix

U-W

unitary matrix Q

variance

white noise

Wiener filter