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Detection, Estimation modulation theory part 1 - Vantress H.

Vantress H. Detection, Estimation modulation theory part 1 - Wiley & sons , 2001. - 710 p.
ISBN 0-471-09517-6
Download (direct link): sonsdetectionestimati2001.pdf
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h0(t9 u) optimum linear matrix filter
70(*) modified Bessel function of 1st kind and order zero
Il912 integrals
/ incomplete Gamma function
I identity matrix
J(t9 u) information kernel
Jij elements in J-1
J~\t9 u) inverse information kernel
Jij elements in information matrix
JK(t9 u) &th term approximation to information kernel
J information matrix (Fishers)
JD data component of information matrix
JP a priori component of information matrix
Glossary 677
J f
3()
ʻ)
Kna(t, U)
Kne(t, ) Kni(t, u) Kx(t, u)
k{t, r(u))
MO
kd(/, v) kf(u, v)
/(R), / KA)
L
I
A
A(R)
((/),
AB
As
3db

A*(0

At
Atch
Atr
In
l0ga
total information matrix transform of /(r) transform of -1()
actual noise covariance (sensitivity discussion) effective noise covariance
error in noise covariance (sensitivity discussion) covariance function of x(t)
Boltzmanns constant operation in reversibility proof covariance matrix linear transformation of x(r)
matrix filter with p inputs and q outputs relating a(r) and d(0
matrix filter with p inputs and n outputs relating a(r) and x(w)
sufficient statistic likelihood function
actual sufficient statistic (sensitivity problem) sufficient statistics corresponds to cosine and sine components
a set of sufficient statistics
a parameter which frequently corresponds to a signal-
to-noise ratio in message ERB
likelihood ratio
likelihood ratio
likelihood function
signal-to-noise ratio in reference bandwidth for
Butterworth spectra
effective signal-to-noise ratio
generalized likelihood ratio
parameter in phase probability density
signal-to-noise ratio in 3-db bandwidth
covariance matrix of vector x
covariance matrix of state vector (= x(f, t))
Lagrange multiplier
eigenvalue of matrix or integral equation eigenvalues of channel quadratic form total eigenvalue natural logarithm logarithm to the base a
678 Glossary
Mx(jv), Mx(jy) characteristic function of random variable : (or x) mx{t) mean-value function of process
M matrix used in colored noise derivation
m mean vector
pis) exponent of moment-generating function
N dimension of observation space
N number of coefficients in series expansion
N(m, a) Gaussian (or Normal) density with mean m and stan-
dard deviation a N(oj2) numerator of spectrum
Ne{ effective noise level
N0 spectral height (joules)
n(t) noise random process
nc(t) colored noise (does not contain white noise)
nEi(t) external noise
rii /th noise component
nRi(t) receiver noise
n*(t) noise component at output of whitening filter
nCr(t) MMSE realizable estimate of colored noise component
wCu(0 MMSE unrealizable estimate of colored noise com-
ponent
N noise correlation matrix numbers)
, n noise random variable (or vector variable)
gae cross-correlation between error and actual state vector
?/ expected value of interval estimation error
?,/0 elements in error covariance matrix
?mi variance of ML interval estimate
$P(t) expected value of realizable point estimation error
?Pi(t) variance of error of point estimate of /th signal
fPn(0 normalized realizable point estimation error
?pn normalized error as function of prediction (or lag) time
?Poo expected value of point estimation error, statistical
steady state (u optimum unrealizable error
(un normalized optimum unrealizable error
f*(f) mean-square error using nonlinear operation
?ac actual covariance matrix
?d(0 covariance matrix in estimating d(t)
?Poo steady-state error covariance matrix
Glossary 679
carrier frequency (radians/second)
a>D Doppler shift
p power
Pr(<) probability of error
Pd probability of detection (a conditional probability)
Pel effective power
Pf probability of false alarm (a conditional probability)
Pi a priori probability of ith hypothesis
Pm probability of a miss (a conditional probability)
PM probability of detection for a particular value of
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