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Notation Index

σfD

σ2g

σ2hit

σ2launcher

σl2n

σ2m

σ2measi

σ2mes

σ2miss

σ2missile

σ2n

σ2out

σ2piin

σ2piout

σ2rj

σ2q

σ2qΣ

σS2i

σ2td

σ2xm

2

ˆ

 

 

σZ

(ρ)

 

ση

 

 

 

σζ21

 

 

σζ22

 

 

σζ2Σ

 

 

σ2ˆ

 

 

 

θ jaccept

 

σξ

 

 

 

σ22

− ξ

2

ξ

AFΣ

PFΣ

 

 

σθ

στ τ

τ0

τav

τclean

τcor

τcycleread

τcyclerec

τDS

τex

τi

593

the. root-mean-square value of potential error under the measurement of the Doppler frequency

the variance of target maneuver intensity for each target the error variance to hit the target by missile

the error variance of antitarget guidance by a launcher

the variance of error of lth parameter estimation at nth filtering step

the variance of the target maneuver intensity

the variance of errors of coordinate measurement of the ith target pip

the variance of estimation error the variance of miss

the error variance of missile flight path the white Gaussian noise variance

the total error variance at the digital filter output

the variance of the passive interference at the equalizer input the variance of the passive interference at the equalizer output

the variance of estimation of the target range measure by a single reading the variance of quantization errors

the variance of statical quantization errors the variance of target return signal amplitude

the variance of error of a single reading of the time delay td the variance of coordinating measuring errors

the. variance of decision statistic when input process samples are correlated with each other

.the mean-square deviations of true target pips from the gate center along the axes η

the variance of amplitude quantization errors the variance of amplitude sampling errors

the summary additive amplitude quantization and sampling interference variance

the acceptable value of filtering error variance at the line of the release of information

.the mean-square deviations of true target pips from the gate center along the axes ξ.

the variance of the total background noise and interferences forming at the DGD output

.the root-mean-square value of potential error under measurement of the angular coordinates

the root-mean-square value of potential error under measurement of delay the pulse duration

the duration of the sampled signal

the average duration of spike of stochastic process realization at the level M the time to clean memory cells

the correlation interval the cycle time at reading

the cycle time at recording

the average request queuing time

the interval of extrapolation time

the average request queuing time during the ith phase

594

Notation Index

 

memory

the average time to fill out the memory

τ

τqueue

the time of a single request queue

τqueue

the average time queue

τread

the time to read information

τrebuild

the time to repair information destroyed under reading

τrec

the time to record information

τs

the duration of scanning signal

τscan

the average time of directional analysis, in which there are targets

τscancomp

the duration of compressed linear-frequency scanning signal

τsearch

the time to search information

τtg

the average time interval between two considered events (the target traverses)

Φ(x)

the standard normal Gaussian pdf

Φ0(x)

the integral of probability

φ0

.the one-half main beam width of the radar antenna directional diagram at zero

φk(t)

level

the orthogonal functions

φ(ϑ)

the function characterizing the shape of radar antenna directional diagram

φ(t)

the phase modulation law of the narrowband signal

φdd

.the width of radar antenna directional diagram in the searching plane at the

φi

given power P level

the energy to scan the ith cell

χDS

the loading factor

χMTI

the MTI loading factor

Ω

the switching function frequency

ω0

the resonance frequency

ϖ(ij|i0j0)

the set of the weight coefficients

(·)

the coefficient of asymptotic relative efficiency

[z]

the nearest integer NLE z

1(ω)

the Fourier transform of the normalized correlation function envelope ρen(τ)

(f)

the filter transfer function module

 

the generalized loss factor

 

the total loss factor

(x|θ)

the conditional likelihood ratio

(θN)

the likelihood function of the vector parameter θN estimated by sequent measure-

 

 

ments {YN}

(βtg)

the likelihood function of the estimated target angular coordinate βtg

(γ, E)

the quadratic loss function

(γ, l)

the loss function

ac

the coefficient taking into consideration losses under accumulation process

g

the likelihood ratio for the generalized signal processing algorithm

g

the accumulated likelihood ratio over μ − 1 steps

 

µ−1

 

tg

the target importance

(ti)

the noise

0

the two-sided power spectral density of white noise

Σ

the total noise power spectral density at the receiver input

activein

the average power spectral density of active interferences

N(l)

the normalized noise function

 

the value of classification factor

av(), (γ)

the average risk

Notation Index

595

m

the Bayes risk

post(γ)

the a posteriori risk

(i )

the normalized correlation function of observed stochastic process

(τ)

the normalized correlation function

S(l)

the normalized signal function

S(ω)

.the Fourier transform of mathematical expectation of the function s(t) – the

S(jω)

spectral density

the frequency characteristic of the low-pass filter

(ω)

the spectral power density

Electrical Engineering

SIGNAL PROCESSING

in RADAR SYSTEMS

An essential task in radar systems is to find an appropriate solution to the problems related to robust signal processing and the definition of signal parameters. Signal Processing in Radar Systems addresses robust signal processing problems in complex radar systems and digital signal processing subsystems. It also tackles the important issue of defining signal parameters.

The book presents problems related to traditional methods of synthesis and analysis of the main digital signal processing operations. It also examines problems related to modern methods of robust signal processing in noise, with a focus on the generalized approach to signal processing in noise under coherent filtering. In addition, the book puts forth a new problem statement and new methods to solve problems of adaptation and control by functioning processes. Taking a systems approach to designing complex radar systems, it offers readers guidance in solving optimization problems.

Organized into three parts, the book first discusses the main design principles of the modern robust digital signal processing algorithms used in complex radar systems. The second part covers the main principles of computer system design for these algorithms and provides real-world examples of systems. The third part deals with experimental measurements of the main statistical parameters of stochastic processes. It also defines their estimations for robust signal processing in complex radar systems.

Written by an internationally recognized professor and expert in signal processing, this book summarizes investigations carried out over the past 30 years. It supplies practitioners, researchers, and students with general principles for designing the robust digital signal processing algorithms employed by complex radar systems.

K11252

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