144
6 Detection of Radio Signals and Its Parameters Measuring
Solution of Eq. (6.36) permits to find a value of α s parameter, at which the likelihood function L(α s ) = p(y/α s ) reaches its maximum value. Consequently, the
optimum measuring (estimation) unit of radar signal parameters is a unit of maximum
positioner of correlation integral and finding of corresponding to it value of ˆ
α s parameter. Often an optimum unit is called an optimum discriminator, underlying the meter
capability to determine a deviation degree of true value of α t parameter apart of its
value ˆ
α in maximum (peak) point Ψ (α s ).
By performing of differentiation in α s in (6.36) expression, we obtain an equation,
which permits to find a value ˆ
α s , corresponding to maximum Ψ (α s ):
y out =
∞
−∞
y(t)
d
dα s
S(t, α s )
α s = ˆ
α s
dt = 0
(6.37)
In accordance with (6.37), the functional chart of optimal meter can be represented
as shown in Fig. 6.9.
It includes the differentiation circuit of reference signal S(t, α s ), multiplier and
integrator, performing accumulation of signal for a time t acc (existence time of desired
signal). At parameter α s change relatively to point ˆ
α, a signal at integrator output
is also changed proportionally to derivative of signal envelope Ψ (α s ) (Fig. 6.10a).
At signal presence, reflected from a target, at input the zero value of output signal
corresponds to estimation α s = ˆ
α s of coordinate or parameter of target movement
(Fig. 6.10b).
Input signal of discriminator is a function of mismatching α s − ˆ
α s . If we send a
signal (α s − ˆ
α s ) to control circuit and close (lock) a feedback path, by supplying a
Fig. 6.9 Functional chart of optimal meter (discriminator)
6 Detection of Radio Signals and Its Parameters Measuring
Solution of Eq. (6.36) permits to find a value of α s parameter, at which the likelihood function L(α s ) = p(y/α s ) reaches its maximum value. Consequently, the
optimum measuring (estimation) unit of radar signal parameters is a unit of maximum
positioner of correlation integral and finding of corresponding to it value of ˆ
α s parameter. Often an optimum unit is called an optimum discriminator, underlying the meter
capability to determine a deviation degree of true value of α t parameter apart of its
value ˆ
α in maximum (peak) point Ψ (α s ).
By performing of differentiation in α s in (6.36) expression, we obtain an equation,
which permits to find a value ˆ
α s , corresponding to maximum Ψ (α s ):
y out =
∞
−∞
y(t)
d
dα s
S(t, α s )
α s = ˆ
α s
dt = 0
(6.37)
In accordance with (6.37), the functional chart of optimal meter can be represented
as shown in Fig. 6.9.
It includes the differentiation circuit of reference signal S(t, α s ), multiplier and
integrator, performing accumulation of signal for a time t acc (existence time of desired
signal). At parameter α s change relatively to point ˆ
α, a signal at integrator output
is also changed proportionally to derivative of signal envelope Ψ (α s ) (Fig. 6.10a).
At signal presence, reflected from a target, at input the zero value of output signal
corresponds to estimation α s = ˆ
α s of coordinate or parameter of target movement
(Fig. 6.10b).
Input signal of discriminator is a function of mismatching α s − ˆ
α s . If we send a
signal (α s − ˆ
α s ) to control circuit and close (lock) a feedback path, by supplying a
Fig. 6.9 Functional chart of optimal meter (discriminator)