92
5 Performance Characteristics of Radar Location …
Fig. 5.7 Clarification to
(5.41) formula
|grad p| =
∂ p
x
2
+
∂ p
y
2
+
∂ p
z
2
,
(5.39)
|grad p| =
∂ p
x
2
+
∂ p
y
2
(5.40)
Let us determine a detection accuracy of position lines for range-finding,
goniometric and differential range-finding measuring techniques of navigational
parameters.
Range-finding radio navigational systems (RNS) define a navigational parameter
representing either a range in case of radio range finder without responder or doubled
range in case of radio range finder with responder. To range-finding radio navigational
systems refers a radio-altimeter as well, determining a parameter p = 2H , where
H—flight altitude. Position line of range-finding RNS has a circle shape (Fig. 5.7).
Let us find a mean-square value of detection error of position line σ l , stipulated
by measurement error of distance D. In Fig. 5.7, M is the true position of an object,
offset (shifted) position of an object, determined based on measuring of navigational
parameters; D is the distance from navigational guide point NGP (radio beacon) up
to an object; O is the positioning of NGP (responder); l is the linear offset (shift) of
position line, caused by range measurement error. At selected system of coordinates,
D =
x 2 + y 2 according to (5.40) |gradD| = 1, l = D.
Consequently,
σ l = σ D =
c
2
σ τ ,
(5.41)
where σ D —mean-square value of measuring error D; σ τ —mean-square value of
measuring error of signal delay time interval; c—adio wave propagation velocity.
In goniometric RNS, a measured navigational parameter is an angle α (Fig. 5.8),
which is measured with an error α. In Fig. 5.8, the same notations are admitted as
5 Performance Characteristics of Radar Location …
Fig. 5.7 Clarification to
(5.41) formula
|grad p| =
∂ p
x
2
+
∂ p
y
2
+
∂ p
z
2
,
(5.39)
|grad p| =
∂ p
x
2
+
∂ p
y
2
(5.40)
Let us determine a detection accuracy of position lines for range-finding,
goniometric and differential range-finding measuring techniques of navigational
parameters.
Range-finding radio navigational systems (RNS) define a navigational parameter
representing either a range in case of radio range finder without responder or doubled
range in case of radio range finder with responder. To range-finding radio navigational
systems refers a radio-altimeter as well, determining a parameter p = 2H , where
H—flight altitude. Position line of range-finding RNS has a circle shape (Fig. 5.7).
Let us find a mean-square value of detection error of position line σ l , stipulated
by measurement error of distance D. In Fig. 5.7, M is the true position of an object,
offset (shifted) position of an object, determined based on measuring of navigational
parameters; D is the distance from navigational guide point NGP (radio beacon) up
to an object; O is the positioning of NGP (responder); l is the linear offset (shift) of
position line, caused by range measurement error. At selected system of coordinates,
D =
x 2 + y 2 according to (5.40) |gradD| = 1, l = D.
Consequently,
σ l = σ D =
c
2
σ τ ,
(5.41)
where σ D —mean-square value of measuring error D; σ τ —mean-square value of
measuring error of signal delay time interval; c—adio wave propagation velocity.
In goniometric RNS, a measured navigational parameter is an angle α (Fig. 5.8),
which is measured with an error α. In Fig. 5.8, the same notations are admitted as