5.2 Accuracy of Radar Location and Radio Navigation Systems
93
Fig. 5.8 Clarification to
(5.42) formula
in Fig. 5.7. Position line represents a straight line OM. Let us find a root-mean-square
error of position line finding σ l . From Fig. 5.8, we can see that α = arctg
x
y
. Then,
according to (5.40) |gradα| =
1
√
x 2 +y 2
=
1
D
, l = Dα.
Consequently,
σ l = Dσ α ,
(5.42)
where σ α —mean-square value of an error α. Clearly, a value σ l at constant value
σ α is proportional to distance D from NGP to an object.
Differential range-finding RNS determines a navigational parameter p == D p =
D A − D B —range difference of an object to two NGP (Fig. 5.9), where D A and D B —
object ranges to two NGP. Position line of such RNS represents hyperbolic curve. In
Fig. 5.9, d is the base of radio-navigational system; is the angle, at which a base is
Fig. 5.9 Clarification to
(5.44) formula
93
Fig. 5.8 Clarification to
(5.42) formula
in Fig. 5.7. Position line represents a straight line OM. Let us find a root-mean-square
error of position line finding σ l . From Fig. 5.8, we can see that α = arctg
x
y
. Then,
according to (5.40) |gradα| =
1
√
x 2 +y 2
=
1
D
, l = Dα.
Consequently,
σ l = Dσ α ,
(5.42)
where σ α —mean-square value of an error α. Clearly, a value σ l at constant value
σ α is proportional to distance D from NGP to an object.
Differential range-finding RNS determines a navigational parameter p == D p =
D A − D B —range difference of an object to two NGP (Fig. 5.9), where D A and D B —
object ranges to two NGP. Position line of such RNS represents hyperbolic curve. In
Fig. 5.9, d is the base of radio-navigational system; is the angle, at which a base is
Fig. 5.9 Clarification to
(5.44) formula