5.2 Accuracy of Radar Location and Radio Navigation Systems
91
point (base) on pulses envelope. Particularly, at noises absence, a range measurement
can be conducted with equal success as both for leading edge and trailing edge of
pulses.
Concentrate in more detail on accuracy of radio navigational systems, where
examine separately an accuracy of positioning systems and dead reckoning systems.
In positioning systems, a detection accuracy of position lines (surfaces) and
detection accuracy of object position should be distinguished.
Detection accuracy of position lines (surfaces). Detection error of surface (line)
position equals to normal distance between two surfaces (lines) of position corresponding to true and measured values of navigational parameter. Equation of navigational parameter in arbitrary Cartesian coordinates has a form p = p(x, y, z)—in
space, p = p(x, y)—on surface. Each space (plane) point can be associated with
a certain numeric value of reduced function. In such a way, there is a three-(two) dimensional scalar field of navigational parameter p. Surface (line) position is a
surface (line) of level. Within limits of radio navigation system operating space
(coverage), the navigational parameter p represents a continuous and differentiable
function, and then, changing of scalar field of parameter p is convenient to describe
it by gradient. If unit vector
l represents a normal vector to a surface (line) position directed to rise of navigational parameter p, then an expression, determining a
gradient, has the following form:
∂ p
∂l
=
lgrad p,
(5.36)
where gradient modulus
|grad p| =
∂ p
∂l
.
(5.37)
Gradient grad p is a vector variable, showing a direction of quickest rise of navigational parameter p, where gradient modulus |grad p| characterizes a change rate of
scalar function p.
Gradient gives a possibility to connect an error of measuring navigational parameter p with an error of surfaces (lines) position finding l. By transitioning in (2.2)
to finite decrements, we obtain:
l =
p
|grad p|
.
(5.38)
From (5.38), it is obvious that to reduce errors in detection of surfaces and lines
of position, a field gradient of navigational parameter and its measuring accuracy
should be increased.
If function p is given analytically in arbitrary Cartesian reference system, then a
gradient modulus for surface and line of position correspondingly has the following
form:
91
point (base) on pulses envelope. Particularly, at noises absence, a range measurement
can be conducted with equal success as both for leading edge and trailing edge of
pulses.
Concentrate in more detail on accuracy of radio navigational systems, where
examine separately an accuracy of positioning systems and dead reckoning systems.
In positioning systems, a detection accuracy of position lines (surfaces) and
detection accuracy of object position should be distinguished.
Detection accuracy of position lines (surfaces). Detection error of surface (line)
position equals to normal distance between two surfaces (lines) of position corresponding to true and measured values of navigational parameter. Equation of navigational parameter in arbitrary Cartesian coordinates has a form p = p(x, y, z)—in
space, p = p(x, y)—on surface. Each space (plane) point can be associated with
a certain numeric value of reduced function. In such a way, there is a three-(two) dimensional scalar field of navigational parameter p. Surface (line) position is a
surface (line) of level. Within limits of radio navigation system operating space
(coverage), the navigational parameter p represents a continuous and differentiable
function, and then, changing of scalar field of parameter p is convenient to describe
it by gradient. If unit vector
l represents a normal vector to a surface (line) position directed to rise of navigational parameter p, then an expression, determining a
gradient, has the following form:
∂ p
∂l
=
lgrad p,
(5.36)
where gradient modulus
|grad p| =
∂ p
∂l
.
(5.37)
Gradient grad p is a vector variable, showing a direction of quickest rise of navigational parameter p, where gradient modulus |grad p| characterizes a change rate of
scalar function p.
Gradient gives a possibility to connect an error of measuring navigational parameter p with an error of surfaces (lines) position finding l. By transitioning in (2.2)
to finite decrements, we obtain:
l =
p
|grad p|
.
(5.38)
From (5.38), it is obvious that to reduce errors in detection of surfaces and lines
of position, a field gradient of navigational parameter and its measuring accuracy
should be increased.
If function p is given analytically in arbitrary Cartesian reference system, then a
gradient modulus for surface and line of position correspondingly has the following
form: