100
5 Performance Characteristics of Radar Location …
where x m (t) and y m (t)—measured (calculated) coordinates of an object; x(t) and
y(t)—true values of object coordinates.
As it follows from (5.56), errors x(t) and y(t) appeared by a reason that initial
coordinates x 0 and y 0 , comprising a path velocity W
x and W
y , and orthodromic (great
circle) course 0 are determined with errors as well.
Dispersions of object coordinates finding errors in axes OX and OY correspondingly are equal:
σ
2
x (t) = M
◦
x(t)
2
,
σ
2
y (t) = M
◦
y(t)
2
,
where index «°» means a centralized value of random value.
By defining with required accuracy with mathematical models of initial coordinates errors x 0 and y 0 , comprising a vector of a full path velocity W
x and W
y and
course 0 , according to (5.56), the values σ
2
x (t) and σ
2
y (t) are calculated. Then,
based on (5.55), a mean-square value of radial error of object position finding σ r (t)
is determined.
5.3 Operating Space of Radar Location and Radio
Navigation Systems
To estimate RNS possibilities and comparison them between each other a definition
of operating space (functional area) is used. Operating space (area) is defined by
operational range of the system, admitted error of object position finding and directional patterns of antennas. For different RNS types, operating areas have different
sizes and contours.
Plotting of RNS operating space resolves into determination (for assigned position points of ground-based stations) of curves of admitted object position errors
calculation; curves, limiting an operational range, and sectors, defined by directional
patterns of antennas. Further, for simplicity, we examine RNS operating zones, corresponding to multi-directional operation mode of ground-based stations. Herewith,
mathematically operating area (zone) is defined by the following in equations:
D ≤ Dmax, σ r ≤ σ r dr ,
(5.57)
where σ r dr —admissible limit value of mean-square value of object position finding.
Value σ r is calculated according to (5.46). Operating zones of applied in practice
RNS of different types will be examined bellow. Outer boundary of RNS operating
area is generated after plotting of curves on a map corresponding to D = Dmax and
σ r = σ r dr , as a boundary of general part of surface area, surrounded by these curves.
5 Performance Characteristics of Radar Location …
where x m (t) and y m (t)—measured (calculated) coordinates of an object; x(t) and
y(t)—true values of object coordinates.
As it follows from (5.56), errors x(t) and y(t) appeared by a reason that initial
coordinates x 0 and y 0 , comprising a path velocity W
x and W
y , and orthodromic (great
circle) course 0 are determined with errors as well.
Dispersions of object coordinates finding errors in axes OX and OY correspondingly are equal:
σ
2
x (t) = M
◦
x(t)
2
,
σ
2
y (t) = M
◦
y(t)
2
,
where index «°» means a centralized value of random value.
By defining with required accuracy with mathematical models of initial coordinates errors x 0 and y 0 , comprising a vector of a full path velocity W
x and W
y and
course 0 , according to (5.56), the values σ
2
x (t) and σ
2
y (t) are calculated. Then,
based on (5.55), a mean-square value of radial error of object position finding σ r (t)
is determined.
5.3 Operating Space of Radar Location and Radio
Navigation Systems
To estimate RNS possibilities and comparison them between each other a definition
of operating space (functional area) is used. Operating space (area) is defined by
operational range of the system, admitted error of object position finding and directional patterns of antennas. For different RNS types, operating areas have different
sizes and contours.
Plotting of RNS operating space resolves into determination (for assigned position points of ground-based stations) of curves of admitted object position errors
calculation; curves, limiting an operational range, and sectors, defined by directional
patterns of antennas. Further, for simplicity, we examine RNS operating zones, corresponding to multi-directional operation mode of ground-based stations. Herewith,
mathematically operating area (zone) is defined by the following in equations:
D ≤ Dmax, σ r ≤ σ r dr ,
(5.57)
where σ r dr —admissible limit value of mean-square value of object position finding.
Value σ r is calculated according to (5.46). Operating zones of applied in practice
RNS of different types will be examined bellow. Outer boundary of RNS operating
area is generated after plotting of curves on a map corresponding to D = Dmax and
σ r = σ r dr , as a boundary of general part of surface area, surrounded by these curves.