314
16 Hyperbolic Radio Navigation Systems
neighboring digitized position lines has to be used. This required a certain skill.
It’s necessary to note that one of the existing HRNS disadvantages is conversion
complexity of an object hyperbolic coordinates in geographical ones, used often in
ship- and aircraft navigation.
Dependence of D on phase difference of two coherent oscillations, created at
receiving point by two ground-based stations located in positions with the known
coordinates, has been accepted as a basis for phase HRNS operation. The measured
phase difference is in certain relation with difference of distances from a moving
object to ground-based stations that permits to determine an object position line by
the measured phase difference.
Position line (hyperbolas) family is set up by two ground-based stations forming
a system base. To determine an object position, as for pulsed HRNS, it is necessary
as a minimum two pairs of stations, creating position lines. An object position is
determined as an intersection point of two position lines, created by different pairs
of stations.
All discussions relatively to pulsed HRNS are correct for phased HRNS as well,
excluding a method accepted as a basis for measuring of distance difference, i.e.,
phase difference measurements of two oscillations at receiving point (onboard an
object).
Phase difference measurement of two oscillations can be carried out either on high
(carrier) frequency or on beat (difference) frequency. Grids of position lines can be
determined by a frequency, different from a frequency on which the measurements
are performed. Correspondingly, phased HRNS are distinguished with grids set up
of position lines: on carrier frequency; on reduced pattern frequency; beat frequency;
on combination frequencies.
As an example, let’s examine HRNS operation principle with phase difference
measurement at carrier frequency.
For simplicity of arguments let’s consider that a pair of ground-based stations
radiates oscillations of the same frequency ω 0 and that operation of these stations
is coincided in the way that difference of initial phases ϕ 0 of radiated oscillations
remains unchangeable and can be admitted as equal to zero. Then current phases ϕ A
and ϕ B of oscillations radiated by both stations will be written as follows:
ϕ A = ϕ B = ω 0 t + ϕ 0 .
(16.5)
Oscillations of A station in M point are received with a phase
ϕ AM = ω 0 t + ϕ 0 −
ω 0
s
D A ,
(16.6)
and oscillations of B station—with a phase
ϕ BM = ω 0 t + ϕ 0 −
ω 0
s
D B ,
(16.7)
16 Hyperbolic Radio Navigation Systems
neighboring digitized position lines has to be used. This required a certain skill.
It’s necessary to note that one of the existing HRNS disadvantages is conversion
complexity of an object hyperbolic coordinates in geographical ones, used often in
ship- and aircraft navigation.
Dependence of D on phase difference of two coherent oscillations, created at
receiving point by two ground-based stations located in positions with the known
coordinates, has been accepted as a basis for phase HRNS operation. The measured
phase difference is in certain relation with difference of distances from a moving
object to ground-based stations that permits to determine an object position line by
the measured phase difference.
Position line (hyperbolas) family is set up by two ground-based stations forming
a system base. To determine an object position, as for pulsed HRNS, it is necessary
as a minimum two pairs of stations, creating position lines. An object position is
determined as an intersection point of two position lines, created by different pairs
of stations.
All discussions relatively to pulsed HRNS are correct for phased HRNS as well,
excluding a method accepted as a basis for measuring of distance difference, i.e.,
phase difference measurements of two oscillations at receiving point (onboard an
object).
Phase difference measurement of two oscillations can be carried out either on high
(carrier) frequency or on beat (difference) frequency. Grids of position lines can be
determined by a frequency, different from a frequency on which the measurements
are performed. Correspondingly, phased HRNS are distinguished with grids set up
of position lines: on carrier frequency; on reduced pattern frequency; beat frequency;
on combination frequencies.
As an example, let’s examine HRNS operation principle with phase difference
measurement at carrier frequency.
For simplicity of arguments let’s consider that a pair of ground-based stations
radiates oscillations of the same frequency ω 0 and that operation of these stations
is coincided in the way that difference of initial phases ϕ 0 of radiated oscillations
remains unchangeable and can be admitted as equal to zero. Then current phases ϕ A
and ϕ B of oscillations radiated by both stations will be written as follows:
ϕ A = ϕ B = ω 0 t + ϕ 0 .
(16.5)
Oscillations of A station in M point are received with a phase
ϕ AM = ω 0 t + ϕ 0 −
ω 0
s
D A ,
(16.6)
and oscillations of B station—with a phase
ϕ BM = ω 0 t + ϕ 0 −
ω 0
s
D B ,
(16.7)