5.6 Methods of Large-Scale Navigation
359
be seen: the pulse period is 2 s; the pulse wavelength is 2c where c is the velocity of
light; the distance and phase of point A are, respectively, 0.5c and 0.25; the distance
and phase of point B are, respectively, 6.5c and 3.25.
For any given time, the total pulse cycle phase F can be expressed as the sum of
the number N of integer cycles and a fraction φ of a cycle, and thus the measurement
equation using the pulse phase is expressed as
δρ p = −n SC · δ p − cδt SC + η p ,
(5.111)
where δρ p = λ
N + ˜
φ
− n SC · (D − ˜
p) − d Rel ; λ is the wavelength of pulse signal;
η p is the phase measurement noise.
The pulse phase measurement is to measure the phase within a pulse cycle. When
a pulsar is continuously tracked and observed, the number of integer cycles during the
entire observation segment can be recorded, but that at the initial epoch is unknown.
In the XPNAV, the integer-cycle number of the spacecraft relative to the pulsar is not
solved, but that of the spacecraft relative to the SSB or a known point. Generally, it
is considered that there is no error for solving the number of pulse cycles. If there
is the error of one pulse cycle, it will result in the ranging error of hundreds or
even thousands of kilometers. For the spacecraft’s orbit determination, this is an
intolerable gross error, which is detected and offset easily.
5.6.5.3 Measurement Equation for Absolute Navigation
The absolute navigation is to determine the three-dimensional position and velocity
of the spacecraft in the BCRS, so as to obtain the relative relationship between
spacecraft and its near celestial objects, control the spacecraft to avoid obstacles,
and guide it to fly along the predetermined orbit. By comparing the time difference
between the same pulse arriving at the spacecraft and at the SSB, the time delay of
the spacecraft relative to the SSB along the line of sight of the pulsar can be gotten.
That is to say, the ranging observables can be gotten. Without loss of generality, the
simplified time delay model (5.106) is adopted here. For a given epoch t k , using the
detecting data from pulsar i, the measurement equation of the spacecraft relative to
the SSB can be expressed as
δρ i = n i · δr SC,k + cδ t k + η i ,
(5.112)
where
δρ i = ct SSB − ct SC − n i · ˜
r SC,k
+
1
2D 0
n i · ˜
r SC,k
2 − r
2
+ 2(n i · b)
n i · ˜
r SC,k
− 2
b · ˜
r SC,k
359
be seen: the pulse period is 2 s; the pulse wavelength is 2c where c is the velocity of
light; the distance and phase of point A are, respectively, 0.5c and 0.25; the distance
and phase of point B are, respectively, 6.5c and 3.25.
For any given time, the total pulse cycle phase F can be expressed as the sum of
the number N of integer cycles and a fraction φ of a cycle, and thus the measurement
equation using the pulse phase is expressed as
δρ p = −n SC · δ p − cδt SC + η p ,
(5.111)
where δρ p = λ
N + ˜
φ
− n SC · (D − ˜
p) − d Rel ; λ is the wavelength of pulse signal;
η p is the phase measurement noise.
The pulse phase measurement is to measure the phase within a pulse cycle. When
a pulsar is continuously tracked and observed, the number of integer cycles during the
entire observation segment can be recorded, but that at the initial epoch is unknown.
In the XPNAV, the integer-cycle number of the spacecraft relative to the pulsar is not
solved, but that of the spacecraft relative to the SSB or a known point. Generally, it
is considered that there is no error for solving the number of pulse cycles. If there
is the error of one pulse cycle, it will result in the ranging error of hundreds or
even thousands of kilometers. For the spacecraft’s orbit determination, this is an
intolerable gross error, which is detected and offset easily.
5.6.5.3 Measurement Equation for Absolute Navigation
The absolute navigation is to determine the three-dimensional position and velocity
of the spacecraft in the BCRS, so as to obtain the relative relationship between
spacecraft and its near celestial objects, control the spacecraft to avoid obstacles,
and guide it to fly along the predetermined orbit. By comparing the time difference
between the same pulse arriving at the spacecraft and at the SSB, the time delay of
the spacecraft relative to the SSB along the line of sight of the pulsar can be gotten.
That is to say, the ranging observables can be gotten. Without loss of generality, the
simplified time delay model (5.106) is adopted here. For a given epoch t k , using the
detecting data from pulsar i, the measurement equation of the spacecraft relative to
the SSB can be expressed as
δρ i = n i · δr SC,k + cδ t k + η i ,
(5.112)
where
δρ i = ct SSB − ct SC − n i · ˜
r SC,k
+
1
2D 0
n i · ˜
r SC,k
2 − r
2
+ 2(n i · b)
n i · ˜
r SC,k
− 2
b · ˜
r SC,k