5.6 Methods of Large-Scale Navigation
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time. The triple difference refers to the difference between two double differences of
observing more than two pulsars synchronously within different observation time.
The common error terms, and the parameters which are difficult to be measured
accurately, can be eliminated or weakened through the differencing measurements,
so as to simplify the measurement equations and improve the system-state-estimated
accuracy.
Usually, the pulsar timing model is defined by taking the SSB as the reference
point, from which the single differencing measurement equation is obtained. This
single differencing equation is the measurement equation for the absolute navigation.
In order to simply the data processing, at any given epoch, the pulse arrival-time
predicted by the pulsar timing model defined at the SSB can be transformed to any
known reference positions, such as the centers of mass of the Earth, Moon and
Mars, the Lagrange points between the Earth–Moon or the Earth–Sun, as well as
another spacecraft or a base station. For two spacecrafts on which the detectors
are installed, the X-ray photons radiated from the same pulsar are detected by the
detectors, and the communication link between the two spacecrafts needs to be
established for the differencing measurements to transmit the measurement data,
which is the relative navigation mode in real sense. Choosing the SSB or the center of
mass of a certain celestial body as the reference point, it is not required to transmit the
measurement data for establishing the differencing measurement equations, which
can be achieved only by calling the corresponding models and databases stored in
the onboard computer.
5.6.6 Determination of Attitude Parameters
The attitude measurements of the spacecraft using X-ray pulsars are similar to the
optical sensors, and their difference is that the X-ray photons are used to replace the
visible light, resulting in the different signal processing algorithms. The pulse profile
is the unique identifier of a pulsar. Once the pulse profile information is extracted, the
one-to-one correspondence between the observed and the catalogued pulsars in the
database will be established [29]. The fundamental problem of attitude determination of the spacecraft is to determine the attitude parameters of the spacecraft-body
coordinate system (b-system) relative to the reference coordinate system (r-system),
which is called three-axis attitude determination; or for a certain direction vector
(unit vector) in the b-system, the process of determining its coordinates relative to the
r-system is called single axis attitude determination. In this section, the three-axis
attitude determination of the spacecrafts in the Earth orbits is mainly discussed, and
for the deep-space probes, it can be processed similarly.
In the measurement coordinate system of the onboard detector, the measured
direction vectors of pulsars are the basic observables of the spacecraft’s attitude determination. The X-ray photons radiated from the pulsars are positioned and imaged
with the mechanical collimators and by using optical focusing methods, and for the
soft X-rays, the coded-aperture imaging technology can also be used. Supposed that
361
time. The triple difference refers to the difference between two double differences of
observing more than two pulsars synchronously within different observation time.
The common error terms, and the parameters which are difficult to be measured
accurately, can be eliminated or weakened through the differencing measurements,
so as to simplify the measurement equations and improve the system-state-estimated
accuracy.
Usually, the pulsar timing model is defined by taking the SSB as the reference
point, from which the single differencing measurement equation is obtained. This
single differencing equation is the measurement equation for the absolute navigation.
In order to simply the data processing, at any given epoch, the pulse arrival-time
predicted by the pulsar timing model defined at the SSB can be transformed to any
known reference positions, such as the centers of mass of the Earth, Moon and
Mars, the Lagrange points between the Earth–Moon or the Earth–Sun, as well as
another spacecraft or a base station. For two spacecrafts on which the detectors
are installed, the X-ray photons radiated from the same pulsar are detected by the
detectors, and the communication link between the two spacecrafts needs to be
established for the differencing measurements to transmit the measurement data,
which is the relative navigation mode in real sense. Choosing the SSB or the center of
mass of a certain celestial body as the reference point, it is not required to transmit the
measurement data for establishing the differencing measurement equations, which
can be achieved only by calling the corresponding models and databases stored in
the onboard computer.
5.6.6 Determination of Attitude Parameters
The attitude measurements of the spacecraft using X-ray pulsars are similar to the
optical sensors, and their difference is that the X-ray photons are used to replace the
visible light, resulting in the different signal processing algorithms. The pulse profile
is the unique identifier of a pulsar. Once the pulse profile information is extracted, the
one-to-one correspondence between the observed and the catalogued pulsars in the
database will be established [29]. The fundamental problem of attitude determination of the spacecraft is to determine the attitude parameters of the spacecraft-body
coordinate system (b-system) relative to the reference coordinate system (r-system),
which is called three-axis attitude determination; or for a certain direction vector
(unit vector) in the b-system, the process of determining its coordinates relative to the
r-system is called single axis attitude determination. In this section, the three-axis
attitude determination of the spacecrafts in the Earth orbits is mainly discussed, and
for the deep-space probes, it can be processed similarly.
In the measurement coordinate system of the onboard detector, the measured
direction vectors of pulsars are the basic observables of the spacecraft’s attitude determination. The X-ray photons radiated from the pulsars are positioned and imaged
with the mechanical collimators and by using optical focusing methods, and for the
soft X-rays, the coded-aperture imaging technology can also be used. Supposed that