5.6 Methods of Large-Scale Navigation
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shift of pulsating signal and position of pulsar’s image. According to the different
requirements for solving the navigation parameters, the different observables can be
extracted from them.
The pulse-arriving time (or pulse TOA) is a basic observable to determine the
position and time parameters of spacecrafts. When the X-ray photons radiated from
pulsars enter the field of view of the onboard X-ray detectors, the photon counter
will record the number of the incident X-ray photons, whose arriving times are
marked by the onboard clock. Consequently, the number and arrival-time of photons
are the original observables in practice. However, it is difficult to obtain the basic
characteristics of pulsars from the arrival-time of single photon. The arrival-time of
photons will be transformed into the BCRS to make the signal processing, so as to
obtain the average pulse profile curve during integration time. As a result, the time
corresponding to the peak of the pulse profile near the middle segment during the
integration time is taken as the TOA of the pulse, and the peak corresponds to a fixed
point in the beam area radiated from the pulsar.
The Doppler frequency shifts of pulsating signals are the basic observables to
determine the velocity of spacecrafts. The pulsars radiate the periodic pulse signals.
When the spacecrafts move toward the pulsars, the observed pulse frequencies are
greater than the transmitting ones, and when the spacecrafts move away from the
pulsars, the observed pulse frequencies are less than the transmitting ones. The differences between the transmitting and receiving pulse frequencies are the Doppler shifts.
By calculating the derivative of pulsar timing model, the pulse frequency can be
predicted. The Doppler frequency shifts are determined by comparing the measured
pulse signal frequencies with the predicted ones. The velocities of the spacecrafts
along the line of sight of pulsars can be computed by the Doppler frequency shifts. In
this way, the velocity measurement equations can be established. When the Doppler
frequency shifts of more than four pulsars are observed at the same time, the threedimensional velocities and clock frequency drifts of spacecrafts can be estimated
directly by using the method of least squares.
The positions of pulsar’s images are the basic observables to determine the attitude
parameters of spacecrafts. The positions of the images generated by the pulsars on the
detector’s plane can be read directly from the plane grid. When the detector is installed
on a three-axis gimbaled platform, the rotation angles of the detector coordinate
system relative to the spacecraft-body coordinate system can be directly obtained
from the rotation of the platform frame. Obviously, it is equivalent to measuring the
position coordinates of the pulsar’s image in the spacecraft-body coordinate system.
The identifiers of the pulsars in the navigation database can be identified by the crosscorrelation processing between the measured and standard pulse profiles, and then
the angular positions of the pulsars in the BCRS can be looked up in the navigation
database using the identifiers. Through the coordinate transformation, the angular
positions of the pulsars in the orbital coordinate system are obtained. So, from the
rotation transformation matrix between the spacecraft-body coordinate system and
the orbital coordinate system, the attitude angle components of spacecrafts can be
gotten. The imaging time of the pulsars on the detector’s plane relies on the rotation
343
shift of pulsating signal and position of pulsar’s image. According to the different
requirements for solving the navigation parameters, the different observables can be
extracted from them.
The pulse-arriving time (or pulse TOA) is a basic observable to determine the
position and time parameters of spacecrafts. When the X-ray photons radiated from
pulsars enter the field of view of the onboard X-ray detectors, the photon counter
will record the number of the incident X-ray photons, whose arriving times are
marked by the onboard clock. Consequently, the number and arrival-time of photons
are the original observables in practice. However, it is difficult to obtain the basic
characteristics of pulsars from the arrival-time of single photon. The arrival-time of
photons will be transformed into the BCRS to make the signal processing, so as to
obtain the average pulse profile curve during integration time. As a result, the time
corresponding to the peak of the pulse profile near the middle segment during the
integration time is taken as the TOA of the pulse, and the peak corresponds to a fixed
point in the beam area radiated from the pulsar.
The Doppler frequency shifts of pulsating signals are the basic observables to
determine the velocity of spacecrafts. The pulsars radiate the periodic pulse signals.
When the spacecrafts move toward the pulsars, the observed pulse frequencies are
greater than the transmitting ones, and when the spacecrafts move away from the
pulsars, the observed pulse frequencies are less than the transmitting ones. The differences between the transmitting and receiving pulse frequencies are the Doppler shifts.
By calculating the derivative of pulsar timing model, the pulse frequency can be
predicted. The Doppler frequency shifts are determined by comparing the measured
pulse signal frequencies with the predicted ones. The velocities of the spacecrafts
along the line of sight of pulsars can be computed by the Doppler frequency shifts. In
this way, the velocity measurement equations can be established. When the Doppler
frequency shifts of more than four pulsars are observed at the same time, the threedimensional velocities and clock frequency drifts of spacecrafts can be estimated
directly by using the method of least squares.
The positions of pulsar’s images are the basic observables to determine the attitude
parameters of spacecrafts. The positions of the images generated by the pulsars on the
detector’s plane can be read directly from the plane grid. When the detector is installed
on a three-axis gimbaled platform, the rotation angles of the detector coordinate
system relative to the spacecraft-body coordinate system can be directly obtained
from the rotation of the platform frame. Obviously, it is equivalent to measuring the
position coordinates of the pulsar’s image in the spacecraft-body coordinate system.
The identifiers of the pulsars in the navigation database can be identified by the crosscorrelation processing between the measured and standard pulse profiles, and then
the angular positions of the pulsars in the BCRS can be looked up in the navigation
database using the identifiers. Through the coordinate transformation, the angular
positions of the pulsars in the orbital coordinate system are obtained. So, from the
rotation transformation matrix between the spacecraft-body coordinate system and
the orbital coordinate system, the attitude angle components of spacecrafts can be
gotten. The imaging time of the pulsars on the detector’s plane relies on the rotation