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5 X-ray Pulsar-Based Navigation: Theories and Experiments
Lagrange points between the Earth and the Sun, the Mar’s center of mass and the
position of anther spacecraft. And hence, the photon’s arrival-time can also be transformed to a known reference point rather than the SSB. In this case, it is only needed
that the SSB’s position vector b in the above time delay transformation formula is
replaced by the position vector of the corresponding reference point. Moreover, in
the process of photon’s arrival-time transformation, the parameters like the positions
and velocities of spacecrafts are needed to use, which are exactly the navigation
parameters required to solve. The usually adopted approach is firstly, the approximate state parameters of the spacecrafts are used for the time delay transformation
to get the basic observables, and then the more accurate state parameters are solved;
secondly, the solved state parameters are used for the time delay transformation again;
finally, the iterative approximation way is used until the accuracy requirements are
met. Generally, only will a few iterations needed meet the accuracy requirements by
using the short-term orbit propagation of spacecrafts.
5.6.3 Methods of Getting Pulse Profiles
5.6.3.1 Pulse Profile Folding
The pulse profiles of X-ray pulsars are composed of a sequence of the photons. A
two-dimensional array grid detector is used to measure the number, position and
arrival-time of the X-ray photons entering the field of view, in which the photon
arriving time is measured by the onboard clock. Each photon provides a quantified
unit of energy within the detector grid. According to the number and energy level
of the photons received per unit time, it can be judged whether the pulse signals are
detected. In order to observe the selected pulsars, the detectors are required to aim at
the lines of sight of the pulsars. As a photon is detected, the onboard clock records
the time when the photon arrives at the detector, which means that each photon is
marked with a time-stamp. For a pulsar, during the given observation time, when
there are n X-ray photons recorded, the time sequence from τ 0 to τ n-1 is composed
of the measuring time of each photon arriving at the detector coordinate frame,
and through the timescale and time delay transformations, the time sequence of the
photons arriving at the SSB in the TCB or TDB is obtained. Thus, the arrival-time of
the n photons is transformed to the quasi-inertial coordinate system which is almost
at rest relative to the pulsar. Usually, the given observation time is much longer than
single pulse period, so the n detected photons span over countless pulse cycles. Each
photon is only an energy point of a single pulse, so it is difficult to extract the pulse
profile information from single photon. Obviously, for the n photons, the photon
measuring data is essentially their arrival-time sequence.
In order to get the pulse profile, all of the measured photons must be aligned
according to the time of arrival and arranged within a pulse cycle. The process of
data processing in which the measured photons are arranged into a pulse cycle is
called pulse profile folding, or epoch folding. In other words, the epoch folding is
5 X-ray Pulsar-Based Navigation: Theories and Experiments
Lagrange points between the Earth and the Sun, the Mar’s center of mass and the
position of anther spacecraft. And hence, the photon’s arrival-time can also be transformed to a known reference point rather than the SSB. In this case, it is only needed
that the SSB’s position vector b in the above time delay transformation formula is
replaced by the position vector of the corresponding reference point. Moreover, in
the process of photon’s arrival-time transformation, the parameters like the positions
and velocities of spacecrafts are needed to use, which are exactly the navigation
parameters required to solve. The usually adopted approach is firstly, the approximate state parameters of the spacecrafts are used for the time delay transformation
to get the basic observables, and then the more accurate state parameters are solved;
secondly, the solved state parameters are used for the time delay transformation again;
finally, the iterative approximation way is used until the accuracy requirements are
met. Generally, only will a few iterations needed meet the accuracy requirements by
using the short-term orbit propagation of spacecrafts.
5.6.3 Methods of Getting Pulse Profiles
5.6.3.1 Pulse Profile Folding
The pulse profiles of X-ray pulsars are composed of a sequence of the photons. A
two-dimensional array grid detector is used to measure the number, position and
arrival-time of the X-ray photons entering the field of view, in which the photon
arriving time is measured by the onboard clock. Each photon provides a quantified
unit of energy within the detector grid. According to the number and energy level
of the photons received per unit time, it can be judged whether the pulse signals are
detected. In order to observe the selected pulsars, the detectors are required to aim at
the lines of sight of the pulsars. As a photon is detected, the onboard clock records
the time when the photon arrives at the detector, which means that each photon is
marked with a time-stamp. For a pulsar, during the given observation time, when
there are n X-ray photons recorded, the time sequence from τ 0 to τ n-1 is composed
of the measuring time of each photon arriving at the detector coordinate frame,
and through the timescale and time delay transformations, the time sequence of the
photons arriving at the SSB in the TCB or TDB is obtained. Thus, the arrival-time of
the n photons is transformed to the quasi-inertial coordinate system which is almost
at rest relative to the pulsar. Usually, the given observation time is much longer than
single pulse period, so the n detected photons span over countless pulse cycles. Each
photon is only an energy point of a single pulse, so it is difficult to extract the pulse
profile information from single photon. Obviously, for the n photons, the photon
measuring data is essentially their arrival-time sequence.
In order to get the pulse profile, all of the measured photons must be aligned
according to the time of arrival and arranged within a pulse cycle. The process of
data processing in which the measured photons are arranged into a pulse cycle is
called pulse profile folding, or epoch folding. In other words, the epoch folding is