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5 X-ray Pulsar-Based Navigation: Theories and Experiments
pulse cycle to generate the measurement pulse profile; by comparing the measurement pulse profile with the standard pulse profile, the pulse TOA can be measured;
by taking a series of the pulse TOA as the basic observables, and using the method
of least squares, the parameters, such as the pulsating signal frequency, and its firstorder and second-order derivatives, can be estimated. In this way, the pulsar timing
model is established, and the standard pulse profile template will be improved further.
For most of the pulsars, the radiation fluxes are very weak, and pulse signals
are often submerged in the background noise. For the ground-based observation of
pulsars, due to the different signal strength, waveform and polarization of single
pulse, it is difficult to obtain a stable pulse signal. However, in an observational
frequency band, the average waveform obtained by folding of hundreds or thousands
of single pulses is very stable and repeatable. Therefore, the pulsar timing observation
usually requires a long signal integration time to obtain the average pulse profile with
enough high SNR. The peak on the average pulse profile is selected as the reference
point, corresponding to a fixed point in the pulsar’s radiation region, which is used to
measure the pulse TOA. The time span of pulsar observation is usually several weeks,
and continual observation for many years can obtain a high-precision pulsar timing
model. TOA measuring is based on the atomic time. The reference atomic clocks
are regularly compared with the laboratories of the TAI, so that the measurement of
TOA can take the TAI as reference. An observer can measure the TOA from pulsar i,
which corresponds to a certain moment of pulsar time PT i . In theory, any event can
be compared with the pulse TOA, just as any event can be compared with the second
of atomic time.
5.5.2 Pulsar Timing Reference Frame
In the process of establishing the pulsar timing model, there are some undetermined
parameters, such as the pulsar’s rotation periods and change rates, angular position
and proper motions, as well as the orbital parameters for X-ray binary systems. Using
the differences between the atomic time that is the pulse TOA measured by the atomic
clocks at observation station and the pulsar time that is the pulse TOA predicted by
an initiative pulsar timing model, the iterative approximation estimation is carried
out by the method of least squares, and finally the best estimation values of the
undetermined parameters can be obtained. As a result, the dependence of the pulsar
time on the atomic time is introduced. It is shown that the rate of change of pulse
period is unable to be obtained without the dependence of the atomic time. In other
words, the rotation of a pulsar cannot provide an independent time unit. Moreover,
for the dependence of the pulsar time on the atomic time, the requirements for the
atomic timescale to be adopted are correspondingly put forward, such as good longterm stability, high precision of time interval unit (i.e., it is required to be consistent
with the length of second in the SI units), no frequency drift, no seasonal frequency
variation and enough readout accuracy. So, the TT is an ideal timescale for the pulsar
timing measurement.
5 X-ray Pulsar-Based Navigation: Theories and Experiments
pulse cycle to generate the measurement pulse profile; by comparing the measurement pulse profile with the standard pulse profile, the pulse TOA can be measured;
by taking a series of the pulse TOA as the basic observables, and using the method
of least squares, the parameters, such as the pulsating signal frequency, and its firstorder and second-order derivatives, can be estimated. In this way, the pulsar timing
model is established, and the standard pulse profile template will be improved further.
For most of the pulsars, the radiation fluxes are very weak, and pulse signals
are often submerged in the background noise. For the ground-based observation of
pulsars, due to the different signal strength, waveform and polarization of single
pulse, it is difficult to obtain a stable pulse signal. However, in an observational
frequency band, the average waveform obtained by folding of hundreds or thousands
of single pulses is very stable and repeatable. Therefore, the pulsar timing observation
usually requires a long signal integration time to obtain the average pulse profile with
enough high SNR. The peak on the average pulse profile is selected as the reference
point, corresponding to a fixed point in the pulsar’s radiation region, which is used to
measure the pulse TOA. The time span of pulsar observation is usually several weeks,
and continual observation for many years can obtain a high-precision pulsar timing
model. TOA measuring is based on the atomic time. The reference atomic clocks
are regularly compared with the laboratories of the TAI, so that the measurement of
TOA can take the TAI as reference. An observer can measure the TOA from pulsar i,
which corresponds to a certain moment of pulsar time PT i . In theory, any event can
be compared with the pulse TOA, just as any event can be compared with the second
of atomic time.
5.5.2 Pulsar Timing Reference Frame
In the process of establishing the pulsar timing model, there are some undetermined
parameters, such as the pulsar’s rotation periods and change rates, angular position
and proper motions, as well as the orbital parameters for X-ray binary systems. Using
the differences between the atomic time that is the pulse TOA measured by the atomic
clocks at observation station and the pulsar time that is the pulse TOA predicted by
an initiative pulsar timing model, the iterative approximation estimation is carried
out by the method of least squares, and finally the best estimation values of the
undetermined parameters can be obtained. As a result, the dependence of the pulsar
time on the atomic time is introduced. It is shown that the rate of change of pulse
period is unable to be obtained without the dependence of the atomic time. In other
words, the rotation of a pulsar cannot provide an independent time unit. Moreover,
for the dependence of the pulsar time on the atomic time, the requirements for the
atomic timescale to be adopted are correspondingly put forward, such as good longterm stability, high precision of time interval unit (i.e., it is required to be consistent
with the length of second in the SI units), no frequency drift, no seasonal frequency
variation and enough readout accuracy. So, the TT is an ideal timescale for the pulsar
timing measurement.