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5 X-ray Pulsar-Based Navigation: Theories and Experiments
(4) The short-term stability of the PT is not as good as that of the AT. For short
observation time, the PT accuracy generally gets to the microsecond level,
which is relied on the accuracy level of currently measuring the pulse TOA.
Only by observing the millisecond pulsars continually during the long term and
accurately measuring their parameters, a precise timing model can be established
and its timing stability improved further. As establishing the pulsar timing model,
the angular position accuracy of pulsars is required to reach 0.1 milliarcseconds
to accurately make the time transformation of the TOA. In addition, the long-term
component errors in the solar system ephemeris, as well as the influences of the
selected TOA transforming and timing models, should be considered. Generally, the
error caused by imperfection of the TOA timing model is 5−10 times larger than
that of the fitting of least squares. Thereby, the high-precision PT can be obtained
only by processing the cumulatively observed data for many years. Moreover, the
angular positions, proper motions, distances and other parameters of some pulsars are
obtained by the VLBI observations. It is required that the VLBI observation reaches
the accuracy level of 0.1 milliarcseconds, and the connection between the BCRF or
GCRF and the VLBI reference frame should also reach the corresponding accuracy
level. At present, except for a few millisecond pulsars like PSR B1937+21, whose
angular position accuracy using the VLBI reaches the order of 0.1 milliarcseconds,
most pulsars are only the order of 10 milliarcseconds due to their low radiation flux
density. The VLBI is used to measure the pulsar’s angular positions to avoid the
fluctuation errors from the atomic time introduced in the pulsar’s parameters fitting.
With the development of the VLBI, the accuracy of measuring the pulsar’s angular
positions will be improved further.
For the pulsar timing residuals, besides the intrinsic noises of the atomic time
and millisecond pulsar’s rotation, there are also the errors of interstellar dispersion,
gravitational wave background and solar system planetary ephemeris. Except for the
noise of atomic time itself, other error sources are independent of one another for
different pulsars, and thus the ensemble pulsar time can be established by weighting
every single pulsar time. In this way, the influence of various independent noise
sources can be weakened, and the ensemble pulsar time should be more stable than
the single pulsar time. With the utilized pulsar number and the observational time
increasing, the influence of random errors on the long-term stability of the ensemble
pulsar time is weakened, and thus the stability of the ensemble pulsar time will finally
reach or be better than the level of the atomic time.
For the short-term stability of pulsar timing, it is far lower than the comparison
accuracy of the atomic time. Currently, the comparison accuracy of the atomic time
based on the TWSTFT technique of GNSS satellites has been better than 3 ns level,
and the short-term noise of pulsar is still larger than the atomic time. Generally
speaking, only by using a few months of pulsar’s observation data, the pulsar time
cannot reach the level of stability of the atomic time yet. On the one hand, the pulsar
time is defined by the TOA analysis model, but the model parameters cannot be
accurately determined in advance, usually obtained by the least squares fitting with
the TOA observables. On the other hand, using the timing residual AT–PT to fit the
5 X-ray Pulsar-Based Navigation: Theories and Experiments
(4) The short-term stability of the PT is not as good as that of the AT. For short
observation time, the PT accuracy generally gets to the microsecond level,
which is relied on the accuracy level of currently measuring the pulse TOA.
Only by observing the millisecond pulsars continually during the long term and
accurately measuring their parameters, a precise timing model can be established
and its timing stability improved further. As establishing the pulsar timing model,
the angular position accuracy of pulsars is required to reach 0.1 milliarcseconds
to accurately make the time transformation of the TOA. In addition, the long-term
component errors in the solar system ephemeris, as well as the influences of the
selected TOA transforming and timing models, should be considered. Generally, the
error caused by imperfection of the TOA timing model is 5−10 times larger than
that of the fitting of least squares. Thereby, the high-precision PT can be obtained
only by processing the cumulatively observed data for many years. Moreover, the
angular positions, proper motions, distances and other parameters of some pulsars are
obtained by the VLBI observations. It is required that the VLBI observation reaches
the accuracy level of 0.1 milliarcseconds, and the connection between the BCRF or
GCRF and the VLBI reference frame should also reach the corresponding accuracy
level. At present, except for a few millisecond pulsars like PSR B1937+21, whose
angular position accuracy using the VLBI reaches the order of 0.1 milliarcseconds,
most pulsars are only the order of 10 milliarcseconds due to their low radiation flux
density. The VLBI is used to measure the pulsar’s angular positions to avoid the
fluctuation errors from the atomic time introduced in the pulsar’s parameters fitting.
With the development of the VLBI, the accuracy of measuring the pulsar’s angular
positions will be improved further.
For the pulsar timing residuals, besides the intrinsic noises of the atomic time
and millisecond pulsar’s rotation, there are also the errors of interstellar dispersion,
gravitational wave background and solar system planetary ephemeris. Except for the
noise of atomic time itself, other error sources are independent of one another for
different pulsars, and thus the ensemble pulsar time can be established by weighting
every single pulsar time. In this way, the influence of various independent noise
sources can be weakened, and the ensemble pulsar time should be more stable than
the single pulsar time. With the utilized pulsar number and the observational time
increasing, the influence of random errors on the long-term stability of the ensemble
pulsar time is weakened, and thus the stability of the ensemble pulsar time will finally
reach or be better than the level of the atomic time.
For the short-term stability of pulsar timing, it is far lower than the comparison
accuracy of the atomic time. Currently, the comparison accuracy of the atomic time
based on the TWSTFT technique of GNSS satellites has been better than 3 ns level,
and the short-term noise of pulsar is still larger than the atomic time. Generally
speaking, only by using a few months of pulsar’s observation data, the pulsar time
cannot reach the level of stability of the atomic time yet. On the one hand, the pulsar
time is defined by the TOA analysis model, but the model parameters cannot be
accurately determined in advance, usually obtained by the least squares fitting with
the TOA observables. On the other hand, using the timing residual AT–PT to fit the