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5 X-ray Pulsar-Based Navigation: Theories and Experiments
difference of pulse phase cycle between the corresponding point of the pulse arrivaltime measured at the spacecraft and that of the pulse arrival-time predicted at the
SSB or a known reference point is usually called integer ambiguity.
For the absolute navigation of spacecraft, once the problem of integer ambiguity
of the pulse phase cycle is solved, and the measuring and predicting pulses belong
to the same pulse cycle, the time delay of the spacecraft relative to the SSB can be
measured, and the orbital parameters of the spacecraft relative to the SSB can be
determined in real time. In other words, as long as there are enough observation data
and the appropriate algorithm is used to solve the unknown of integer cycles, the
autonomous navigation parameters can be provided by using the X-ray pulsars for
spacecrafts in the near-earth orbits, deep space and interstellar space.
The integer ambiguity of XPNAV can be studied by the analogy with GNSS
carrier phase measuring, but the specific solving processes are different, due to the
discrepancies between the two systems. Without loss of generality, the GPS is taking
as an example to explain. The discrepancies between the XPNAV and GPS are shown
in the following aspects:
(1) There is the discrepancy in differencing measurement mechanism. For the
GPS, multiple receiving antennas can be used to measure the ambiguity of
two differencing stations. For the XPNAV, its basic observables are gotten
by comparing the pulse arrival-time measured by the detector onboard the
spacecraft and that predicted by the pulsar timing model defined at the SSB,
so as to determine the absolute position coordinates of the spacecraft. In fact,
there is not any physical detector placed at the SSB. Of course, in the relative
navigation application of two spacecrafts, multiple detectors can be installed
at different positions to determine the relative position.
(2) There are the discrepancies in periods and wavelengths. Currently, each satellite of the GPS constellation mainly broadcasts the navigations signals on
three central frequencies L1 (1575.42 MHz), L2 (1227.60 MHz) and L5
(1176.45 MHz), with wavelengths of 19.0 cm, 24.0 cm and 25.5 cm, respectively, and thus single carrier or multiple carrier observables can be used to
solve the ambiguity. For the XPNAV, the pulse profile of each X-ray pulsar is
unique, and the pulse periods are completely different, typically from a few
milliseconds to a few seconds, even a few minutes, which is advantageous to
solving the integer ambiguity. The wavelengths of the pulse cycles are more
than several hundred kilometers, which is an easily-detected “large cycle slip”.
(3) There is the discrepancy in system mechanism. The GPS is a man-made system,
its satellites orbit around the Earth, and their signal strengths mainly meet the
needs of the users on the ground and in the near-earth space. The pulsars belong
to natural celestial system. Although their distance away from the solar system
is very far distant and the intensities of their radiation signals are also not
controlled artificially, the stably periodic radiation signals can be detected in
the whole solar system or Galactic System.
(4) There is the discrepancy in electromagnetic wave band for emitting the signals.
The navigation signals of the GPS satellites are modulated in the L-band. The
5 X-ray Pulsar-Based Navigation: Theories and Experiments
difference of pulse phase cycle between the corresponding point of the pulse arrivaltime measured at the spacecraft and that of the pulse arrival-time predicted at the
SSB or a known reference point is usually called integer ambiguity.
For the absolute navigation of spacecraft, once the problem of integer ambiguity
of the pulse phase cycle is solved, and the measuring and predicting pulses belong
to the same pulse cycle, the time delay of the spacecraft relative to the SSB can be
measured, and the orbital parameters of the spacecraft relative to the SSB can be
determined in real time. In other words, as long as there are enough observation data
and the appropriate algorithm is used to solve the unknown of integer cycles, the
autonomous navigation parameters can be provided by using the X-ray pulsars for
spacecrafts in the near-earth orbits, deep space and interstellar space.
The integer ambiguity of XPNAV can be studied by the analogy with GNSS
carrier phase measuring, but the specific solving processes are different, due to the
discrepancies between the two systems. Without loss of generality, the GPS is taking
as an example to explain. The discrepancies between the XPNAV and GPS are shown
in the following aspects:
(1) There is the discrepancy in differencing measurement mechanism. For the
GPS, multiple receiving antennas can be used to measure the ambiguity of
two differencing stations. For the XPNAV, its basic observables are gotten
by comparing the pulse arrival-time measured by the detector onboard the
spacecraft and that predicted by the pulsar timing model defined at the SSB,
so as to determine the absolute position coordinates of the spacecraft. In fact,
there is not any physical detector placed at the SSB. Of course, in the relative
navigation application of two spacecrafts, multiple detectors can be installed
at different positions to determine the relative position.
(2) There are the discrepancies in periods and wavelengths. Currently, each satellite of the GPS constellation mainly broadcasts the navigations signals on
three central frequencies L1 (1575.42 MHz), L2 (1227.60 MHz) and L5
(1176.45 MHz), with wavelengths of 19.0 cm, 24.0 cm and 25.5 cm, respectively, and thus single carrier or multiple carrier observables can be used to
solve the ambiguity. For the XPNAV, the pulse profile of each X-ray pulsar is
unique, and the pulse periods are completely different, typically from a few
milliseconds to a few seconds, even a few minutes, which is advantageous to
solving the integer ambiguity. The wavelengths of the pulse cycles are more
than several hundred kilometers, which is an easily-detected “large cycle slip”.
(3) There is the discrepancy in system mechanism. The GPS is a man-made system,
its satellites orbit around the Earth, and their signal strengths mainly meet the
needs of the users on the ground and in the near-earth space. The pulsars belong
to natural celestial system. Although their distance away from the solar system
is very far distant and the intensities of their radiation signals are also not
controlled artificially, the stably periodic radiation signals can be detected in
the whole solar system or Galactic System.
(4) There is the discrepancy in electromagnetic wave band for emitting the signals.
The navigation signals of the GPS satellites are modulated in the L-band. The