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You are here: Allan's TIME > Publications > ION GPS 2001 > Appendix A -- Navigation and Timing Accuracy at the 30 Centimeter and Sub-Nanosecond Level

Appendix A

Navigation and Timing Accuracy at the 30 Centimeter and Sub-Nanosecond Level


David W Allan
Allan's Time Interval Metrology Enterprise
P.O. Box 66
Fountain Green, UT USA 84632


Neil Ashby
Department of Physics Campus Box 390
University of Colorado
Boulder CO USA 80309


Past and current navigation systems using clocks in orbiting satellites require earth-based monitor stations which are used to estimate the space clocks' times and frequencies as well as the satellites' velocity and positions (orbital elements or ephemerides). The geometries and atmospheric delays limit current technology such that the best navigation accuracies are several meters for real-time systems.

Better accuracies, after the tact, can be calculated with large amounts of averaging. Differential GPS delivers very good accuracies, but is a much more complicated approach, and it is not conveniently available globally.

This invention combines three technological realities in a way that provides navigation accuracies more than ten times better (sub 30 cm) -- than are currently available. These three technologies are as follows.

First, atomic clocks are now being made whose frequencies in space can be known without calibration or reference to an earth monitor station. Having an independent frequency standard in space, being measured with an earth monitor station frequency standard of comparable accuracy, provides frequency Doppler shift information which can be used for very accurate orbit period determination.

Second, the poorest geometries limiting current navigation systems can be bypassed if the satellites' basic equations of motion are truly followed. For example, the period of orbit of a satellite is directly relatable to its radius vector from the center of mass of the earth. We can utilize the significant advantage that the satellite moves at right angles to the radius vector -- giving an optimum geometrical view. Hence, if the orbit period is well known, the radius is well known. Using the Doppler shift relationships, the period can be determined very accurately, and its uncertainty is not limited by atmospheric delay uncertainties. Thus, both the geometric limitations and the atmospheric delay uncertainties causing most of the inaccuracies in current navigation systems are circumvented with this invention.

Third, the basic equations of motion will be followed if compensation can be made for effects perturbing the satellites' orbits. These include but are not limited to solar winds and pressure, radiation pressure and atmospheric drag. Drag-free systems have been developed and tested in space which compensate for these effects. In well designed systems, the residual forces cause accelerations significantly less than 10-11g, where "g" is the gravitational acceleration on the surface of the earth. For GPS orbits, 10-11g would amount to an 8 cm error in one orbit.

As an illustration of combining the three technologies outlined above, consider Kepler's second law:  T2 = (2pi)2r2/GMe, where "T" is the satellite's orbit period, "r" is the distance from the satellite to the center of mass of the Earth, "G" is the universal constant of gravitation, and "Me" is the mass of the Earth.Each time the satellite's clock is observed from a monitor station's clock, one can conceptualize that point where the Doppler shift will be zero. The satellite clock's frequency and that of the monitor station agree with proper relativistic terms included. This can be viewed as a fiducial point in the satellite's orbit. Hence from pass to pass the Doppler frequency behavior can be used to determine the orbit period. For example if the orbit period could be determined with an uncertainty of 175 microseconds, then the uncertainty of the absolute length of the radius vector to the satellite from the center of mass of the Earth would be 7 cm at GPS altitudes. This level of uncertainty would be available using the Doppler effect if the accuracy of the satellite's clock frequency were 10-11.  This approach effectively bypasses the need of having an accurate measurement of the time- of-flight of the satellite's signal through the ionosphere and troposphere. Rather, it is based on the constancy of the gravitational constant and of the mass of the Earth -- along with the fact that gravitational fields are not perturbed by the atmosphere.

This invention provides that by having two or more monitor stations, or by having one with the satellites in non-synchronous sidereal orbits, the position and the velocity are determinable in real-time for each of the satellites configured with this invention. Accurate time and frequency information are natural bi-products.  

Utilizing current technology, and experience gained from previous navigation and timing systems, we have the opportunity, using this invention, to improve accuracy for navigation and timing by about an order of magnitude over current GPS numbers. The simulated accuracies are about 30 cm, and less than a nanosecond for timing.

It may also be possible to simplify system management. For example, as compared to GPS, only one monitor station is needed, and even if two or more are used for redundancy and robustness, data do not need to be communicated to one central location for the calculation of satellite ephemerides. The satellite can broadcast its position in real-time, and each pass over a monitor station provides a slight correction update. Neither is communication between the satellites necessary as is designed into the next generation of GPS Block 2-R satellites, which will deliver 3 meter accuracy.


  1. Potential to provide real-time navigation accuracies better than one meter for avionics and terrestrial vehicles, and to reach accuracies better than 10 centimeters. For example, this invention could provide sub one meter precision approaches which are so important in blind conditions for aircraft.
  2. Potential to provide root mean square (RMS) errors for satellites' orbital elements of 10 centimeter or better available in real-time. This level of accuracy can be achieved with state-of-the-art cesium-beam frequency standards.
  3. Potential to provide an international time reference with sub-one-nanosecond accuracy.
  4. Potential to provide normalized frequency-transfer uncertainties between any two timing centers on the surface of the Earth such that the full accuracy of the best primary frequency standards involved may be realized.
  5. Potential to provide an independent inertial reference from which fine detail of Earth dynamics may be studied: short-term UTI variations; Earth and ocean tides; ocean currents; polar motion; Earth core-mantle slippage; correlations of Earth dynamics with earthquakes and as a potential element in earthquake prediction.
  6. Potential to provide collision avoidance assist for land, sea and aircraft.
  7. Potential to provide harbor control and avoidance of sea craft collisions with natural hazards: reefs, rocks, shallow areas (correlating tides, acean currents and underwater objects for safety purposes).

  8. Taken to its practical limit with currently available technology, the invention could reach less than I cm navigation accuracies. This could be done with hydrogen maser clocks in the satellites and in the monitor station(s), calibrated using timing signals to assure accuracies of both at the 10-14 level. Because of the excellent short-term stabilities of H-masers, the frequency during one pass can be resolved to this accuracy level. By way of example, at GPS orbits the radius could be resolved to 7 mm.
  9. This invention has the potential to provide an external-to-the-Earth inertial-reference frame. Any long-term drift in this frame could be calibrated using Very Long Baseline Interferometry (VLBI), which can reference fixed radio stars in space. These two methodologies taken together could open up some very important opportunities in our understandings of Earth dynamics. The Earth has day-to-day random variations amounting to about 7 cm (a point at the equator speeding up or slowing down in an RMS sense, this amount).  VLBI can resolve earth movements, but this invention pushes the accuracy another factor often better in the short-term, and could, potentially be much more convenient and cost effective. There is the very real possibility that these movements could be correlated with earthquake phenomena and Earth plate tectonics. Understanding the Earth's dynamics as a whole system could be extremely useful. This could also open up increased understanding of the higher order moments describing the mass distribution within the Earth as well help observe Earth core-mantle slippage.
  10. Potential to provide high-accuracy orbital elements for satellites which are semi-independent of the signal delay through the atmosphere. In other words, most other satellite systems, such as GPS, depend on measured time delay through the atmosphere. Given a fixed and unknown delay, the frequency, which this invention uses does not change.

ION GPS 2001 paper context

return to ION GPS paper



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