The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.

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Relativity in the Global Positioning System

We need general relativity to understand extreme astrophysical realms. But the theory also turns out to be essential for the many mundane activities that nowadays rely on the precision of the GPS.

Relativity and the Global Positioning System

Techniques are provided for presenting a route in a manner that emphasizes the route and provides context information. For example, a vivid color or vivid colors may be used to display the route, and pastel colors or other desaturated colors may be used for non-route context information. This may result in a map in which the vivid colors of the route stand out over the faded style of the non-route context information to emphasize the route. In this manner, the map may both emphasize the route and provide context information for the route.

Presenting a travel route using more than one presentation style

: This publication is a listing of journal articles and conference papers by Naval Research Laboratory authors for 1994. The bibliographic information is taken, primarily, from the Institute of Scientific Information database, Science Citation Index Expanded. Additional citations are generated from reprints of publications which are received in the Laboratory's Ruth H. Hooker Research Library. All references are unclassified. Citations are arranged alphabetically by author. An author index is included at the end of the citation listing. An HTML version of this publication is mounted on the Website of the Ruth H. Hooker Research Library - http://infoweb.nrl.navy.mil.

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1994 Bibliography of NRL Journal Articles and Conference Papers

For more than four decades, caesium atomic clocks have been the backbone in a variety of demanding applications in science and technology. Neither satellite based navigation systems, like the US Global Positioning System, nor the syntonization of telecommunication networks at the presently prescribed levels, would function without them. Recent years have brought major breakthroughs in the development, operation and mutual comparison of frequency standards based on the same hyperfine transition in caesium as used previously, but now incorporating the technique of laser cooling. Several cold-atom fountains have been developed. Mutual agreement to within about one part in 1015 has been demonstrated for two of them operated side by side, and also for two operated simultaneously, in the US and Germany. This paper gives an overview of currently available commercial caesium clocks and primary standards developed in national metrology institutes.

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Caesium atomic clocks: function, performance and applications

: Navigation Technology Satellite 2 (NTS-2) was successfully launched on June 23, 1977, into a near-12-hour circular orbit. Precise frequency and timing signals are derived from the two cesium frequency standards. This report discusses the launch and preliminary results, which include verification of the relativistic clock effect. An international time-transfer experiment is planned, and a worldwide synchronization accuracy of less than 100 nanoseconds is anticipated, based on preliminary time-transfer results between Cape Kennedy and the U.S. Naval Observatory. A proposed NASA laser-tracking network will be used to verify the accuracy of the Global Positioning System (GPS) orbits.

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Initial Results of the NAVSTAR GPS NTS-2 Satellite

The Naval Research Laboratory analyzes the performance of the on-orbit Navstar clocks for the Global Positioning System (GPS) Joint Program Office and conducts special analyses for the GPS master control station (MCS) whenever a clock exhibits anomalous behavior. This analysis focuses on the long-term behavior of the cesium and rubidium clocks using sample times of one day or more. It includes frequency and aging histories, frequency-stability profiles, time-domain noise process profiles, and anomaly detection. Events that perturb the normal clock behavior are of particular interest. The semiannual eclipse seasons will be superimposed on selected plots to investigate the temperature sensitivity of the clocks. Of particular interest is the nonstationary stochastic behavior of one of the cesium clocks, illustrated by its frequency-stability history, showing that the frequency stability is not always time-invariant. The frequency stability is presented for sample times of one day to 300 days. Time-domain noise-process analysis shows the dominant noise type to be white frequency noise for sample times of one day to ten days. >

Analysis of the frequency stability of on-orbit GPS Navstar clocks

The Naval Research Laboratory (NRL) analyses the performance of the on-orbit Navstar clocks in the Global Positioning System (GPS). This work is sponsored by the GPS Joint Program Office and is done in cooperation with the GPS Master Control Station. NRL has analyzed the performance of more than 50 Navstar atomic clocks with a total lifetime of more than 150 years. The results presented in this paper are a summary ofthe performance of the 25 Navstar atomic clocks that were operational during 1995. NRL analysis of on-orbit Navstar clocks is per formed using a multi-year database that includes data from initial activation of each clock through the first quarter of 1995. The Navstar pseudorange data was observed using single and dual-frequency GPS Precise Positioning Service (PPS) receivers that correct for the effects of selective availability. Quality of clock operation is calculated using both broadcast and post-processed precise ephemerides. This presentation includes a description ofthe Navstar clocks that are currently operating in the GPS constellation. The Navstar clock performance in the time domain is characterized by frequency-stability profiles with sample times that range from. 1 to 10 days, or more. The results presented show an improvement in the frequency stability over earlier Block I Navstar clocks with the majority of the currently operating Navstar clocks having a frequency stability for a sample time of one day of 1 pp 10/sup 13/ or better.

Performance of global positioning system (GPS) on-orbit Navstar clocks

The two-sample Allan variance has been the standard metric for assessing the frequency stability of atomic clocks which may be characterized by nonstationary noise processes. The convergence of the Allan variance for the noise types typical of atomic clocks might appear to suggest that the variance could be estimated to an arbitrary degree of accuracy by processing more data, over longer and longer periods of time, which would lead to progressively smaller confidence intervals. This tacit assumption, however, was called into question because of the behavior of one of the Global Positioning System (GPS) on-orbit Navstar atomic clocks whose frequency stability profile exhibited significant change with the processing of additional data. Because of the peculiar nonstationary behavior of this clock, a model for the frequency stability history was developed and is now incorporated as a routine part of the analysis of Navstar clocks conducted by the Naval Research Laboratory (NRL). The frequency stability history corresponds to the output of an N-sample moving average filter operating on the sequence of squared first differences of the M-day frequency offset measurements. This procedure assumes that the stochastic process has increments whose second order properties are slowly evolving over time such that, to a reasonable approximation, it has stationary increments over the N sample-interval. Frequency stability histories are presented using from one to 120-sample averages-the number of samples averaged representing a compromise between the time resolution and the stability of the estimate. Included are frequency stability histories for both cesium and rubidium on-orbit Navstar clocks. The results indicate that the frequency stability of most of the Navstar clocks is invariant over the useful life of the clock, that the frequency stability of some of the clocks degrades over the life of the clock, and that the frequency stability of still others improves after an initial transient. The frequency stability history is now used to detect and measure degradation in the frequency stability. Significant changes in the frequency stability are reported to the GPS Master Control Station (MCS).

Analysis of the frequency stability history of GPS Navstar clocks

: The Navigation Technology Satellites, developed by the Naval Research Laboratory, have been provided as a vehicle for the design and test of basic satellite navigation technology currently in use in the NAVSTAR Global Positioning System (GPS). Two satellites, TIMATION I and II, were flown in 1967 and 1969 to demonstrate the concept of using synchronized clocks to provide time ranging for navigational purposes. Navigation Technology Satellite 1 (NTS-1), flown in 1974, introduced a rubidium atomic clock, and NTS-2, flown in 1977, introduced a cesium clock. Both clocks provided increasingly superior navigation accuracy. A hydrogen maser clock for even better performance and reduced dependency on ground updating is being developed. In addition to the clock development the technology satellites have tested the effect of the radiation environment, the use of retroreflectors for laser tracking, and improved solar cells and batteries. As a result of NTS-2 tests the Air Force's Space and Missile Systems Organization (SAMSO) program office stated that the NAVSTAR GPS concept had been successfully validated.

Thomas B. McCaskill

Papers

Initial Results of the NAVSTAR GPS NTS-2 Satellite

Analysis of the frequency stability of on-orbit GPS Navstar clocks

Performance of global positioning system (GPS) on-orbit Navstar clocks

Analysis of the frequency stability history of GPS Navstar clocks

The Contribution of Navigation Technology Satellites to the Global Positioning System