### Confirmation of the Theory of Invariable Time-Intervals

Robert Howard Kroepel
Lakeside Studios
New Durham, NH USA 03855

The Concept and Principle of Infinity and The Infinite
The Concept of the Universe
The Three Realities Which Comprise The Universe
1. The Spatial Reality
2. The Temporal Reality
3. The Physical Reality
The Theory of Invariable Time-Intervals (TITI
The Operational Definition of Time (TITI)
The Unit of Measurement of Time: The Time-Interval (TI)
The Continuum of Time
The Two Types of Time-Intervals (TIs)
The 1971 Hafele-Keating Experiment
The Philosophical Concepts and Principles of Physics Changed by the TITI
Absolute Time (AT) and Absolute Space (AS)
Absolute Rest (AR), the Absolute Rest Reference Frame (ARRF), and Absolute Motion (AM)
Simultaneity
The Criteria for Proof of the Confirmation of the TITI
Confirmation of the TITI
The US GPS Nav System
The 1971 Hafele-Keating Experiment
Summary

### The Concept and Principle of Infinity and The Infinite

Infinity is operationally defined as having no physical or mathematical limits.

That which is infinite has no physical or mathematical limits.

Finity is operationally defined as having physical or/and mathematical limits.

That which is finite has physical or/and mathematical limits.

### The Concept of the Universe

The universe is operationally defined to be all reality, all there is, all that exists as reality, all that exists combined in a single actuality.

There exists one and only one universe.

Any claim of multiple or parallel universes is denied by the fact that there is one and only one universe which contains all there is, including additional 'universes.'

### The Three Realities Which Comprise The Universe

The universe is comprised of three realities:

1. The Spatial Reality—Space: The infinite/unbounded volume within which exist time and physics (matter/energy, m/e).

Intuitable by the expression x + i wherein x is a volume of finite radius/diameter, and x-volume, and i is a surrounding infinite volume, the i-volume.

The principle is that any finite x-volume can be surrounded by the infinite i-volume. The result is that there is no limit to the volume of the universe which is space.

Space is thus infinite in volume and duration. It cannot be created, nor can it be destroyed.

If space were devoid of time and physics (matter/energy), then its volume would be a pure vacuum.

2. The Temporal Reality—Time: The sequence of events measurable by time-intervals—the history of the universe.

Time is operationally defined as the use of time-intervals as units of measurement for the measurement of the occurrences, durations and simultaneities of events.

Time is infinite in duration.

By the use of time-intervals as units of measurement for the measurement of time, time can be counted without mathematical limits forwards into the future or backwards into the past.

#### The Continuum of Time

The Continuum of Time is infinite:

Past Infinity<- ... <- (T-2) <- (T-1) <- T0 (Origin) -> (T+1) -> (T+2) -> ... -> Future Infinity

T0 = Timepoint of Origin, 0, where time is begun to be counted by observers including organisms and machines (computers).

3. The Physical Reality—Physics: The Matter/Energy (M/E) of the Universe.

Matter/energy (m/e) is infinite in duration, confirmed by experiments which have confirmed the conservation of matter, the conservation of energy (and the electric charge, and momentum), and by experiments which have confirmed e = mc2 and m = e/c2.

The m/e of the universe—the physical reality–is a closed m/e system because m/e cannot be added to it (where would the additional m/e come from?) and m/e cannot be removed from it (where would the removed m/e go?).

The presence of m/e in an area of space causes that area to not be a pure vacuum.

Causality is the phenomena wherein people/objects/events who/which are comprised of m/e and are causes causing/creating people/objects/events who/which are comprised of m/e and are effects.

Causality is thus causes causing effects.

The infinite duration of m/e proves that there was never a cause of causality but, instead, m/e is the source of causality, the source of causes causing effects.

The infinite duration of m/e but also the infinite duration of space considered together prove that prior to any Big Bangs there existed space and m/e within space and after any Big Crunches there existed space and m/e within space.

Thus, there never was a beginning to space, time and physics (m/e), nor will there be an ending to space, time and physics.
"To be perfectly honest, neither scientists nor philosophers really know what time is or why it exists. The best thing they can say is that time is an extra dimension akin (but not identical) to space. ..."

Paul Davies, That Mysterious Flow, Scientific American, Special Edition: A Matter of Time, September, 2002, p. 41.

### The Theory of Invariable Time-Intervals (TITI)

The Theory of Invariable Time-Intervals (TITI) is a theory of time.

The TITI is a theory of the use of a unit of measurement called a time-interval for the measurement of time by the measurement of the occurrences of events in sequences of events.

The TITI will change many but not all philosophical concepts/principles of modern physics.

### The Operational Definition of Time (T)

In the TITI, time is operationally defined as the use of time-intervals (TIs) as units of measurement for the measurement of the occurrences of events in sequences of events.

### The Unit of Measurement of Time: The Time-Interval (TI)

The essence of time, of time-measurement, is the time-interval, which is the unit of measurement of time.

The time-interval is a duration, a duration of time, between a beginning and an ending of a cycle, between the beginning and the ending of a regularly recurring periodic motion or physical cycle.

Once a time-interval is abstracted—once its duration is abstracted—from its original cycle/periodic motion, the time-interval's duration is independent of the original cycle/periodic motion; thus, if the original cycle/periodic motion changes, the change will not affect the abstracted time-interval.

### The Two Types of Time-Intervals (TIs)

Two types of TIs/time-intervals have been identified:

1. the variable time-interval (VTI);
2. the invariable time-interval (ITI).

VTIs are found in variable time-interval clocks (VTICs) whose rates of operation (RoOs) are affected by changes of velocity (speed and motion) and/or gravity (which creates a force field which changes or otherwise can change the velocity of objects within it); acceleration causes a decrease in the RoO of a VTIC and therefore a decrease/shortening of the duration of its VTI while deceleration causes an increase in its RoO and therefore a increase/lengthening of the duration of its VTI.

ITIs are found in invariable time-interval clocks (ITICs) whose RoOs are affected by changes of velocity and/or gravity but whose RoOs (A) are adjusted internally by a motion-sensing and self-adjusting mechanism and relevant computer (these ITICs are referred to as motion-sensing/self-adjusting invariable time-interval clocks, or MASSITICs) or (B) are adjusted externally by radio signals from a master clock (the master invariable time-interval clock is referred to as an MITIC while the radio-controlled invariable time-interval clocks—the slave clocks whose RoO/TI/ITI/timing is controlled by the MITIC—are referred to as slave invariable time-interval clocks or SITICs) with the result that the TI/ITI in ITICs is essentially and effectively a constant duration and the ITICs' RoO likewise is essentially and effective constant and therefore invariable.

### The 1971 Hafele-Keating Experiment

The 1971 Hafele-Keating experiment ...

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.htm

... explains how ITICs can be confirmed to be a reality.

"During October, 1971, four cesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40+/-23 nanoseconds during the eastward trip and should have gained 275+/-21 nanoseconds during the westward trip ... Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59+/-10 nanoseconds during the eastward trip and gained 273+/-7 nanosecond during the westward trip, where the errors are the corresponding standard deviations. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks."

J.C. Hafele and R. E. Keating, Science 177, 166 (1972)

In the Hafele-Keating experiment, three sets of atomic clocks were synchronized (time-coordinated) and all were therefore using the same time-interval [TI].

One set of clocks was placed aboard a westbound jet airliner, another set was placed aboard an eastbound set airliner, and thus both sets of airborne clocks were accelerated and decelerated during the normal flight routines of the airliners and then returned to the Earth, where their readouts (time counts/time measurements) were compared to the readouts of the clocks which remained on Earth.

In this experiment, the Earth was one reference frame, and the airliner, because of its acceleration and altitude, was another reference frame, in analogy with Einstein's gedankenexperiment (thought experiment/intuition) in which a railway embankment was one reference frame and a moving railway carriage was another reference frame (see Relativity. by Albert Einstein, pp. 17-25):
Earth = Railway Embankment [K Reference Frame]

Airliner = Railway Carriage [K' Reference Frame]
When the readouts of the accelerated airborne clocks were compared to the readouts of the non-accelerated Earth-bound clocks, the accelerated airborne clocks' readouts were uniformly lesser than the non-accelerated Earth-bound clocks' readouts, an indication that time had been dilated, and a confirmation of relativity, which predicted time-dilation for accelerated/decelerated clocks.

We note that the determination of time-dilation is conducted in the originating reference frame and not by any method whereby observers in one reference frame observe objects/events in another reference frame. By the use of the single originating reference frame Lorentz relativistic transformation problems (disagreements of time and length measurements by observers in different inertial reference frames) are eliminated.

The clocks used for the Hafele-Keating experiment were clocks whose time-intervals (TIs) were variable time-intervals (VTIs) thus the clocks themselves were variable time-interval clocks (VTICs) whose time-intervals were variable in duration, in time, when subjected to changes of velocity (speed and direction) and/or gravity. When the air-borne VTICs were accelerated, their TIs/VTIs were lengthened, their RoOs were slowed, and their counting of TIs/VTIs was decreased, their readouts/time counts/time-measurements decreased, with the result that their readouts were less than the readouts/time counts/time-measurements of the Earth-bound/non-accelerated VTICs.

If invariable time-interval clocks (ITICs—either MSSAITICs or MITICs controlling SITICs) were used in a replication of the Hafele-Keating experiment, then the prediction is that upon their return to the Earth the airborne accelerated ITICs would show the same/identical readouts as the non-accelerated Earth-bound ITICs, and, thus, time would not be dilated.

Again, the use of the single originating reference frame eliminates the Lorentz relativistic transformation problems.

### The Philosophical Concepts and Principles of Physics Changed by the TITI

With the confirmation of the TITI the philosophical concepts/principles of absolute time (AT)/universal time (UT), absolute space (AS), absolute rest (AR), the absolute rest reference frame (ARRF), absolute motion (AM), and simultaneity will be definable/specifiable and therefore established as realities.

### Absolute Time (AT) and Absolute Space (AS)

The TIs/ITIs in ITICs produce absolute time (AT), or universal time (UT) wherein from the originating reference frame, K, time, t, is the same for all other reference frames, K', K'', K''', etc.; thus for K, K', K'', K''', etc., t = t' = t'' = t''' ... etc. When AT/UT is established, time becomes independent of space, and space, likewise, becomes independent of time, and, therefore, space becomes absolute space (AS).

Albert Einstein, Relativity, Chapter IX:

"Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference." [p. 27]

We note that for a clock to measure absolute time it must be "independent of the state of motion of [its] body of reference."

The TIs, rates of ticking (RoT), timepoints and timelines of ITICs are adjusted to compensate for the affects on TIs, RoTs, timepoints, and timelines of VTICs caused by accelerations and decelerations, therefore ITICs are "independent of the state of motion of [their bodies] of reference."

Any ITIC is therefore "independent of the state of motion of [its] body of reference" and is therefore measuring absolute time and is not measuring local time within its "body of reference."

### Absolute Rest (AR), the Absolute Rest Reference Frame (ARRF), and Absolute Motion (AM)

If a VTIC is linked to an ITIC, in what will be referred to as a VTIC/ITIC combo, and while Earth-bound/non-accelerated (non-decelerated) the TIs are synchronized, so VTI = ITI, the VTIC/ITIC combo produces a clock mechanism which can be used to detect absolute rest (AR), the absolute rest reference frame (ARRF), and absolute motion (AM).

If the spacecraft containing a VTIC/ITIC combo is launched into space, and, disregarding the effects of gravity, a force is applied 180 degrees opposite the direction of motion of the spacecraft, the spacecraft with the VTIC/ITIC combo will decelerate, its velocity (speed and direction) will become temporarily zero (no motion = no speed and no direction), hence its AM will be zero, it will be at AR, and it will have entered the ARRF, and if the force is continued, then the spacecraft will accelerate in the direction 180 degrees opposite its original direction.

During these transition phases, the RoO of the VTIC in the VTIC/ITIC combo will change from its original non-accelerated (non-decelerated) RoO in the Earth's reference frame to a maximum RoO at AR in the ARRF when its AM is zero while the RoO of the ITIC will remain constant.

Thus, the maximum RoO of any machine or organism will be achieved at AM = zero at AR in the ARRF.

Observers on the Earth will observe the RoO of the VTIC to increase with deceleration to a maximum and then to decrease with acceleration in the opposite direction while the RoO of the ITIC remains constant.

Observers on the spacecraft, whose RoOs will vary directly with the RoO of the VTIC, will observe the RoO of the VTIC to remain constant while the RoO of the ITIC will increase with acceleration to a maximum at AM = zero at AR in the ARRF and then to decrease with acceleration in the opposite direction.

We know that the RoO of any machine or organism should be zero at the speed of light (SOL/186,000 mps).

Between a maximum RoO at AM = zero at AR in the ARRF and the minimum RoO/RoO = zero at the SOL we have a calibratable cosmic speedometer which can be used to determine the AM, the absolute motion, of a spacecraft equipped with a VTIC/ITIC combo.

When the AM = the AM of the Earth's reference frame, the VTIC's RoO = the ITIC's RoO for both Earth-bound/non-accelerated observers and the space-borne/accelerated observers.

Whether Earth-bound/non-accelerated or space-borne/accelerated, observers can use the difference of RoOs between the VTIC and the ITIC of a VTIC/ITIC combo to determine the AM of the spacecraft.

### Simultaneity

Simultaneity is established (A) when invariable time-intervals (ITIs) are used in ITICs to measure time and (B) when two (or more) events can be determined to have occurred at the same timepoint.

Earth-bound/non-accelerated observers can keep track of VTIC/ITIC combos in other reference frames (either aboard accelerated/decelerated spacecraft or on astronomical objects) and if the distance from a VTIC/ITIC combo to an event is known and as short as possible, then radio telemetry can be used to radio information inre: the ITIC timepoint at which an event occurred in its reference frame and this information can be compared to information inre: the ITIC timepoints at which other events occurred, and concurrence of ITIC timepoints will operationally define simultaneity—events occurring at the same ITIC timepoints will be simultaneous.

Events occurring at other ITIC timepoints will not be simultaneous.

Observers not in the Earth's reference frame can be directed to use the ITIC timepoints generated by the ITIC of their local VTIC/ITIC combo—the VTIC/ITIC combo within their reference frame for simultaneity/non-simultaneity; those events occurring at the same ITIC timepoints will thus be simultaneous with all other events occurring at the same ITIC timepoints.

At all AMs not equal to the AM of the originating reference frame there will be a RoO difference and therefore a difference of timepoints between the VTIC RoO/timepoints and the ITIC RoO/timepoints.

Earth-bound observers will observe the ITIC RoO to be constant in any reference frame and the ITIC timepoints to be useable for simultaneity/non-simultaneity of events in different reference frames; space-borne observers who have AMs different from the Earth's AM will observe their local VTIC RoO to be constant, but, nevertheless, although they will observe their ITIC RoO to change they will also observe the ITIC to generate its own set of timepoints which they can use to relate events, and, thus, any events occurring at the same ITIC timepoints within their own reference frame will be simultaneous and all events occurring at the same ITIC timepoints in any other reference frames will also be simultaneous.

### The Criteria for Proof of the Confirmation of the TITI

One of the criterion for the confirmation of the Theory of Invariable Time-Intervals (ITI) will be the actual use of invariable time-intervals (ITIs) in invariable time-interval clocks (ITICs) of either Design A/Type A motion-sensing/self-adjusting invariable time-interval clocks (MSSAITICs) which are internally controlled and self-correcting or Design B/Type B radio-controlled invariable time-interval clocks (SITICs) which are externally controlled by radio signals/telemetry from master invariable time-interval clocks (MITICs).

Prediction: Design A/Type A MSSAITICs or/and Design B/Type B SITICs controlled by MITICs will be used for time control in spacecraft and satellites including the Global Positioning System (GPS).

### Confirmation of the TITI

#### The US GPS Nav System

Confirmation
: Navstar GPS User Equipment Introduction. (September 1996, Public Release Version)

http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf
CHAPTER 1: SYSTEM OVERVIEW

1.1 GENERAL DESCRIPTION

The Navstar Global Positioning System (GPS) is a space-based radio-positioning and time-transfer system. GPS provides accurate position, velocity, and time (PVT) information to an unlimited number of suitably equipped ground, sea, air and space users. Passive PVT fixes are available world-wide in all-weathers in a world-wide common grid system. Normally GPS contains features which limit the full accuracy of the service only to authorized users and protection from spoofing (hostile imitation). GPS comprises three major system segments, Space, Control, and User ... .

The Space Segment consists of a nominal constellation of 24 Navstar satellites. Each satellite broadcasts RF ranging codes and a navigation data message. The Control Segment consists of a network of monitoring and control facilities which are used to manage the satellite constellation and update the satellite navigation data messages. The User Segment consists of a variety of radio navigation receivers specifically designed to receive, decode, and process the GPS satellite ranging codes and navigation data messages. The Space, Control, and User Segments are described in more detail in paragraph 1.2.

The ranging codes broadcast by the satellites enable a GPS receiver to measure the transit time of the signals and thereby determine the range between each satellite and the receiver. The navigation data message enables a receiver to calculate the position of each satellite at the time the signals were transmitted. The receiver then uses this information to determine its own position, performing calculations similar to those performed by other distance-measuring navigation equipment. Conceptually, each range measurement defines a sphere centered on a satellite. The common intersection point of the spheres on or near the earth's surface defines the receiver position.

For GPS positioning, a minimum of four satellites are normally required to be simultaneously "in view" of the receiver, thus providing four range measurements. This enables the receiver to calculate the three unknown parameters representing its (3-D) position, as well as a fourth parameter representing the user clock error. Treating the user clock error as an unknown enables most receivers to be built with an inexpensive crystal oscillator rather than an expensive precision oscillator or atomic clock. Precise time estimates are required for precise positioning, since a time error of 3 nanoseconds is roughly equivalent to a range error of 1 metre. Less than four satellites can be used by a receiver if time or altitude is precisely known or if these parameters are available from an external source. A more detailed explanation of the GPS theory of operation is provided in paragraph 1.4.

The satellites transmit ranging signals on two D-band frequencies: Link 1 (Ll ) at 1575.42 MHz and Link 2 (L2) at 1227.6 MHz. The satellite signals are transmitted using spread-spectrum techniques, employing two different ranging codes as spreading fictions, a 1.023 MHz coarse/acquisition code (C/A-code) on L1 and a 10.23 MHz precision code (P-code) on both L1 and L2. Either the C/A-code or the P-code can be used to determine the range between the satellite and the user, however, the P-code is normally encrypted and available only to authorized users. When encrypted, the P-code is known as the Y-code. A 50 Hz navigation message is superimposed on both the P(Y)-code and the C/A-code. The navigation message includes satellite clock-bias data, satellite ephemeris (precise orbital) data for the transmitting satellite, ionospheric signal-propagation correction data, and satellite almanac (coarse orbital) data for the entire constellation. Refer to paragraph 1.4 for additional details regarding the ranging codes and navigation message.

1.2.2 Control Segment

The Control Segment primarily consists of a Master Control Station (MCS), at Falcon Air Force Base (AFB) in Colorado Springs, USA, plus monitor stations (MS) and ground antennas (GA) at various locations around the world. The monitor stations are located at Falcon AFB, Hawaii, Kwajalein, Diego Garcia, and Ascension. All monitor stations except Hawaii and Falcon AFB are also equipped with ground antennas (see Figure 1-3). The Control Segment includes a Prelaunch Compatibility Station (PCS) located at Cape Canaveral, USA, and a back-up MCS capability.

The MCS is the central processing facility for the Control Segment and is responsible for monitoring and managing the satellite constellation. The MCS functions include control of satellite station-keeping maneuvers, reconfiguration of redundant satellite equipment, regularly updating the navigation messages transmitted by the satellites, and various other satellite health monitoring and maintenance activities. The monitor stations passively track all GPS satellites in view, collecting ranging data from each satellite. This information is transmitted to the MCS where the satellite ephemeris and clock parameters are estimated and predicted. The MCS uses the ground antennas to periodically upload the ephemeris and clock data to each satellite for retransmission in the navigation message. Communications between the MCS the MS and GA are typically accomplished via the U.S. Defense Satellite Communication System (DSCS). The navigation message update function is graphically depicted in Figure 1-4.

The PCS primarily operates under control of the MCS to support prelaunch compatibility testing of GPS satellites via a cable interface. The PCS also includes an RF transmit/receive capability that can serve as a Control Segment ground antenna, if necessary. The U.S. Air Force Satellite Control Network (AFSCN) consists of a multipurpose worldwide network of ground- and space-based satellite control facilities. Various AFSCN resources are available to support GPS but are not dedicated exclusively to GPS.

1.2.3 User Segment

The User Segment consists of receivers specifically designed to receive, decode, and process the GPS satellite signals. Receivers can be stand-alone, integrated with or embedded into other systems. GPS receivers can vary significantly in design and function, depending on their application for navigation, accurate positioning, time transfer, surveying and attitude reference.

Chapter 2 provides a general description of GPS receiver types and intended applications.

1.3 GPS SERVICES

Two levels of service are provided by the GPS, the Precise Positioning Service (PPS) and the Standard Positioning Service (SPS).

1.3.1 Precise Positioning Service

The PPS is an accurate positioning velocity and timing service which is available only to authorized users. The PPS is primarily intended for military purposes. Authorization to use the PPS is determined by the U.S. Department of Defense (DoD), based on internal U.S. defense requirements or international defense commitments. Authorized users of the PPS include U.S. military users, NATO military users, and other selected military and civilian users such as the Australian Defense Forces and the U.S. Defense Mapping Agency. The PPS is specified to provide 16 metres Spherical Error Probable (SEP) (3-D, 50%) positioning accuracy and 100 nanosecond (one sigma) Universal Coordinated Time (UTC) time transfer accuracy to authorized users. This is approximately equal to 37 metres (3-D, 95%) and 197 nanoseconds (95%) under typical system operating conditions. PPS receivers can achieve 0.2 metres per second 3-D velocity accuracy, but this is somewhat dependent on receiver design.

Access to the PPS is controlled by two features using cryptographic techniques, Selective Availability (SA) and Anti-Spoofing (A-S). SA is used to reduce GPS position, velocity, and time accuracy to the unauthorized users. SA operates by introducing pseudorandom errors into the satellite signals. The A-S feature is activated on all satellites to negate potential spoofing of the ranging signals. The technique encrypts the P-code into the Y-code. Users should note the C/A code is not protected against spoofing.

Encryption keys and techniques are provided to PPS users which allow them to remove the effects of SA and A-S and thereby attain the maximum accuracy of GPS. PPS receivers that have not been loaded with a valid cryptographic key will have the performance of an SPS receiver.

PPS receivers can use either the P(Y)-code or C/A-code or both. Maximum GPS accuracy is obtained using the P(Y)-code on both L1 and L2. P(Y)-code capable receivers commonly use the C/A-code to initially acquire GPS satellites.

1.3.2 Standard Positioning Service

The SPS is a less accurate positioning and timing service which is available to all GPS users. In peacetime, the level of SA is controlled to provide 100 metre (95%) horizontal accuracy which is approximately equal to 156 metres 3D (95%). SPS receivers can achieve approximately 337 nanosecond (95%) UTC time transfer accuracy. System accuracy degradations can be increased if it is necessary to do so, for example, to deny accuracy to a potential enemy in time of crisis or war. Only the President of the United States, acting through the U.S. National Command Authority, has the authority to change the level of SA to other than peacetime levels.

The SPS is primarily intended for civilian purposes, although it has potential peacetime military use. Refer to "Technical Characteristics of the Navstar GPS" for additional details regarding SPS performance characteristics.

1.4 GPS THEORY OF OPERATION

The ranging codes broadcast by the satellites enable a GPS receiver to measure the transit time of the signals and thereby determine the range between a satellite and the user. The navigation message provides data to calculate the position of each satellite at the time of signal transmission.

From this information, the user position coordinates and the user clock offset are calculated using simultaneous equations. Four satellites are normally required to be simultaneously "in view" of the receiver for 3-D positioning purposes. The following paragraphs give a description of the GPS satellite signals and GPS receiver operation.

1.4.1 GPS Satellite Signals

1.4.1.1 C/A-Code

The C/A-code consists of a 1023 bit pseudorandom noise (PRN) code with a clock rate of 1.023 MHz which repeats every 1 millisecond. The short length of the C/A-code sequence is designed to enable a receiver to rapidly acquire the satellite signals which helps the receiver transition to the longer P-code. A different PRN is assigned to each GPS satellite and selected from a set of codes called Gold codes. The Gold codes are designed to minimize the probability that a receiver will mistake one code for another (minimize the cross-correlation). The C/A-code is transmitted only on L1. The C/A-code is not encrypted and is therefore available to all users of GPS.

1.4.1.2 P(Y)-Code

The P-code is a 10.23 MHz PRN code sequence that is 267 days in length. Each of the GPS satellites is assigned a unique seven-day segment of this code that restarts every Saturday/Sunday midnight GPS time (GPS time is a continuous time scale maintained within 1 microsecond of UTC, plus or minus a whole number of leap seconds). The P-code is normally encrypted into the Y-code to protect the user from spoofing. Since the satellites have the capability to transmit either the P- or Y-code, it is often referred to as the P(Y)-code. The P(Y)-code is transmitted by each satellite on both L1 and L2. On L1, the P(Y)-code is 90 degrees out of carrier phase with the C/A-code.

A 50 Hz navigation message is superimposed on both the P(Y) code and the C/A-code. The navigation message includes data unique to the transmitting satellite and data common to all satellites. The data contains the time of transmission of the message, a Hand Over Word (HOW) for the transition from C/A-code to P(Y)-code tracking, clock correction, ephemeris, and health data for the transmitting satellite, almanac and health data for all satellites, coefficients for the ionospheric delay model, and coefficients to calculate UTC.

The navigation message consists of 25 frames of data, each frame consisting of 1,500 bits. Each frame is divided into 5 subframes of 300 bits each (see Figure 1-5). At the 50 Hz transmission rate, it takes 6 seconds to receive a subframe, 30 seconds to receive one data frame, and 12.5 minutes to receive all 25 frames. Subframes 1, 2, and 3 have the same data format for all 25 frames. This allows the receiver to obtain critical satellite-specific data within 30 seconds. Subframe 1 contains the clock correction for the transmitting satellite, as well as parameters describing the accuracy and health of the broadcast signal. Subframes 2 and 3 contain ephemeris (precise orbital) parameters used to compute the location of the satellite for the positioning equations.

...

1.4.2.2 Satellite Signal Acquisition

The satellite signal power at or near the earth's surface is less than the receivers thermal (natural) noise level, due to the spread spectrum modulation of the signal, orbital height and transmitting power of the satellite. To extract the satellite signal the receiver uses code correlation techniques. An internal replica of the incoming signal is generated and aligned with the received satellite signal. The receiver shifts the replica code to match the incoming code from the satellite. When the codes match, the satellite signal is compressed back into the original carrier frequency band. ...

The delay in the receiver's code is a measure of the transit time of the signals between the satellite and the receiver's antenna and hence, the range between the satellite position and receiver position. This measurement is called a pseudorange measurement, rather than a range measurement, because the receiver's clock bias has not been removed.

Receivers typically use phase-locked-loop techniques to synchronize the receiver's internally generated code and carrier with the received satellite signal. A code tracking loop is used to track the C/A- and P-code signals while a carrier tracking loop is used to track the carrier frequency. The two tracking loops work together in an interactive process, aiding each other, in order to acquire and track the satellite signals. ...

1.4.2.3 Down Conversion

The received RF signal is converted, usually through two intermediate frequencies (IF), down to a frequency near the code baseband, that can be sampled by an analogue to digital (A/D) converter. Inphase and quadrature digital samples are taken to preserve the phase information in the received signal. The samples are usually two bits to reduce conversion losses. The sampling rate must be higher than the code chipping rate for a non return to zero code, that is, greater than 10.23 MHz for the P(Y)-code. To ensure the phase of the received signal is maintained, all local oscillators are derived from, and phased locked through, a series of synthesizers derived from the receiver's master oscillator. Following the A/D conversion there is a final phase rotation circuit that enables the doppler in the satellite signal to be precisely
tracked.

1.4.2.4 Code Tracking

The code tracking loop is used to make pseudorange measurements between the GPS satellites and the GPS receiver. The receiver's code tracking loop generates a replica of the C/A-code of the targeted satellite. The estimated doppler is removed by the phase rotation circuit prior to the correlator.

In order to align the received signal with the internally generated replica, the internally generated code is systematically slewed past the received signal. Typically the output of the correlator is integrated over 1 to 10 ms. If correlation is not detected the phase of the internally generated code is advanced by one chip. If correlation is not detected after the whole code has been searched the doppler is adjusted and the process repeated until correlation is achieved. Code synchronization is initially maintained by also correlating the received signal with half chip early and late codes. A simple feedback system keeps the prompt ("on time") code correctly positioned. To extract the carrier which is still modulated by the navigation message, the prompt code is subtracted from the incoming signal. The delay that the receiver must add to the replica code to achieve synchronization (correlation), multiplied by the speed of light, is the pseudorange measurement. Once the carrier is reconstructed, the center frequency of the replica code is adjusted using Doppler measurements from the carrier tracking loop to achieve a precise frequency lock to the incoming signal, thereby allowing more precise pseudorange measurements. The bandwidth of the code tracking loop is typically 0.1 Hz, which implies that independent measurements are available at approximately 10 s intervals.

1.4.2.5 Carrier Tracking and Data Detection

The receiver tracks the satellite carrier by adjusting the frequency synthesizers to produce a stationary phase at the output of the code tracking loop. The inphase and quadrature components are used to calculate the carrier's phase and doppler. A data bit is detected by a sudden change in the phase of the detected signal. The bandwidth of the carrier tracking loop is typically 6 Hz for a military airborne receiver, resulting in independent measurements being available every 150 ms.

Doppler is measured to provide an estimate of the relative velocity between the receiver and the satellite. These measurements are typically termed pseudorange rate measurements or they can be integrated over regular time intervals to produce deltarange measurements.

The receiver uses the doppler measurements from four (or more) satellites to determine the receiver velocity (in three dimensions) plus the receiver's master oscillator frequency bias. The deltarange measurements of the carrier tracking loop are also used to aid the code tracking loop to ensure code tracking is maintained during dynamic maneuvers where the simple code tracking system would be unable to maintain lock.

1.4.2.6 Data Demodulation

Once the carrier tracking loop is locked, the 50 Hz navigation data message can be read. Each subframe of the navigation message begins with a preamble contained in the Telemetry Word, enabling the receiver to detect the beginning of each subframe. Each subframe is identified by bits contained in the Handover Word (HOW), enabling the receiver to properly decode the subframe data.

1.4.2.7 P(Y)-Code Signal Acquisition

The one millisecond C/A-code length permits a relatively narrow search window for code correlation even if the receiver must "search the sky" to find the first satellite. However the week long P(Y)-code sequence at 10.23 MHz does not allow the same technique to be used. Precise time must be known by the receiver in order to start the code generator within a few hundred chips of the correlation point of the incoming signal. The HOW contained in the GPS navigation message provides satellite time and hence the P(Y)-code phase information. A P(Y)-code receiver may attempt to acquire the P(Y)-code directly, without first acquiring the C/A-code, if it has accurate knowledge of position, time and satellite ephemeris from a recent navigation solution. External aiding and/or an enhanced acquisition technique are usually required to perform direct P(Y)-code acquisition.

1.4.2.8 PVT Calculations

When the receiver has collected pseudorange measurements, deltarange measurements, and navigation data from four (or more) satellites, it calculates the navigation solution, PVT. Each navigation data message contains precise orbital (ephemeris) parameters for the transmitting satellite, enabling a receiver to calculate the position of each satellite at the time the signals were transmitted. The ephemeris data is normally valid and can be used for precise navigation for a period of four hours following issue of a new data set by the satellite. New ephemeris data is transmitted by the satellites every two hours.

As illustrated in Figure 1-10, the receiver solves a minimum of four simultaneous pseudorange equations, with the receiver (3-D) position and clock offset as the four unknown variables. Each equation is an expression of the principle that the true range (the difference between the pseudorange and the receiver clock offset) is equal to the distance between the known satellite position and the unknown receiver position. This principle is expressed below mathematically using the same notation as Figure 1-10.

These are simplified versions of the equations actually used by GPS receivers. A receiver also obtains corrections derived from the navigation messages which it applies to the pseudoranges. These include corrections for the satellite clock offset, relativistic effects, ionospheric signal propagation delays. Dual frequency receivers can measure the delay between the L1 and L2 P(Y)-codes, if available, to calculate an ionospheric correction. Single frequency (either C/A-or P(Y)-code) receivers use parameters transmitted in the navigation message to be used in an ionospheric model. The receiver (3-D) velocity and frequency offset are calculated using similar equations, using deltaranges instead of pseudoranges.

The PVT calculations described here result in a series of individual point solutions. For receivers that are required to provide a navigation solution under dynamic conditions a smoothed or filtered solution that is less sensitive to measurement noise is employed. One of the most common types of filters used in GPS receivers is the Kalman filter. Kalman filtering is described in detail in Chapter 9.

The rate at which GPS receivers calculate the PVT solution is governed by their application. For flight control applications a 10 Hz rate is required whereas in handheld equipment a fix may only be required once every 4 to 5 seconds or at even longer intervals. A 1 Hz rate is typical for many equipment. In this scenario pseudorange measurements are typically only made every 4 to 5 seconds; pseudorange rate measurements are made more frequently and can be used to propagate the filter solution between updates. If a Kalman filter is used the measurements may be incorporated independently into the filter removing the requirement for symmetrical measurements from all channels. The filter also allows the solution to be extrapolated if measurements are interrupted, or data is available from other navigation sensors.

A minimum of four satellites are normally required to be simultaneously "in view" of the receiver, thus providing four pseudorange and four deltarange measurements. Treating the user clock errors as unknowns enable most receivers to be built with an inexpensive crystal oscillator rather than an expensive precision oscillator or atomic clock. Less than four satellites can be used by a receiver if time or altitude are precisely known or if these parameters are available from an external source.

GPS receivers perform initial position and velocity calculations using an earth-centered earth-fixed (ECEF) coordinate system. Results may be converted to an earth model (geoid) defined by the World Geodetic System 1984 (WGS 84). WGS 84 provides a worldwide common grid system that may be translated into local coordinate systems or map datums. (Local map datums are a best fit to the local shape of the earth and not valid worldwide.) For more details regarding WGS 84, refer to Annex B. For more details regarding how a receiver uses WGS 84, refer to "Technical Characteristics of the Navstar GPS".

For navigation purposes, it is usually necessary for a GPS receiver to output positions in terms of magnetic North rather than true North as defined by WGS 84. For details regarding how the receiver calculates the magnetic variation from true North, refer to "Technical Characteristics of the Navstar GPS".

During periods of high levels of jamming, the receiver may not be able to maintain both code and carrier tracking. The receiver normally has the capability to maintain code tracking even when carrier tracking is no longer possible. If only code tracking is available, the receiver will slew the locally generated carrier and code signals based on predicted rather than measured Doppler shifts. These predictions are performed by the receiver processor, which may have additional PVT information available from an external aiding source. See Chapter 7 for additional discussion of GPS receiver aiding.

CHAPTER 2: TYPES OF GPS RECEIVERS
AND THEIR INTENDED APPLICATIONS

Modern military GPS receivers use predominantly a continuous satellite tracking architecture. However, some receivers use alternative architectures, either sequential or multiplex tracking to reduce hardware complexity.

One of the more common uses of GPS is for precise time dissemination applications. Several manufacturers offer this type of equipment commercially. These precise time GPS receivers need only one GPS satellite for precise time dissemination if the receiver is stationary on a precisely known location and the only "unknown" is its own clock offset from GPS time and therefore from UTC. To obtain the necessary precise position, the receiver either receives it as an operator input or uses four satellites to determine its own position. These receivers typically include an internal oscillator or an optional external frequency source (rubidium or cesium). Whenever the receiver is tracking a satellite, it generates 1, 5, or 10 MHz reference frequencies that are synchronized to UTC time. If no satellites are visible, the reference frequencies are derived from the internal or external frequency source. The receivers can provide either stand-alone (uncoordinated) or coordinated time-transfer operations. In SPS receivers, use of SA will reduce the time and position accuracy available. The manufacturers of time transfer receivers claim time accuracies in the 20 to 50 nanoseconds range, but this accuracy requires algorithms that average pseudorange measurements over time (10 - 60 minutes). A stand-alone PPS time receiver normally provides time accuracy in the 100 nanoseconds range. The advantage of having an external frequency source interface designed into the receiver is that the long term error in the frequency source can be adjusted when the receiver has satellites in view. A stationary PPS GPS receiver with a precise time and time interval (PTTI) interface should be able to provide UTC to an accuracy of 50 to 60 nanoseconds.

AND ANCILLARY EQUIPMENT

4.3 PRECISE TIME AND TIME INTERVAL INTERFACE

4.3.1 Introduction

GPS is becoming recognized as the primary time dissemination system for military and commercial applications. An example of a system which may use time transfer from GPS is the calibration of atomic clocks.

4.3.2 Precise Time Inputs

A time input is used to reduce the uncertainty of the receivers initial time estimate and thus reduce TTFF, or it may be used instead of a satellite in the navigation solution.

The precise time input to a GPS receiver is accomplished by using a 1 pulse per second rate representing UTC one-second-rollover and a Binary Code Decimal (BCD) time code describing the pulse per second time from an atomic clock. The pulse input indicates the moment of the time to UTC, and the BCD time code identifies what time it was at the UTC one-second-rollover.

The MIL-STD-1553 PTTI Input Message time transfer mechanism uses the same time rollover pulse input. However, instead of labeling the time with a BCD time input, the HV supplies a PTTI input message via the MIL-STD-1553 MUX bus to label the time epoch.

4.3.3 Precise Time Outputs

The primary function of these outputs is to calibrate an atomic clock, or to support other systems that require precise time. The outputs are 1 pulse per second or 1 pulse per minute to indicate the one second or one minute rollover of UTC, and a BCD time code that indicates the time at the rollover epoch (Hours, Minutes, Seconds, Day of Year, Time Figure of Merit (TFOM)).

Another means of precise time transfer from the GPS receiver is to use the 1 pulse per second output in conjunction with the PTTI output message available on the MIL-STD-1553 multiplex bus.
We can note herein the use of MITICs to control SITICs and thus confirmation of the TITI.
Chapter 11: Special Applications for Navstar GPS

11.1 INTRODUCTION

Navstar GPS is a positioning system that will be a definite force enhancer in military operations. Since GPS will also be available to civilian users and has the potential to enhance military operations other than weapon delivery, several special applica tions for GPS have been developed. This chapter will discuss four special applications already developed to indicate the variety of GPS uses. The four special applications discussed are as follows:

1. DGPS Applications
2. GPS used as an attitude reference system
3. Precise time and GPS
4. Orbit determination using GPS

11.4 PRECISE TIME AND GPS

11.4.1 Introduction

Precise time is important for a growing number of military, civilian, and scientific applications. Precise time references accurate to a few milliseconds or better have historically been complicated and costly to obtain, but GPS will afford the means to do it very simply and economically. Navstar GPS provides precise time, globally, to an absolute accuracy of approximately 200 nanoseconds (ns) relative to UTC (USNO).

(This figure and others given in 11.3 and its subsections are subject to implementation factors and might be considered usual values; with careful implementations and under circumstances, much better accuracies are possible.)

11.4.2 Applications of Precise Time

Both scientific and civilian precise-time interests can be served by GPS. Some examples of civilian/scientific applications are described below:

1. Simultaneous observations of space objects from observatories
2. Use by national standards laboratories
3. Research into the theory of general relativity
4. Development and calibration of frequency standards
5. Use of Time Division Multiplexed (TDM) and other communications disciplines requiring precise time coordination between sites.

11.4.3 Interrelationship Between Different Definitions of Time

A number of different time definitions will be described here.

11.4.3.1 Time Based on the Rotation of the Earth On Its Axis

There are several definitions of time based on the rotation of the earth, but they are all interrelated ... .

1. Universal Time (UT)

UT is mean solar time on the Greenwich meridian. It is used in the

2. Universal Time 0 (UT 0)

UT 0 is determined directly from astronomical observations. It is
non-uniform due to the irregular rotation of the earth on its axis and to
polar motion.

3. Universal Time 1 (UT 1)

UT 1 is UT 0 corrected for polar motion and is therefore more uniform
than UT 0. UT 1 is the same as Greenwich Mean Time.

4. Universal Time 2 (UT 2)

UT 2 is UT 1 corrected for mean seasonal variations and is therefore more
uniform than UT 1.

11.4.3.2 Atomic Time/UTC Time

Atomic time is based on quantified energy transitions within the atom. The atomic second is defined as 9192631770 cycles of the cesium resonance and is the unit of time used in International Systems of Units (SI). Atomic time is obtained practically by use of cesium beam clocks. However, no practical clock can be considered perfect at deriving the defined frequency. UTC is a type of atomic time maintained by the U.S. Naval Observatory (USNO), and others. UTC is occasionally adjusted in steps (leap seconds) to maintain agreement with UT-1 to within 0.9 seconds. Leap seconds are necessary because of the effects on UT-1 of the irregular rotation of th e earth over time. The International Earth Rotation Service in Paris, France determines when step adjustments are necessary. A number of observatories/ laboratories maintain atomic clocks as very precise time references. They usually synchronize these clocks to UTC, which is the commonly used reference time. UTC represents an average of time from 58 different laboratories around the world. Each major country maintains its own version of UTC and defines national standards of time. Therefore, there is no one "Coordinated Universal Time". Instead, there is an International Atomic Time (TAI), kept in Paris by the International Bureau of Weights and Measures (BIPM), and several versions of UTC. The TAI is a weighted average of the times kept by the 58 laboratories which cooperate with BIPM to form this average. For the past few years, the majority of time comparisons used to form TAI have been done using GPS. The difference between TAI and the various national UTC time references are closely monitored and are therefore well known. National UTC references will therefore be steered to TAI when necessary and for GPS users, steering of UTC (USNO) will be experienced once every couple of years. For U.S. agencies, UTC is maintained by the U.S. Naval Observatory (USNO) in Washington, D.C. GPS time is required by the U.S. DoD to be referenced to UTC (USNO).

11.4.3.3 GPS Time

The internal reference time used by the three segments (Space -, Control- and User-Segment) in the GPS system is called GPS time. GPS time is a continuous time count, with no discontinuities, from the GPS epoch. GPS time is estimated and maintained by the MCS by estimating the ensemble satellite and monitor station time off sets. To aid USNO in providing a stable and accurate reference to the system, an ensemble of cesium-beam clocks is also maintained at the GPS Monitor Station that is collocated with the MCS. As a Precise Time Reference Station, it maintains time and rate very accurately traceable to UTC (USNO). It normally maintains a UTC (USNO) reference to an accuracy of a few nanoseconds. GPS time will normally be steered to within 30 nanoseconds of UTC (USNO) after accounting for the leap seconds which have accumulated in UTC since the GPS epoch of 0 hours 6 January 1980 (UTC). The remaining difference between GPS time and UTC (USNO) is transmitted in the NAV msgs from the satellites. The relationship between GPS time and UTC is:

GPS time = UTC time + DUTC time

where, DUTC time = Number of leap seconds + GPS-to-UTC bias

As of May 1995 the leap second difference between GPS and UTC is 10 seconds. The GPS receiver uses the NAV msg data to provide UTC (USNO) time outputs.

11.4.4 Precise Time Dissemination from GPS

GPS satellites have highly stable atomic clocks onboard with a known or predictable offset from GPS time. USNO monitors all the satellites when in view of the USNO in Washington DC, U.S.A. and compares the GPS time and UTC (USNO) time transmitted by the satellites with the (USNO) Master Clock. Based on this comparison USNO determines the accuracy of the GPS/UTC time information provided by each GPS satellite and transfers this information to the MCS ... . This GPS to UTC time bias and drift offsets, as well as the number of leap seconds, are uploaded in the satellite almanac data message. This information is used in the GPS receiver algorithms to determine UTC (USNO) time from GPS. The result is a world-wide time reference system for UTC (USNO) available to every user of GPS ... .

The absolute time accuracy available to the user depends on several factors described in Table 11-1, but the relative time accuracy between two GPS users can be much better than the absolute time accuracy. If the stations simultaneously track the same GPS satellites for time dissemination, then the effects of certain Control Segment and satellite-induced errors on the relative time accuracy are much reduced, and relative time accuracy can be as good as 10 -20 ns. Almost all users employ local clocks or oscillators of some kind to satisfy system requirements for long- and short-term accuracy and stability, or to avoid the need for continuous updates from an external reference, such as GPS. Slaving the clocks too tightly to GPS time would impart to them the shorter-term instability associated with reception and interpretation of GPS signals and with the instabilities previously mentioned. Longer -term measurements that are required to obtain an accurate rate or frequency would not enjoy the short-term advantage of simultaneous tracking, since over a period of time, most of the space and Control Segment functions would effect the stability of the dissemination function.

11.4.5 Time Transfer Using GPS

Time transfers (clock comparisons) may be made in a number of ways using the GPS satellites. The time dissemination process described in paragraph 11.4.4 is a "passive" method, in which the user acquires an accurate time reference without having to transmit timing signals or data. Other ways that can provide more accurate comparisons are described in this section.

11.4.5.1 Coordinated Simultaneous-View Time Transfer

In this method, a pair of stations simultaneously observes the same satellite(s); then (through some communications medium) they exchange readings of their local clock time against the time disseminated by GPS. The difference between these readings is quite accurately the difference between the stations' clocks. The satellite clock is primarily a transfer clock and does not directly affect the time transfer accuracy. This method might be used where the user clocks are required to maintain time or frequency agreement more precisely than UTC can be disseminated through GPS. The method works particularly well when the participating clocks are located reasonably close together (within some hundreds of kilometers). The method can also substantially reduce the effects of S/A on time transfers made with the C/A-code, because both ephemeris and ionospheric effects are reduced. Unless the time transfer is made with USNO or a UTC(USNO)-traceable reference, the result is relative rather than absolute time accuracy.

11.4.5.2 Coordinated Simultaneous -View Time Transfer with USNO

USNO uses a coordinated simultaneous-view method as shown in Figure 11-5, to provide more accurate UTC (USNO) to certain Precise Time Stations within simultaneous-view range. Both USNO and the distant observer track the same GPS satellite(s), derive UTC (USNO) from the satellite's NAV msg and pseudorange measurements, and compare this time with the time maintained by their local atomic clocks. USNO compares UTC (USNO) derived from the GPS satellites with the USNO Master Clock. Thus, USNO can deter mine the Control Segment and Satellite-induced errors that the observer will have in his GPS-derived UTC(USNO). The distant observer can then correct his GPS derived UTC (USNO) with corrections received from USNO via a data link. Now the distant observer can correct his clock very accurately to serve as a local reference traceable to UTC (USNO). The time accuracies that can be obtained by this method are shown in Table 11-1. The Table 11-1 values are valid for time transfer using C/A-code only when SA is switched off. Smoothing of the time measurements brings the error down to what can be expected for a P-code receiver.

The errors due to ephemeris uncertainties and ionospheric delay usually cancel out of if the two receivers are close to each other. This is because they have nearly the same line of sight to the satellites, and the signals travel through the same part of the ionosphere. In some cases where the two receivers are close to each other, the use of both L1 and L2 to compensate for ionospheric delay will be less accurate than not correcting for ionospheric delay at all. This is due to the fact that dual frequency com pensation for ionospheric delay is not perfect, and use of the ionospheric delay broadcast by the satellite by both parties produces more accurate results. For most cases where characters per second is used for coordinated simultaneous -view time transfer, the average of the values listed in Table 11-2 can be expected with distances of hundreds of kilometers between two receivers.

Compared with the uncoordinated simultaneous -view technique described in paragraph 11.4.4, coordinated time transfers with USNO can provide not only more accurate relative timing in the shorter term, but also better absolute timing and better long -term stability for setting and rating high -quality clocks.
We thus can note that in the language used in this manual UT = universal time, UTC = universal time coordinated, MCS = master control station.

We therefore can note that where UT = universal time, then UT = AT/absolute time, and, therefore, the developers of the GPS were and are aware of the necessity for establishing UT/AT for time coordination among ground stations, satellites, and GPS receivers.

The MCS/master control station is obviously an MITIC controlling SITICs:

MCS/Master Control Station = MITIC/Master Invariable Time-Inerval Clock

Thus, by the direct statement of the use of MCS in the GPS we have confirmation of the prediction that either Design A/Type A MASSAITICs or Design B/Type B MITICs controlling SITICs will be used for spacecraft/satellite/GPS time coordination/establishment of UT/AT.
ANNEX A: GLONASS: RUSSIA'S

A.1 HISTORICAL PERSPECTIVE

Similarly to the US TRANSIT, Russia operates CICADA, since the 1970's, the system consists of dual frequency VHF signals (150 MHz and 400 MHz) from satellites in near polar, low earth orbit. As the US has built up the Navstar GPS to replace TRANSIT, the Russians have developed an equivalent system, the Global Navigation Satellite Service, GLONASS. GLONASS uses a similar architecture to GPS for most components of its system. Users navigate with GLONASS in the same manner as GPS.

The system saw its origins in the mid 1970s at the Scientific Production Association of Applied Mechanics (NPO PM) a developer of military satellite in Kransnoyarsk-26. Since 1982 a range of GLONASS satellites have been launched three at a time, from the Tyuratam space centre. Although there was some doubt concerning the Russians' intentions in the early 1990's, however several statements concerning the systems future particularly to ICAO, and launches during 1994 and 1995 have confirmed GLONASS will reach full operation by late 1995.

GLONASS is owned and operated by Military Space Forces of the Russian Ministry of Defence. The Russian Institute of Radio Navigation and Time in St Petersburg designed and supports the synchronization of master clock systems, maintains satellite and Earth based time and frequency standards and develops receivers.

A.2 PURPOSE OF GLOBAL SATELLITE NAVIGATION SYSTEMS

GLONASS as Navstar GPS provides precision position fixing and time reference systems for world wide continuous use. An observer makes time-of-arrival measurements simultaneously to four satellites and by using the received data to compute the position of the satellites solves the four range equations for his three unknown position coordinates and time.

It is presumed the primary purpose of GLONASS is similarly to GPS for weapon system navigation and guidance. However as with GPS the wide interest in the use of satellite navigation systems has resulted in parts of the system being offered for international civil use.

A.4 MONITOR AND CONTROL SUBSYSTEM

As for GPS, GLONASS is controlled and monitored by a complex ground system. Data defining satellite position, system time and navigation message is uploaded to the satellites every 24 hrs with the satellite timing synchronized on every orbit, Ref 3.

The GLONASS monitor and control segment consists of:
- Ground control centre (GCC) Moscow
- Central synchronizer (CS) Moscow
- TT&C stations Saint Petersburg, Yeniseisk, Komsomolsk-on-Amur
- navigation signal phase control system (PCS) Moscow
- quantum-optical station (QOS), Komsomolsk-on-Amur
- navigation field control equipment (NFCE) Moscow, Komsomolsk-on-Amur

The monitoring and control subsystem operates autonomously and receives the data of Earth rotation parameters, corrections to the system time relative to Russian Time & Frequency Standard (UTC SU) externally.
We can note that the Russians were also using MITICs in the GCC/Ground Control Centre/Central Synchronizer to control SITICs for their GLONASS system.

We thus have from the Russians confirmation of the TITI by their use of Russian MITICs to control Russian SITICs for UT/time coordination/synchronization.

### The 1971 Hafele-Keating Experiment

The 1971 Hafele-Keating experiment ...

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.htm

... provides the conditions under which ITICs can be confirmed to be a reality.

"During October, 1971, four cesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40+/-23 nanoseconds during the eastward trip and should have gained 275+/-21 nanoseconds during the westward trip ... Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59+/-10 nanoseconds during the eastward trip and gained 273+/-7 nanosecond during the westward trip, where the errors are the corresponding standard deviations. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks."

J.C. Hafele and R. E. Keating, Science 177, 166 (1972)

In the Hafele-Keating experiment, three sets of atomic clocks were synchronized (time-coordinated) and all clocks were therefore using the same time-interval [TI].

One set of clocks was placed aboard a westbound jet airliner, another set was placed aboard an eastbound set airliner, and thus both sets of airborne clocks were accelerated and decelerated during the normal flight routines of the airliners and then returned to the Earth, where their readouts (time counts/time measurements) were compared to the readouts of the clocks which remained on Earth.

In this experiment, the Earth was one reference frame, and each airliner, because of its acceleration and altitude, was another reference frame, in analogy with Einstein's gedankenexperiment (thought experiment/intuition) in which a railway embankment was one reference frame and a moving railway carriage was another reference frame (see Relativity by Albert Einstein, pp. 17-25):

Earth = Railway Embankment [K Reference Frame]

Airliner = Railway Carriage [K' Reference Frame]

When the readouts of the accelerated airborne clocks were compared to the readouts of the non-accelerated Earth-bound clocks, the accelerated airborne clocks' readouts were uniformly lesser than the non-accelerated Earth-bound clocks' readouts, an indication that time had been dilated, and a confirmation of relativity, which predicted time-dilation for accelerated/decelerated clocks.

We note that the determination of time-dilation is conducted in the originating reference frame and not by any method whereby observers in one reference frame observe objects/events in another reference frame. By the use of the single originating reference frame Lorentz relativistic transformation problems are eliminated.

The clocks used for the Hafele-Keating experiment were clocks whose time-intervals (TIs) were variable time-intervals (VTIs) thus the clocks themselves were variable time-interval clocks (VTICs) whose time-intervals were variable in duration, in time, when subjected to changes of velocity (speed and direction) and/or gravity. When the air-borne VTICs were accelerated, their TIs/VTIs were lengthened, their RoOs were slowed, and their counting of TIs/VTIs was decreased, their readouts/time counts/time-measurements/face-readings decreased, with the result that their readouts were different from and less than the readouts of the Earth-bound/non-accelerated VTICs.

If invariable time-interval clocks (ITICs—either motion-sensing/self-adjusting invariable time-interval clocks [MSSAITICs] or master invariable time-interval clocks [MITICs] controlling slave invariable time-interval clocks [SITICs]) were used in a replication of the Hafele-Keating experiment, then the prediction is that upon their return to the Earth the airborne accelerated ITICs would show the same/identical readouts as the non-accelerated Earth-bound ITICs, and, thus, time would not be dilated.

Again, the use of the single originating reference frame eliminates the Lorentz relativistic transformation problems.

What is of critical importance herein is the fact that machines which are subject to changes of their rates of operation [RoOs] caused by accelerations and/or decelerations were used, and the predicted and observed changes of their RoOs is supposed to be proof of time dilation predicted by Einstein in his theory of relativity, and, thus, in the Haefele-Keating experiments there was in fact an observed change of RoOs in the airborne clocks and, thus, the predictions of time-dilation appeared to have been confirmed, and, thus, the relativistic theory of time was supposed to have been physically verified.

The question was never raised of what would happen to machines whose RoOs were adjusted to compensate for the predicted and expected changes of RoOs caused by accelerations/decelerations. The predictions of the Operational Physics Theory of Time [OpPhysToT] suggest that when airborne ITICs, as MITICs<->SITICs, are used instead of VTICs that the face-readings of the airborne and therefore accelerated/decelerated ITICs would be the same as similar Earthbound ITICs or VTICs which have identical TIs. To date an experiment to confirm/disconfirm the OpPhysToT has not been conducted.

The OpPhysToT has been confirmed by the use of an Earthbound master clock [MITICs] which control earthbound slave clocks [SITICs] which function as relays of the master clock for the control of spaceborne slave clocks [SITICs] in satellites in the US GPS navigational system, and by the similar use of and earthbound master clock controlling other Earthbound slave clocks controlling spaceborne slave clocks in satellites in the Russian GLONASS nav system.

We also have confirmation of the existence and usage of radio clocks which either control other clocks or otherwise are used as time references.

A radio clock is a clock that is synchronized by a time code transmitted by a radio transmitter connected to a time standard such as an atomic clock.

Terrestrial time signals

Radio clocks synchronized to terrestrial time signals can usually achieve an accuracy of around 1 millisecond relative to the time standard, generally limited by uncertainties and variability in radio propagation.

Time signals that can be used as references for radio clocks include:

* the WWV, WWVB and WWVH radio stations in the United States
* the DCF77 radio station in Germany
* the MSF radio station in the United Kingdom
* the JJY radio station in Japan

Time signal radio stations in general have the following attributes:

* they refer their broadcast frequency to the frequency standard
* they broadcast seconds 'pips' to identify the start of second intervals
* they also broadcast time codes as a way of identifying seconds intervals

Loran-C time signals may also be used for radio clock synchronization, by augmenting their highly accurate frequency transmissions with external measurements of the offsets of LORAN navigation signals against time standards.

GPS clocks

Many modern radio clocks use the GPS satellite positioning system to provide more accurate time than can be obtained from these terrestrial radio stations. These GPS clocks combine time estimates from multiple satellite atomic clocks with error estimates maintained by a network of ground stations. Because they compute the time and position simultaneously from readings from several sources, GPS clocks can automatically compensate for line-of-sight delay and many radio propagation defects, and can achieve sub-microsecond accuracy under ideal conditions.