Satellite Navigation System
Introduction
The development of space based navigation systems commenced in the 1950s with the establishment of the USA Transit system. The current generation began development in the 1970’s and the next generation is already under development. It is intended that GNSS will eventually replace all terrestrial radio navigation facilities. However, despite USA assertions that this is imminent, it is unlikely to be achieved in the foreseeable future.
The current systems have brought a new dimension of accuracy to navigation systems with precision measured in metres, and where special differential techniques are used the potential is for accuracies substantially less than one metre.
At present there are two operational global navigation satellite systems (GNSS), enhancements of the existing systems under development and a planned European system. These systems are:
The NAVSTAR Global Positioning System (GPS) operated by the USA.
The Global Orbiting Navigation Satellite System (GLONASS) operated by Russia. After serious problems following the disintegration of the USSR in 1989/1990 the system is now fully operational.
Satellite Orbits
Johannes Kepler’s laws quantified the mathematics of planetary orbits which apply equally to the orbits of satellites:
Using these laws, and given a starting point, the satellites  space vehicles (SVs) calculate their positions at all points in their orbits.
The SVs’ orbital position is known as ephemeris.
Position Reference System
GNSS use an earth referenced three dimensional Cartesian coordinate system with its origin at the centre of the earth. Because the systems are global, a common model of the earth was required. The World Geodetic Survey of 1984 (WGS84) was selected as the appropriate model for GPS and all GPS terrestrial positions are defined on this model and referenced to the Cartesian coordinate system. Where other models are required, for instance for the UK’s Ordnance Survey maps, a mathematical transformation is available between the models (note this is incorporated as a feature of GPS receivers available in the UK).
Galileo uses the European Terrestrial Reference System 1989 (ETRS89) and the Russian model for GLONASS is known as Parameters of the Earth 1990 (PZ90). WGS84 is the ICAO standard for aeronautical positions, however, since all these systems are mathematical models, transposition from ETRS89 to WGS84, for example, is a relatively simple mathematical process. Mathematically all these models are regular shapes, known as ellipsoids.
The ellipsoids cannot be a perfect representation, nor can they represent geographical features, e.g. mountains and land depressions. The distance of mean sea level from the centre of the earth depends on gravitational forces which vary both locally and globally. Hence mean sea level will not necessarily coincide with the surface of the ellipsoid. The maximum variation between mean sea level and the surface of the ellipsoid for WGS84 is approximately 50 m.
Hence the vertical information provided by any system referenced to this model cannot be used in isolation for vertical positioning, except when in medium/high level cruise with all aircraft using the GNSS reference and in LADGNSS applications  (where the vertical error is removed).
The GPS Segments
GPS comprises three segments:

The Space Segment

The Control Segment and

The User Segment
GPS time is measured in weeks and seconds from 00:00:00 on 06 January 1980 UTC. An epoch is 1024 weeks after which the time restarts at zero. GPS time is referenced to UTC but does not run in direct synchronization, so time correlation information is included in the SV broadcast. In July 2000 the difference was about 13 seconds.
The Space Segment
The operational constellation for GPS is specified as comprising 24 SVs. (Currently the USA has 31 SVs providing a navigational service). The orbits have an average height of 10898 NM (20180 km) and have an orbital period of 12 hours. The orbital planes have an inclination of 55° and are equally spaced around the equator. The spacing of the SVs in their orbits is such that an observer on or close to the surface of the earth will have between five and eight SVs in view, at least 5° above the horizon. The SVs have 3 or 4 atomic clocks of caesium or rubidium standard with an accuracy of 1 nanosecond.
An SV will be masked (that is not selected for navigation use) if its elevation is less than 5° above the horizon.
The SVs broadcast pseudorandom noise (PRN) codes of one millisecond duration on two frequencies in the UHF band and a NAV and SYSTEM data message. Each SV has its own unique code.
L1 Frequency: 1575.42 MHz transmits the coarse acquisition (C/A) code repeated every millisecond with a modulation of 1.023 MHz, the precision (P) code, modulation 10.23 MHz repeats every seven days and the navigation and system data message at 50 Hz. The navigation and system data message is used by both the P and C/A codes.
L2 Frequency: 1227.6 MHz transmitting the P code. The second frequency is used to determine ionospheric delays.
L3 Frequency: 1381.05 MHz has been allocated as a second frequency for nonauthorized users and its use is the same as the L2 frequency.
Only the C/A code is available to civilian users.
The P code is provided for the US military and approved civilian users and foreign military users at the discretion of the US DOD. The P code is designated as the Y code when antispoofing measures are implemented. The Y code is encrypted and therefore only available to users with the necessary decryption algorithms.
The pseudorandom noise PRN codes provide SV identification and a timing function for the receiver to measure SV range.
The information contained in the nav and system data message is:

SV position

SV clock time

SV clock error

Information on ionospheric conditions

Supplementary information, including the almanac (orbital parameters for the SVs), SV health (Pcode only), correlation of GPS time with UTC and other command and control functions.
The two services provided are:

The standard positioning service (SPS) using the C/A code

The precise positioning service (PPS) using the C/A and P codes
GLONASS also has an operational constellation of 24 SVs positioned in three orbital planes inclined at 65° to the equator. The orbital height is 10313 NM (19099 km) giving an orbital period of 11 hours 15 minutes. As in GPS, GLONASS transmits C/A and P codes. The codes are the same for all SVs, but each SV uses different frequencies. The L1 frequency is incremental from 1602 MHz and the L2 frequency from 1246 MHz.
The Control Segment
The GPS control segment comprises:

A Master Control Station

A Backup Control Station

5 Monitoring Stations
The monitoring stations check the SVs’ internally computed position and clock time at least once every 12 hours. Although the calculation of position using Keplerian laws is precise, the SV orbits are affected by the gravitational influences of the sun, moon and planets and are also affected by solar radiation, so errors between the computed position and the actual position occur.
When a positional error is detected by the ground station, it is sent to the SV for the SV to update its knowledge of position. Similarly if an error is detected in the SV clock time this is notified to the SV, but since the clocks cannot be adjusted, this error is included in the SV broadcast.
The User Segment
The User Segment is all the GPS receivers using the space segment to determine position on and close to the surface of the earth. These receivers may be standalone or be part of integrated systems.
There are several types of receiver:
Sequential receivers which use one or two channels and scan the SVs sequentially to determine the pseudoranges.
Multiplex receivers may be single or twin channel and are able to move quickly between SVs to determine the pseudoranges and hence have a faster time to first fix than the sequential receivers.
Multichannel receivers monitor several SVs simultaneously to give instant positional information. These include ‘allinview’ receivers which monitor all the SVs in view and select the best 4 to determine position. Because of the speed of operation these are the preferred type for aviation.
Principle Of Operation
The navigation message is contained in one frame comprising 5 subframes. The subframes each take 6 seconds to transmit, so the total frame takes 30 seconds for the receiver to receive. Frame 1 contains SV clock error, frames 2 and 3 contain the SV ephemeris data, frame 4 contains data on the ionospheric propagation model, GPS time and its correlation with UTC. The fifth frame is used to transmit current SV constellation almanac data. A series of 25 frames is required to download the whole almanac. The almanac data is usually downloaded hourly and is valid from 4 hours to several months dependent on the type of receiver.
Because the orbits are mathematically defined, an almanac of their predicted positions can be and is maintained within the receivers. Thus, when the receiver is switched on, provided it knows its position and time to a reasonable degree of accuracy, it will know which SVs to expect and can commence position update immediately. If the almanac is corrupted, out of date or lost, or if receiver position or receiver clock time are significantly in error it will not find the expected SVs and will download the almanac from the constellation.
The almanac data fills 25 frames so it takes 12.5 minutes to download. When the receiver position is significantly in error it will not detect the expected SVs. Having downloaded the almanac the receiver will now carry out a skysearch, this involves the receiver checking which SVs are above the horizon and selecting the 4 to give the most accurate fix, then commencing position fixing, this takes a least a further 2.5 minutes. Hence the time to first fix will be at least 15 minutes. If there are no problems then the first fix, on initialization, will be obtained within about 30 seconds.
The GPS receiver internally generates the PRN code and compares the relative position of the two codes to determine the time interval between transmission and reception.
The initial measurement of range is known as pseudorange because it has not yet been corrected for receiver clock error.
The receiver uses four SVs and constructs a three dimensional fix using the pseudoranges from the 4 SVs. Each range corresponds to a position somewhere on the surface of a sphere with a radius in excess of 10 900 NM.
The intersection of two range spheres will give a circular position line.
The introduction of a third range sphere will produce two positions several thousand miles apart. One position will be on or close to the surface of the earth, the other position will be out in space, so it would be possible to use just three pseudoranges to produce a position, by rejecting the space position.
However, a fourth range position line is needed because of the way the receiver compensates for receiver time errors. The receiver has an accurate crystal oscillator to provide time. However, the accuracy does not compare with the accuracy of the SV clocks, so there will always be an error in the time measurement, and hence in the computation of range.
Furthermore the receiver clock is deliberately kept in error by a small factor to ensure that the correction process can only go in one direction. This is why the initial calculated range is known as a pseudo range. As a result the position lines will not meet in a point but will form a ‘cocked hat’.
For example, if the receiver clock is permanently 1 millisecond fast, then the receiver will over estimate each range by about 162 NM. So when the receiver sets about calculating the correct ranges it knows that it must reduce the pseudoranges.
The receiver has to correct the X, Y, Z coordinates and time to produce the fix. Since it has each element provided by each SV the receiver can set up 4 linear simultaneous equations each with 4 unknown quantities (X, Y, Z, and T) which it solves by iteration to remove the receiver time error, and hence, range errors.
This means that the use of 4 SVs provides a 3D fix and an accurate time reference, i.e. a 4D fix, at the receiver. The X, Y, and Z coordinates can now be transposed into latitude and longitude or any other earth reference system (e.g. the UK Ordnance Survey grid) and altitude.
GPS Errors
All errors are at the 95% probability level.
Ephemeris Errors
These are errors in the SVs calculation of position caused by the gravitational effects of the sun, moon, planets and solar radiation. The SV position is checked every 12 hours and, where necessary, updated. The maximum error will be 2.5 m.
SV Clock Error
As with SV ephemeris, the SV clock is checked at least every 12 hours and any error is passed to the SV to be included in the broadcast. Maximum error 1.5 m.
Ionospheric Propagation Error
The interaction of the radio energy with the ionized particles in the ionosphere causes the radio energy to be slowed down as it traverses the ionosphere, this is known as the ionospheric delay. The delay is dependent on both the level of ionization and the frequency of the radio waves. The higher the frequency is, the smaller the delay and the higher the levels of ionization, the greater the delay. The receiver contains an average model of the ionosphere which is used to make time corrections to the measured time interval. The state of the ionosphere is continuously checked at the monitoring stations and the required modifications to the model is regularly updated to the SVs and thence to the receivers. However, the propagation path from the SV to the monitoring station will be very different to that to the receiver, so this is only a partial solution.
The ionospheric delay is inversely proportional to the square of the frequencies.
As two different frequencies will experience different delays, by measuring the difference in arrival time of the two signals we can deduce the total delay experienced hence minimising the error and calculate a very accurate range.
This is the most significant of the errors in SV navigation systems. Maximum error for single frequency operation is 5 m.
Tropospheric Propagation Error
Because of the inherent accuracy of SV navigation systems, the effect of variations in tropospheric conditions on the passage of radio waves has become significant. Variations in pressure, temperature, density and humidity affect the speed of propagation, increased density and increased absolute humidity reduce the speed of propagation. For example, a change in transit time of one nanosecond would give an error of 0.3 m. As with ionospheric propagation error this is minimized with the use of two frequencies.
Receiver Noise Error
All radio receivers generate internal noise, which in the case of GNS receivers can cause errors in measurement of the time difference. Maximum 0.3 m.
Multipath Reception
Reflections from the ground and parts of the aircraft result in multipath reception. This can be minimized by careful siting of the aerial and by internal processing techniques. Maximum 0.6 m.
Dilution of Precision (DOP)
The satellite geometry, (angle of cut between position lines), and any error in the pseudo ranges (time synchronization) will degrade the accuracy of the calculated position.
DOP is further divided:

Horizontal dilution of precision (HDOP): This refers to errors in the X and Y coordinates.

Vertical dilution of precision (VDOP): This refers to errors in the Z coordinate.

Position dilution of precision (PDOP): This is a combination of HDOP and VDOP.

Time dilution of precision (TDOP): This refers to timing errors.

Geometric dilution of precision (GDOP): This is a combination of PDOP and TDOP.
Errors caused by PDOP are minimized by the geometry of the positioning of the SVs in their orbits and by the receivers selecting the four best SVs to determine position. The SV geometry that will provide the most accurate fixing information is one SV directly overhead the receiver and the other three SVs close to the horizon and spaced 120° apart.
Effect of Aircraft Manoeuvre
Aircraft manoeuvre may result in part of the aircraft shadowing one or more of the inuse SVs. There are two possible outcomes of this. Firstly, whilst the SV is shadowed, the signal may be lost resulting in degradation of accuracy, or the receiver may lock onto reflections from other parts of the aircraft again with a reduction in accuracy. The effect of manoeuvre can be minimized by careful positioning of the aerial on the aircraft. The optimum position for the antenna is on top of the fuselage close to the aircraft’s centre of gravity.
Selective Availability (SA)
SA was introduced into GPS by the US DOD in about 1995. It deliberately degraded the accuracy of the fixing on the C/A code (i.e. for civilian users). The USA withdrew SA at 0000 on 01 May 2000, and President Clinton stated that it would never be reintroduced.
(SA downgraded the accuracy of position derived from the C/A code to the order of 100 m spherical error). SA was achieved by introducing random errors in the SV clock time, known as dithering the SV clock time.