# GPS

Correcting these errors is a significant challenge to improving GPS position accuracy. Therefore d as in dilution of precision is used.Greater accuracy may be obtained by processing triple difference results for additional sets of three independent time pairs. The receiver is potentially capable of getting a new pseudorange measurement at the beginning of each subframe or every 6 seconds. Then the orbital position data, or ephemeris, from the navigation message is used to calculate precisely where the satellite was at the start of the message.

Ignoring this effect will produce an east-west error on the order of hundreds of nanoseconds, or tens of meters in position. Since GPS signals at terrestrial receivers tend to be relatively weak, natural radio signals or scattering of the GPS signals can desensitize the receiver, making acquiring and tracking the satellite signals difficult or impossible. Space weather degrades GPS operation in two ways, direct interference by solar radio burst noise in the same frequency band In automotive GPS receivers, metallic features in windshields, can act as a Faraday cage, degrading reception just inside the car. Man-made EMI (electromagnetic interference) can also disrupt, or jam, GPS signals. All GPS receivers capable of functioning above 18 km (60,000 ft) altitude and 515 m/s (1,000 knots) are classified as munitions (weapons) for which U.S.

In the same method is discussed but the equations are not shown. A figure, Two Sphere Surfaces Intersecting in a Circle, is shown below depicting this which hopefully will aid the reader in visualizing this intersection.

If correlation is not achieved, the 1023 bits of the receiver s internally generated PRN code are shifted by one bit relative to the satellite s PRN code and the signals are again compared. In this description differences are taken in the order of differencing between satellites, differencing between receivers, and differencing between epochs.

Some systems transmit additional information about sources of error (such as clock drift, ephemeris, or ionospheric delay), others provide direct measurements of how much the signal was off in the past, while a third group provide additional navigational or vehicle information to be integrated in the calculation process. Examples of augmentation systems include the Wide Area Augmentation System, Differential GPS, Inertial Navigation Systems and Assisted GPS. The accuracy of a calculation can also be improved through precise monitoring and measuring of the existing GPS signals in additional or alternate ways. After SA, which has been turned off, the largest error in GPS is usually the unpredictable delay through the ionosphere. Special relativity predicts that atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by about 7.2 μs per day. For the GPS satellites, general relativity predicts that the atomic clocks at GPS orbital altitudes will tick more rapidly, by about 45.9 μs per day, because they have a higher gravitational potential than atomic clocks on Earth s surface. When combined, the discrepancy is about 38 microseconds per day; a difference of 4.465 parts in 1010. GPS observation processing must also compensate for the Sagnac effect.

These delayed signals can cause inaccuracy. Thus low DOP values represents a better GPS positional accuracy due to the wider angular separation between the satellites used to calculate GPS receiver position.

Then the new ephemeris is uploaded and the satellite marked healthy again. The user s GPS receiver is the user segment (US) of the GPS. However the elements of the Q matrix do not represent variances and covariances as they are defined in probability and statistics.

Additional inspiration for the GPS came when the Soviet Union launched the first man-made satellite, Sputnik in 1957. These are the space segment (SS), a control segment (CS), and a user segment (US). The space segment (SS) comprises the orbiting GPS satellites, or Space Vehicles (SV) in GPS parlance.

GPS survey equipment has revolutionized tectonics by directly measuring the motion of faults in earthquakes. The U.S. With a 1% of wave length accuracy in detecting the leading edge, this component of pseudorange error might be as low as 2 millimeters.

To get estimates for an over determined system, least squares can be used. This may require the use of a numerical procedure such as one of those found in the chapter on root finding and nonlinear sets of equations in Numerical Recipes.

Other proprietary protocols exist as well, such as the SiRF and MTK protocols. The amount of adjustment required for maximum correlation is used in estimating phase error.

Each frame contains 1/25th of the almanac, so 12.5 minutes are required to receive the entire almanac from a single satellite. A detailed discussion of the errors is omitted in order to avoid detracting from the description of the methodology.

An important thing to note about navigation data is that each satellite transmits not only its own ephemeris, but transmits an almanac for all satellites. All satellites broadcast at the same two frequencies, 1.57542 GHz (L1 signal) and 1.2276 GHz (L2 signal). Coast Guard s network of LF marine navigation beacons.

To facilitate this on lower cost receivers, a new civilian code signal on L2, called L2C, was added to the Block IIR-M satellites, which was first launched in 2005. Once the receiver s approximate location is known, a mathematical model can be used to estimate and compensate for these errors. Ionospheric delay of a microwave signal depends on its frequency.

Note that is the distance from the computed GPS receiver position to the surface of the sphere corresponding to the fourth satellite. Those for any particular geographical area can be easily calculated by comparing the GPS-measured position to a known surveyed location.

The GPS is used to determine which content to display. In the 1970s, the ground-based Omega Navigation System, based on phase comparison of signal transmission from pairs of stations proposed a test of General Relativity using accurate atomic clocks placed in orbit in artificial satellites.

Also see Preview of Root Finding. A Lorentz transformation is thus applied to convert from the inertial system to the ECEF system.

The amount of error added was set to zero Selective Availability is still a system capability of GPS, and could, in theory, be reintroduced at any time. However, they are based on observations and may not indicate the clock s current state. These problems tend to be very small, but may add up to a few meters (tens of feet) of inaccuracy. For very precise positioning (e.g., in geodesy), these effects can be eliminated by differential GPS: the simultaneous use of two or more receivers at several survey points.

The message data is transmitted at 50 bits per second. This requires specially equipped receivers.

Again the article trilateration clearly shows this mathematically. For automobiles and other near-earth-vehicles, the correct position of the GPS receiver is the intersection closest to the earth s surface. In the future, additional civilian codes are expected to be transmitted on the L2 and L5 frequencies (see GPS modernization).

Since the GPS receiver computes its approximate altitude, this error is relatively simple to correct, either by applying a function regression or correlating margin of atmospheric error to ambient pressure using a barometric altimeter. GPS signals can also be affected by multipath issues, where the radio signals reflect off surrounding terrain; buildings, canyon walls, hard ground, etc. And in fact a view from any horizontal direction would look exactly the same.

Thus with four satellites, the indicated position of the GPS receiver is at or near the intersection of the surfaces of four spheres. Geometric trilateration is used to combine these distances with the satellites locations to obtain the position of the receiver.

The ionospheric data are transmitted via satellite in Satellite Based Augmentation Systems (SBAS) such as WAAS (available in North America and Hawaii), EGNOS (Europe and Asia) or MSAS (Japan), which transmits it on the GPS frequency using a special pseudo-random noise sequence (PRN), so only one receiver and antenna are required. Humidity also causes a variable delay, resulting in errors similar to ionospheric delay, but occurring in the troposphere. The 1023 bits of the satellite PRN signal are compared with the receiver PRN signal.

Each satellite s PRN identifier is unique and in the range from 1 through 32. There are 1025 different Gold codes of length 1023 bits, but only 32 are used. Different vendors have interpreted these limitations differently.

Two distinct CDMA encodings are used: the coarse/acquisition (C/A) code (a so-called Gold code) at 1.023 million chips per second, and the precise (P) code at 10.23 million chips per second. Then the equations becomes: Two of the most important methods of computing GPS receiver position and clock bias are (1) trilateration followed by one dimensional numerical root finding and (2) multidimensional Newton-Raphson calculations.

The messages are sent in frames, each taking 30 seconds to transmit 1500 bits. Transmission of each 30 second frame begins precisely on the minute and half minute as indicated by the satellite s atomic clock according to Satellite message format. For military operations, the ground track repeat can be used to ensure good coverage in combat zones. As of March 2008 About ten satellites are visible from any point on the ground at any one time (see animation at right). The flight paths of the satellites are tracked by U.S.

The command for the frequency generator and any further PRN code shifting required are computed as a function of the phase error and the phase rate error in accordance with the control law used. These standard deviations are computed by taking the square root of the sum of the squares of the individual components (i.e., RSS for root sum squares).

In view of the fact that the receiver, satellite, and time come in alphabetical order as arguments of and to strike a balance between readability and conciseness, let so as to have a concise abbreviation. Collier Trophy, the most prestigious aviation award in the United States.

To obtain a lock, it is necessary that there be an unobstructed line of sight from the receiver to the satellite. A team of U.S.

Kershner were monitoring Sputnik s radio transmissions. Instead they are strictly geometric terms.

Then the maneuver can be carried out, and the resulting orbit tracked from the ground. A receiver is often described by its number of channels: this signifies how many satellites it can monitor simultaneously.

This procedure is repeated until the residuals are sufficiently small in magnitude. Calculating a position with the P(Y) signal is generally similar in concept, assuming one can decrypt it. The Global Positioning System (GPS) is a U.S.

In this approach, determination of range signal can be resolved to a precision of less than 10 centimeters (4 in). The pseudorange is computed as: Assume the message travels at the speed of light, then the pseudorange satisfies the equation: When an approximate solution, rather than the exact solution, is used in equation 1, there is a residual, .

Few civilian receivers have ever used the P-code, and the accuracy attainable with the public C/A code is so much better than originally expected (especially with DGPS) that the antispoof policy has relatively little effect on most civilian users. At the TU Vienna the method was named qGPS and adequate software of post processing was developed. The concept of geometric dilution of precision was introduced in the section, error sources and analysis.

Let denote the unknown clock error or bias, the amount by which the receiver s clock is slow. Using messages received from four satellites, the GPS receiver is able to determine the satellite positions and time sent.

These topics are examined below, one at a time. According to the theory of relativity, due to their constant movement and height relative to the Earth-centered, non-rotating approximately inertial reference frame, the clocks on the satellites are affected by their speed. When the GPS antenna is moving, the false solutions using reflected signals quickly fail to converge and only the direct signals result in stable solutions. While the ephemeris data is transmitted every 30 seconds, the information itself may be up to two hours old.

The receiver can distinguish the signals from different satellites because GPS uses a code division multiple access (CDMA) spread-spectrum technique where the low-bitrate message data is encoded with a high-rate pseudo-random (PRN) sequence that is different for each satellite. Assuming the message traveled at the speed of light, c, the distance traveled, can be computed as .

HDOP, VDOP, PDOP and TDOP are respectively Horizontal, Vertical, Position (3-D) and Time Dilution of Precision. Figure 3.1 Dilution of Precision of provide a graphical indication of how geometry affect accuracy. We now take on the task of how to compute the dilution of precision terms. Although multidimensional numerical root finding can have problems, this disadvantage may be overcome with this good initial estimate.

The offset, O, is computed in a trial and error manner. The almanac serves several purposes.

GPS satellites broadcast signals from space that GPS receivers use to provide three-dimensional location (latitude, longitude, and altitude) plus the time. GPS has become a widely used aid to navigation worldwide, and a useful tool for map-making, land surveying, commerce, scientific uses, tracking and surveillance, and hobbies such as geocaching and waymarking. Receivers subtract this offset from GPS time to calculate UTC and specific timezone values.

Air Force monitoring stations in Hawaii, Kwajalein, Ascension Island, Diego Garcia, and Colorado Springs, Colorado, along with monitor stations operated by the National Geospatial-Intelligence Agency (NGA). Satellite maneuvers are not precise by GPS standards. The first handsets with integrated GPS were launched already in the late 1990’s, and were available for broader consumer availability on networks such as those run by Nextel, Sprint and Verizon in 2002 in response to U.S.

However, these keys are reserved for the military and authorized agencies and are not available to the public. The C/A code is public and used by civilian GPS receivers, while the P code can be encrypted as a so-called P(Y) code which is only available to military equipment with a proper decryption key.

This section describes the derivation of these equations. The time needed to acquire the ephemeris is becoming a significant element of the delay to first position fix, because, as the hardware becomes more capable, the time to lock onto the satellite signals shrinks, but the ephemeris data requires 30 seconds (worst case) before it is received, due to the low data transmission rate. The almanac consists of coarse orbit and status information for each satellite in the constellation, an ionospheric model, and information to relate GPS derived time to Coordinated Universal Time (UTC).

In general, GPS receivers are composed of an antenna, tuned to the frequencies transmitted by the satellites, receiver-processors, and a highly-stable clock (often a crystal oscillator). Being able to synchronize clocks to exacting standards enables time transfer, which is critical in large communication and observation systems.

Let the coordinates of each satellite, and the time the message was sent, be , let the GPS clock s indicated received time be and c be the speed of light. On the other hand, manufacturers prefer to build inexpensive GPS receivers for mass markets.

It would not prevent use in a cruise missile since their altitudes and speeds are similar to those of ordinary aircraft. This rule applies even to otherwise purely civilian units that only receive the L1 frequency and the C/A code and cannot correct for SA, etc. Disabling operation above these limits exempts the receiver from classification as a munition. To correspond to the local horizon plane and the local vertical, x, y, and z should denote positions in either a North, East, Down coordinate system or a South, East, Up coordinate system. The equations for computing the geometric dilution of precision terms have been described in the previous section.

Two points at which the surfaces of the spheres intersect are clearly marked on the figure. The article trilateration shows this mathematically.

The least squares procedure determines the position of receiver 2 which best fits the observed triple difference results for receiver 2 positions under the criterion of minimizing the sum of the squares. The Global Positioning System, while originally a military project, is considered a dual-use technology, meaning it has significant applications for both the military and the civilian industry. The military applications of GPS span many purposes: Many civilian applications benefit from GPS signals, using one or more of three basic components of the GPS: absolute location, relative movement, and time transfer. The ability to determine the receiver s absolute location allows GPS receivers to perform as a surveying tool or as an aid to navigation. As it detects each satellite s signal, it identifies it by its distinct C/A code pattern. The receiver uses the C/A Gold code with the same PRN number as the satellite to compute an offset, O, that generates the best correlation.

Computations were provided to show how PDOP was used and how it effected the receiver position error standard deviation. When visible GPS satellites are close together in the sky (i.e., small angular separation), the DOP values are high; when far apart, the DOP values are low. In the ideal case of no errors, the GPS receiver will be at an intersection of the surfaces of four spheres.

Let . Also errors associated with atmospheric delay and satellite ephemeris have been significantly reduced.

To use such a numerical method, an initial approximation of the position of receiver 2 is required. The x, y, and z components of position and the time sent are designated as where the subscript i denotes which satellite and has the value 1, 2, 3, or 4.

The accurate timing that GPS provides facilitates everyday activities such as banking, mobile phone operations, and even the control of power grids. These two methods along with their advantages are discussed. This section provides a more detailed discussion of the equations used in the second method described in Position calculation advanced. The linearized equations are developed using the appropriate partial derivatives and the algorithm is described.

Thus the quotient, , provides an estimate of and the GPS receiver clock can be advanced if is positive or delayed if is negative. The current GPS consists of three major segments. For instance, when approaching a monument it would tell you about the monument. GPS functionality has now started to move into mobile phones en masse.

Each of these functions has a linear combination of variables with three subscripts as its argument. The rule specifies operation above 18 km and 515 m/s, but some receivers stop operating at 18 km even when stationary.

To achieve accuracy requirements, GPS uses principles of general relativity to correct the satellites atomic clocks. The design of GPS is based partly on similar ground-based radio navigation systems, such as LORAN and the Decca Navigator developed in the early 1940s, and used during World War II. In the 1990s when receivers were quite expensive, some methods of quasi-differential GPS were developed, using only one receiver but reoccupation of measuring points.

In comparison, civil receivers are highly vulnerable to spoofing since correctly formatted C/A signals can be generated using readily available signal generators. This significantly impeded the U.S.

Easton, received the National Medal of Technology on February 13, 2006 at the White House. On February 10, 1993, the National Aeronautic Association selected the Global Positioning System Team as winners of the 1992 Robert J. Let and denote the true coordinates of GPS receiver position at time, .

By eliminating this source of error, CPGPS coupled with DGPS normally realizes between 20 and 30 centimeters (8 to 12 inches) of absolute accuracy. Relative Kinematic Positioning (RKP) is another approach for a precise GPS-based positioning system. Thus the triple difference result has eliminated all or practically all clock bias errors and the integer ambiguity.

The position of the receiver is somewhere on this surface. This can be accomplished by using a combination of differential GPS (DGPS) correction data, transmitting GPS signal phase information and ambiguity resolution techniques via statistical tests—possibly with processing in real-time (real-time kinematic positioning, RTK). While most clocks are synchronized to Coordinated Universal Time (UTC), the atomic clocks on the satellites are set to GPS time.

A more detailed description of how to calculate PDOP is given in the section, geometric dilution of precision computation (GDOP). for the C/A code is given by: The standard deviation of the error in estimated receiver position , again for the C/A code is given by: The error diagram to the right shows the inter relationship of indicated receiver position, true receiver position, and the intersection of the four sphere surfaces. The position calculated by a GPS receiver requires the current time, the position of the satellite and the measured delay of the received signal. Assume that the mean value of the three components of and are zero. where are the errors in pseudoranges 1 through 4 respectively.

Many GPS units also show derived information such as direction and speed, calculated from position changes. Three satellites might seem enough to solve for position, since space has three dimensions. As a first step in computing DOP, consider the unit vector from the receiver to satellite i with components , , and where the distance from receiver to the satellite, , is given by: where denote the position of the receiver and denote the position of satellite i.

This can be done in civilian receivers without decrypting the P(Y) signal carried on L2, by tracking the carrier wave instead of the modulated code. Also, the precise time reference is used in many applications including the scientific study of earthquakes and as a time synchronization source for cellular network protocols. GPS has become a mainstay of transportation systems worldwide, providing navigation for aviation, ground, and maritime operations.

If you are not convinced of this, consider how a side view of the intersecting spheres would look. Consider the unit vectors pointing from the receiver to the satellites.

If the almanac information is not in memory, the receiver enters a search mode and cycles through the PRN numbers until a lock is obtained on one of the satellites. Mere possession of the receiver is insufficient; it still needs the tightly controlled daily key. Before it was turned off on May 1, 2000, typical SA errors were 10 meters (32 ft) horizontally and 30 meters (98 ft) vertically.

This is one reason the GPS spacecraft transmit on at least two frequencies, L1 and L2. These three functions are defined below.

Thus since Note: since Substituting for there follows From equation (7), it follows that the variances of indicated receiver position and time are The remaining position and time error variance terms follow in a straightforward manner. GPS includes a (currently disabled) feature called Selective Availability (SA) that adds intentional, time varying errors of up to 100 meters (328 ft) to the publicly available navigation signals. This was intended to deny an enemy the use of civilian GPS receivers for precision weapon guidance. SA errors are actually pseudorandom, generated by a cryptographic algorithm from a classified seed key available only to authorized users (the U.S.

However, this technique is slow, so it is currently limited to specialized surveying equipment. They discovered that, because of the Doppler effect, the frequency of the signal being transmitted by Sputnik was higher as the satellite approached, and lower as it continued away from them.

Assuming the same one percent of bit pulse width accuracy, the high-frequency P(Y) signal results in an accuracy of or about 30 centimeters. Inconsistencies of atmospheric conditions affect the speed of the GPS signals as they pass through the Earth s atmosphere, especially the ionosphere. Data is actually sent at a much lower rate, which limits the accuracy of the signal sent using RTCM.

These x, y, and z components may be components in a North, East, Down coordinate system a South, East, Up coordinate system or other convenient system. Therefore receivers use four or more satellites to solve for the receiver s location and time.

(see Atmospheric Effects in Sources of Errors in GPS ) The effects of the ionosphere generally change slowly, and can be averaged over time. This compares to 3 meters for the C/A code and 0.3 meters for the P code. However, this 2 millimeter accuracy requires measuring the total phase, that is the total number of wave lengths plus the fractional wavelength.

These effects are smallest when the satellite is directly overhead and become greater for satellites nearer the horizon since the path through the atmosphere is longer (see airmass). Turning off antispoof would primarily benefit surveyors and some scientists who need extremely precise positions for experiments such as tracking the motion of a tectonic plate. DGPS services are widely available from both commercial and government sources.

The GPS-UTC offset field can accommodate 255 leap seconds (eight bits) which, given the current rate of change of the Earth s rotation (with one leap second introduced approximately every 18 months), should be sufficient to last until approximately the year 2300. As opposed to the year, month, and day format of the Gregorian calendar, the GPS date is expressed as a week number and a seconds-into-week number. The equation of the sphere surfaces are given by: Another useful form of these equations is in terms of the pseudoranges, which are simply the ranges approximated based on GPS receiver clock s indicated (i.e., uncorrected) time so that .

military s own battlefield use of GPS, so the military made the decision to turn off SA for the duration of the war. In the 1990s, the FAA started pressuring the military to turn off SA permanently. In practice, in view of the hazards and costs this would induce for U.S.

The second word is the HOW or handover word and it contains timing information which enables the receiver to identify the subframe and provides the time the next subframe was sent. Words 3 through 10 of subframe 1 contain data describing the satellite clock and its relationship to GPS time. A more sensitive receiver will potentially acquire the ephemeris data more quickly than a less sensitive receiver, especially in a noisy environment. This process is repeated for each satellite to which the receiver is listening. Before providing a more mathematical description of position calculation, the introductory material on this topics is reviewed.

PDOP is sometimes approximated as being inversely proportional to the tetrahedron volume. Receivers with internal DGPS receivers can outperform those using external RTCM data.

This equation comes from linearizing the equation relating pseudoranges to receiver position, satellite positions, and receiver clock errors as shown in. These effects also reduce the more precise P(Y) code s accuracy.

The method used here is similar to that used in Global Positioning System (preview) by Parkinson and Spiker Consider the position error vector, , defined as the vector from the intersection of the four sphere surfaces corresponding to the pseudoranges to the true position of the receiver. DGPS also corrects for several other important sources of GPS errors, particularly ionospheric delay, so it continues to be widely used even though SA has been turned off.

The receiver knows the receiver clock time of when the beginning of the next subframe was received from detection of the Telemetry Word thereby enabling computation of the transit time and thus the pseudorange. See also Assisted GPS. The satellite s atomic clocks experience noise and clock drift errors.

scientists led by Dr. This notation has been chosen so as to make it clear what the subscripts i, j, and k mean.

This team consists of researchers from the Naval Research Laboratory, the U.S. (In the ideal case of no errors, the GPS receiver would be at a precise intersection of the four surfaces.) If the surfaces of two spheres intersect at more than one point, they intersect in a circle.

It is feasible to put such ephemeris data on the web so it can be loaded into mobile GPS devices. To describe the basic concept of how a GPS receiver works, the errors are at first ignored.

One of the most significant error sources is the GPS receiver s clock. The receiver knows the PRN codes for each satellite and can use this to reconstruct the actual message data.

If one variable is already known, a receiver can determine its position using only three satellites. Another figure, Surface of Sphere Intersecting a Circle (not disk) at Two Points, illustrates the intersection.

The elements in the fourth column are c where c denotes the speed of light. Then all users will be able to perform dual-frequency measurements and directly compute ionospheric delay errors. A second form of precise monitoring is called Carrier-Phase Enhancement (CPGPS).

There are many such systems in place and they are generally named or described based on how the GPS sensor receives the information. However, even a very small clock error multiplied by the very large speed of light—the speed at which satellite signals propagate—results in a large positional error.

To get the standard deviation of receiver position estimate, these range errors must be multiplied by the appropriate dilution of precision terms and then RSS ed with the numerical error. State Department export licenses are required.

GPS time was set to match Coordinated Universal Time (UTC) in 1980, but has since diverged. Navy developed the Timation satellite which proved the ability to place accurate clocks in space, a technology that GPS relies upon.

For example, the relativistic time slowing due to the speed of the satellite of about 1 part in 1010, the gravitational time dilation that makes a satellite run about 5 parts in 1010 faster than an Earth based clock, and the Sagnac effect due to rotation relative to receivers on Earth. This will result in an over determined system with multiple solutons.

If is a function of the three integer arguments, i, j, and k then it is a valid argument for the functions, : , with the values defined as Also if are valid arguments for the three functions and a and b are constants then is a valid argument with values defined as Receiver clock errors can be approximately eliminated by differencing the phases measured from satellite 1 with that from satellite 2 at the same epoch as shown in BETWEEN-SATELLITE DIFFERENCING. The position accuracy is primarily dependent on the satellite position and signal delay. To measure the delay, the receiver compares the bit sequence received from the satellite with an internally generated version.

The ineffectiveness of SA in the face of widely available DGPS was a common argument for turning off SA, and this was finally done by order of President Clinton in 2000. Another restriction on GPS, antispoofing, remains on. Also we define three functions, : which perform differences between receivers, satellites, and time points respectively.

The GPS time scale is defined in an inertial system but observations are processed in an Earth-centered, Earth-fixed (co-rotating) system, a system in which simultaneity is not uniquely defined. According to John Ruley, IFR pilots should have a fallback plan in case of a GPS malfunction . Augmentation methods of improving accuracy rely on external information being integrated into the calculation process.

As the distance increases, the errors at the two sites will not correlate as well, resulting in less precise differential corrections. During the 1990-91 Gulf War, the shortage of military GPS units caused many troops and their families to buy readily available civilian units. For long delay multipath, the receiver itself can recognize the wayward signal and discard it.

The encryption is essentially a safety mechanism: if a signal can be successfully decrypted, it is reasonable to assume it is a real signal being sent by a GPS satellite. However, this may be misleading since they are actually deterministic sequences. If the almanac information has previously been acquired, the receiver picks which satellites to listen for by their PRNs.

Let denote the phase of the carrier of satellite j measured by receiver i at time . This initial value could probably be provided by a position approximation based on the navigation message and the intersection of sphere surfaces.

The first is to not rely on GPS as a sole source. The spacecraft broadcast ionospheric model parameters, but errors remain.

where bold denotes a vector and , >math>\hat{y}</math>, and denote unit vectors along the x, y, and z axes respectively. The subsection on navigation signals discusses details of the message content.

Disaster relief and emergency services depend upon GPS for location and timing capabilities in their life-saving missions. The x, y, and z components of position, and the time sent, are designated as where the subscript i is the satellite number and has the value 1, 2, 3, or 4.

military claimed to destroy six GPS jammers during the Iraq War, including one that was destroyed ironically with a GPS-guided bomb. Some countries allow the use of GPS repeaters to allow for the reception of GPS signals indoors and in obscured locations, however, under EU and UK laws, the use of these is prohibited as the signals can cause interference to other GPS receivers that may receive data from both GPS satellites and the repeater. Due to the potential for both natural and man-made noise, numerous techniques continue to be developed to deal with the interference. Ionospheric delay is a well-defined function of frequency and the total electron content (TEC) along the path, so measuring the arrival time difference between the frequencies determines TEC and thus the precise ionospheric delay at each frequency. Receivers with decryption keys can decode the P(Y)-code transmitted on both L1 and L2.

Because of the very large value of the speed of light, c, the estimated distances from the GPS receiver to the satellites, the pseudoranges, are very sensitive to errors in the GPS receiver clock. The satellite clock errors will be approximately eliminated by this between receiver differencing.

The position calculation subsection does not require an understanding of the other subsections. To determine the current Gregorian date, a GPS receiver must be provided with the approximate date (to within 3,584 days) to correctly translate the GPS date signal.

An example is CDMA digital cellular. This effect both is more localized and changes more quickly than ionospheric effects, and is not frequency dependent.

Finally, the almanac allows a single-frequency receiver to correct for ionospheric error by using a global ionospheric model. In 1967, the U.S.

military, its allies and a few other users, mostly government) with a special military GPS receiver. space-based global navigation satellite system.

This will eliminate the ambiguity associated with the integral number of wave lengths in carrier phase provided this ambiguity does not change with time. It used a constellation of five satellites and could provide a navigational fix approximately once per hour.

The GPS receiver has four unknowns, the three components of GPS receiver position and the clock bias . They may also include a display for providing location and speed information to the user.

In older hardware, lack of an almanac in a new receiver would cause long delays before providing a valid position, because the search for each satellite was a slow process. The difference is that GPS time is not corrected to match the rotation of the Earth, so it does not contain leap seconds or other corrections which are periodically added to UTC.

Some military and expensive survey-grade civilian receivers calculate atmospheric dispersion from the different delays in the L1 and L2 frequencies, and apply a more precise correction. Words 3 through 10 of subframes 4 and 5 contain a new part of the almanac.

(For example, a ship or plane may have known elevation.) Some GPS receivers may use additional clues or assumptions (such as reusing the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer) to give a degraded position when fewer than four satellites are visible (see,). To provide an introductory description of how a GPS receiver works, errors will be ignored in this section. We are here excluding the unrealistic case for GPS purposes of two coincident spheres.

However, the advancement of technology means that today, civilian GPS fixes under a clear view of the sky are on average accurate to about 5 meters (16 ft) horizontally.(see summary table near end of Sources of Errors in GPS ) The term user equivalent range error (UERE) refers to the standard deviation of a component of the error in the distance from receiver to a satellite. Basic equations describing the geometry of the sphere and the fundamental concept that the satellite message travels at the speed of light are used in the subsection.

Each frame contains 5 subframes of length 6 seconds and with 300 bits. This is typically in the form of a RS-232 port at 4,800 bit/s speed.

The ephemeris is updated every 2 hours and is generally valid for 4 hours, with provisions for updates every 6 hours or longer in non-nominal conditions. This paragraph has described the basic concept of GPS while ignoring errors.

Electronics errors are one of several accuracy-degrading effects outlined in the table above. The second purpose is for relating time derived from the GPS (called GPS time) to the international time standard of UTC.

Farmers, surveyors, geologists and countless others perform their work more efficiently, safely, economically, and accurately using the free and open GPS signals. The first satellite navigation system, Transit, used by the United States Navy, was first successfully tested in 1960. Each base station has a GPS timing receiver to synchronize its spreading codes with other base stations to facilitate inter-cell hand off and support hybrid GPS/CDMA positioning of mobiles for emergency calls and other applications.

This is called Differential GPS or DGPS. When taken together, autonomous civilian GPS horizontal position fixes are typically accurate to about 15 meters (50 ft).

Again trilateration clearly shows this mathematically. Richard B.

The GPS design originally called for 24 SVs, eight each in three circular orbital planes, Orbiting at an altitude of approximately 20,200 kilometers (about 12,550 miles or 10,900 nautical miles; orbital radius of approximately 26,600 km (about 16,500 mi or 14,400 NM)), each SV makes two complete orbits each sidereal day, repeating the same ground track each day. This should make it clear to the reader that the surfaces of the two spheres actually do intersect in a circle. The article, trilateration, shows mathematically how the equation for this circle of intersection is determined.

The next problem is how to process the messages when errors are present. Let denote the clock error or bias, the amount by which the receiver s clock is slow. Another method that is used in GPS surveying applications is carrier phase tracking.

The very accurately computed time is effectively hidden by most GPS applications, which use only the location. By comparing the rising and trailing edges of the bit transitions, modern electronics can measure signal offset to within about one percent of a bit pulse width, , or approximately 10 nanoseconds for the C/A code.

The elements of the Q matrix are designated as: The Greek letter is used quite often where we have used d. This correction is also valid for other receivers in the same general location.

This phenomenon is known as dispersion and can be calculated from measurements of delays for two or more frequency bands, allowing delays at other frequencies to be estimated. The Doppler velocity is computed as a function of the frequency offset from the carrier nominal frequency.

GPS week zero started at 00:00:00 UTC (00:00:19 TAI) on January 6 1980, and the week number became zero again for the first time at 23:59:47 UTC on August 21 1999 (00:00:19 TAI on August 22 1999). This process is repeated until correlation is achieved or all 1023 possible cases have been tried.

Without keys, it is still possible to use a codeless technique to compare the P(Y) codes on L1 and L2 to gain much of the same error information. A circle and sphere surface in most cases of practical interest intersect at two points, although it is conceivable that they could intersect in 0 or 1 point.

The period of the carrier frequency times the speed of light gives the wave length, which is about 0.19 meters for the L1 carrier. The capacity to determine relative movement enables a receiver to calculate local velocity and orientation, useful in vessels or observations of the Earth.

This should not be construed to mean that this is the only order which can be used. The citation accompanying the presentation of the trophy honors the GPS Team for the most significant development for safe and efficient navigation and surveillance of air and spacecraft since the introduction of radio navigation 50 years ago. Other satellite navigation systems in use or various states of development include: DCF77 HBG JJY RJH66 Time from NPL TDF WWVB BPM CHU HD2IOA HLA RWM WWV WWVH YVTO GPS Beidou Galileo GLONASS IRNSS OMA OLB5 VNG Y3S Biological · Complex · Complex adaptive · Conceptual · Database management · Dynamical · Economical · Cabane strut · Canopy · Cruciform tail · Fairing · Fabric covering · Flying wires · Former · Fuselage · Interplane strut · Horizontal stabilizer · Jury strut · Leading edge · Longeron · Nacelle · Rear pressure bulkhead · Rib · Spar · Stabilizer · Stressed skin · Strut · Tailplane · Trailing edge · T-tail · Twin tail · Vertical stabilizer · V-tail · Wing root · Wing tip Aileron · Airbrake · Artificial feel · Autopilot · Canard · Centre stick · Deceleron · Elevator · Elevon · Electro-hydrostatic actuator · Flaperon · Flight control modes · Gust lock · Rudder · Servo tab · Side-stick · Spoiler · Spoileron · Stabilator · Stick pusher · Stick shaker · Trim tab · Yaw damper · Wing warping · Yoke Blown flap · Dog-tooth · Flap · Gouge flap · Gurney flap · Krueger flaps · Leading edge cuff · LEX · Slats · Slot · Stall strips · Strake · Vortex generator · Wing fence · Winglet ACAS · Air data computer · Airspeed indicator · Altimeter · Annunciator panel · Attitude indicator · Compass · Course Deviation Indicator · EFIS · EICAS · Flight data recorder · Flight management system · Glass cockpit · GPS · Heading indicator · Horizontal situation indicator · INAS · TCAS · Transponder · Turn and bank indicator · Pitot-static system · Radar altimeter · Vertical Speed Indicator · Yaw string Autothrottle · Drop tank · FADEC · Fuel tank · Inlet cone · Intake ramp · NACA cowling · Self-sealing fuel tank · Throttle · Thrust lever · Thrust reversal · Townend ring · Wet wing Autobrake · Conventional landing gear · Arrestor hook · Drogue parachute · Landing gear extender · Tricycle gear · Tundra tire · Undercarriage Ejection seat · Escape crew capsule Aircraft lavatory · Auxiliary power unit · Bleed air system · Emergency oxygen system · Environmental Control System · Hydraulic system · Ice protection system · Landing lights · Navigation light · Ram air turbine .

The week number is transmitted as a ten-bit field in the C/A and P(Y) navigation messages, and so it becomes zero again every 1,024 weeks (19.6 years). It provides reliable positioning, navigation, and timing services to worldwide users on a continuous basis in all weather, day and night, anywhere on or near the Earth. GPS is made up of three parts: between 24 and 32 satellites in Medium Earth Orbit, four control and monitoring stations on Earth, and the actual navigation devices users own.

is computed by taking the square root of the sum of the squares of the individual component standard deviations. PDOP is computed as a function of receiver and satellite positions. Capabilities for access by third party software developers to these features were slower in coming, with Nextel opening up those APIs upon launch to any developer, Sprint following in 2006, and Verizon soon thereafter. Two GPS developers received the National Academy of Engineering Charles Stark Draper Prize for 2003: One GPS developer, Roger L.

The phase difference error in the normal GPS amounts to between 2 and 3 meters (6 to 10 ft) of ambiguity. The receiver can then acquire the almanac and determine the satellites it should listen for.

Indeed other orders of taking differences are equally valid. The satellite carrier total phase can be measured with ambiguity as to the number of cycles as described in CARRIER PHASE MEASUREMENT and CARRIER BEAT PHASE. The first word is the telemetry word which indicates the beginning of a subframe and is used by the receiver to synch with the navigation message.

This is done by assigning each satellite a unique binary sequence sequence known as a Gold code, and the signals are decoded, after demodulation, using modulo 2 addition of the Gold codes corresponding to satellites n1 through nk, where k is the number of channels in the GPS receiver and n1 through nk are the PRN identifiers of the satellites. Thus we know that the indicated position of the GPS receiver is at or near the intersection of the surfaces of four spheres.

Let denote the distance from the valid estimate of GPS receiver position to the fourth satellite and let denote the pseudorange of the fourth satellite. The standard deviations, , for the coarse/acquisition and precise codes are also shown in the table.

Because of this, carrier frequency tracking along with PRN code tracking are used to determine when the received satellite s PRN code begins.) are used to estimate adjustment required. If a fast time to first fix (TTFF) is needed, it is possible to upload a valid ephemeris to a receiver, and in addition to setting the time, a position fix can be obtained in under ten seconds.

This triple difference is: Triple difference results can be used to estimate unknown variables. Several systems send this information over radio or other links to allow L1-only receivers to make ionospheric corrections.

Assuming the message traveled at the speed of light, c, the distance traveled, can be computed as . A satellite s position and distance from the receiver define a spherical surface, centered on the satellite. Demodulating the carrier and decoding to separate the signals from the satellites is described.

Air Force, the Aerospace Corporation, Rockwell International Corporation, and IBM Federal Systems Company. FCC mandates for handset positioning in emergency calls.

The first is to assist in the acquisition of satellites at power-up by allowing the receiver to generate a list of visible satellites based on stored position and time, while an ephemeris from each satellite is needed to compute position fixes using that satellite. This difference is designated as Double differencing can be performed by taking the differences of the between satellite difference observed by receiver 1 with that observed by receiver 2.

Multiplying both sides by there results Transposing both sides: Post multiplying the matrices on both sides of equation (2) by the corresponding matrices in equation (3), there results Taking the expected value of both sides and taking the non-random matrices outside the expectation operator, E, there results: Assuming the pseudorange errors are uncorrelated and have the same variance, the covariance matrix on the right side can be expressed as a scalar times the identity matrix. Let denote the time error, the true time minus the receiver indicated time.

Knowing the distance from GPS receiver to a satellite and the position of a satellite implies that the GPS receiver is on the surface of a sphere centered at the position of a satellite. We are here excluding the unrealistic case for GPS purposes of three colinear (lying on same straight line) sphere centers.

These parameters are clearly chosen to prevent use of a receiver in a ballistic missile. and foreign shipping, it is unlikely to be reintroduced, and various government agencies, including the FAA, have stated that it is not intended to be reintroduced. One interesting side effect of the Selective Availability hardware is the capability to add corrections to the outgoing signal of the GPS cesium and rubidium atomic clocks to an accuracy of approximately 2 × 10−13 This represented a significant improvement over the raw accuracy of the clocks. On 19 September 2007, the United States Department of Defense announced that future GPS III satellites will not be capable of implementing SA, A number of sources of error exist due to relativistic effects.

The surfaces of two spheres if they intersect in more than one point intersect in a circle. Because SA affects every GPS receiver in a given area almost equally, a fixed station with an accurately known position can measure the SA error values and transmit them to the local GPS receivers so they may correct their position fixes.

RAIM features do not protect against spoofing, since RAIM only checks the signals from a navigational perspective. User equivalent range errors (UERE) are shown in the table. The accuracy of the corrections depends on the distance between the user and the DGPS receiver.

The navigation message contains corrections for these errors and estimates of the accuracy of the atomic clock. The lack of corrections means that GPS time remains at a constant offset with International Atomic Time (TAI)(TAI - GPS = 19 seconds).

Received frequency offset from the frequency generated by the receiver provides an estimate of phase rate error. Another figure, Surface of Sphere Intersecting a Circle (not disk) at Two Points, is shown below to aid in visualizing this intersection.

However, the distance from the valid estimate of GPS receiver position to the surface of the sphere corresponding to the fourth satellite can be used to compute a clock correction. Triple difference results for three independent time pairs quite possibly will be sufficient to solve for the three components of position of receiver 2.

In one well documented case, the entire harbor of Moss Landing, California was unable to receive GPS signals due to unintentional jamming caused by malfunctioning TV antenna preamplifiers. The U.S. Using messages received from a minimum of four visible satellites, a GPS receiver is able to determine the times sent and then the satellite positions corresponding to these times sent.

The solution for this dilemma is based on the way sphere surfaces intersect in the GPS problem. It is likely that the surfaces of the three spheres intersect, since the circle of intersection of the first two spheres is normally quite large, and thus the third sphere surface is likely to intersect this large circle. The correct position of the GPS receiver is the one that is closest to the fourth sphere.

Carrier frequencies for the messages are stated. The Doppler velocity is the velocity component along the line of sight of the receiver relative to the satellite. As the receiver continues to read successive PRN sequences, it will encounter a sudden change in the phase of the 1023 bit received PRN signal.

This double difference is: Triple differencing can be performed by taking the difference of double differencing performed at time with that performed at time . If all 1023 cases have been tried without achieving correlation, the frequency oscillator is offset to the next value and the process is repeated. Since the carrier frequency received can vary due to Doppler shift, the points where received PRN sequences begin may not differ from O by an exact integral number of milliseconds.

This method has many applications in the field of surveying. We now describe a method which could potentially be used to estimate the position of receiver 2 given the position of receiver 1 using triple differencing followed by numerical root finding, and a mathematical technique called least squares. To address this concern the modernized GPS navigation message uses a 13-bit field, which only repeats every 8,192 weeks (157 years), thus lasting until the year 2137 (157 years after GPS week zero). Utilizing the navigation message to measure pseudorange has been discussed.

Periodic corrections are performed on the on-board clocks to correct relativistic effects and keep them synchronized with ground clocks. The GPS navigation message includes the difference between GPS time and UTC, which as of 2009 is 15 seconds due to the leap second added to UTC December 31 2008. For example if the position of receiver 1 is known but the position of receiver 2 unknown, it may be possible to estimate the position of receiver 2 using numerical root finding and least squares.

Using the values of and determined by this linear equation solution, is evaluated using: Then set in equations 2 through 6, plug the terms from equations 7 into equations 2, set in equations 7, and reevaluate the residuals in equations 2. The resulting signal run time correction has opposite algebraic signs for satellites in the Eastern and Western celestial hemispheres.

Knowing the indicated time the message was received , the GPS receiver can compute the transit time of the message as . This procedure using three time pairs and a fairly good initial value followed by iteration will result in one observed triple difference result for receiver 2 position.

However, it is often better than no correction, since ionospheric error is the largest error source for a single-frequency GPS receiver. This position is then displayed, perhaps with a moving map display or latitude and longitude; elevation information may be included.

Knowing the indicated time the message was received , the GPS receiver can compute the transit time of the message as . This view would look exactly the same as the figure because of the symmetry of the spheres.

There is also a numerical error with an estimated value, , of about 1 meter. The two intersections are marked with dots.

government believes that such jammers were used occasionally during the 2001 war in Afghanistan and the U.S. There can be a delay of up to 30 seconds before the first estimate of position because of the need to read the ephemeris data before computing the intersections of sphere surfaces. After a subframe has been read and interpreted, the time the next subframe was sent can be calculated through the use of the clock correction data and the HOW.

The error, which this corrects, arises because the pulse transition of the PRN is not instantaneous, and thus the correlation (satellite-receiver sequence matching) operation is imperfect. The L1 carrier is modulated by both the C/A and P codes, while the L2 carrier is only modulated by the P code.

The latter include WAAS and the U.S. New GPS units may not show the correct UTC time until after receiving the UTC offset message.

Transforming to the right hand side of the equation there results, A solution will have been found when is zero or sufficiently close to zero for . In order to linearize equation 2, the partial derivatives are computed as: where Linearizing the right hand side of equation 2 about the approximate solution, there results where is the residual due to linearization which is in addition to the residual, , due to an approximate solution. In order to drive closer to zero choose the values such that That is choose the values such that the residual in equation 2 changes by approximately . Let Substituting and transposing to the left hand side of the equation, there results Equations 6 provide a set of four linear equations in four unknowns, the delta terms. The distance between these two points is the diameter of the circle of intersection.

For space vehicles, the intersection farthest from Earth may be the correct one. The correct position for the GPS receiver is also the intersection closest to the surface of the sphere corresponding to the fourth satellite. The method of calculating position for the case of no errors has been explained. Since GPS signals propagate at the speed of light, this represents an error of about 3 meters. This component of position accuracy can be improved by a factor of 10 using the higher-chiprate P(Y) signal.

They realized that since they knew their exact location on the globe, they could pinpoint where the satellite was along its orbit by measuring the Doppler distortion (see Transit (satellite)). After Korean Air Lines Flight 007 was shot down in 1983 after straying into the USSR s prohibited airspace, The first satellite was launched in 1989 and the 24th and last satellite was launched in 1994. Initially the highest quality signal was reserved for military use, and the signal available for civilian use intentionally degraded ( Selective Availability , SA). This encrypts the P-code so that it cannot be mimicked by an enemy transmitter sending false information.

The corrections are not as accurate as augmentation systems like WAAS or dual-frequency receivers. This indicates the beginning of a data bit of the navigation message (see section 1.4.2.5 of and section 2.5.4 of Essentials of Satellite Navigation Compendium ).

Formulate the matrix, Q, as This computation is in accordance with Chapter 11 of The global positioning system by Parkinson and Spilker where the weighting matrix, P, has been set to the identity matrix. Each satellite continually transmits messages which include The receiver measures the transit time of each message and computes the distance to each satellite.

So to change the orbit of a satellite, the satellite must be marked unhealthy , so receivers will not use it in their calculation. This is done by resolving the number of cycles in which the signal is transmitted and received by the receiver.

Selective Availability was ended in 2000, improving the precision of civilian GPS from about 100m to about 20m. For a more complete list, see list of GPS satellite launches A GPS receiver calculates its position by precisely timing the signals sent by the GPS satellites high above the Earth. To address shorter delay multipath from the signal reflecting off the ground, specialized antennas (e.g., a choke ring antenna) may be used to reduce the signal power as received by the antenna.

Originally limited to four or five, this has progressively increased over the years so that, as of 2007 GPS receivers may include an input for differential corrections, using the RTCM SC-104 format. A few specialized GPS applications do however use the time; these include time transfer, traffic signal timing, and synchronization of cell phone base stations. Although four satellites are required for normal operation, fewer apply in special cases.

These Gold codes are quite often referred to as pseudo random noise since they contain no data and are said to look like random sequences. The subsection on multidimensional Newton-Raphson may be of interest only to those readers who want a more detailed understanding on how an algorithm might be written and is unnecessary for the reader who is uninterested in this amount of detail. Each GPS satellite continuously broadcasts a Navigation Message at 50 bit/s giving the time-of-week, GPS week number and satellite health information (all transmitted in the first part of the message), an ephemeris (transmitted in the second part of the message) and an almanac (later part of the message).

This has caused problems with some amateur radio balloon launches as they regularly reach 100,000 feet (30 km). GPS tours are also an example of civilian use. Connecting the tails of these unit vectors forms a tetrahedron.

It is very unlikely that the surface of the sphere corresponding to the fourth satellite will intersect either of the two points of intersection of the first three, since any clock error could cause it to miss intersecting a point. This was very helpful during development, since even with just four satellites, correct alignment means all four are visible from one spot for a few hours each day.

This would save the FAA millions of dollars every year in maintenance of their own radio navigation systems. Advances in hardware have made the acquisition process much faster, so not having an almanac is no longer an issue.

PDOP, TDOP and GDOP are given by in agreement with Section 1.4.9 of PRINCIPLES OF SATELLITE POSITIONING . The horizontal dilution of precision, , and the vertical dilution of precision, , are both dependent on the coordinate system used. Receivers can interface with other devices using methods including a serial connection, USB or Bluetooth. Aspects of navigation are discussed in this section.

A variety of techniques, most notably narrow correlator spacing, have been developed to mitigate multipath errors. The CPGPS approach utilizes the L1 carrier wave, which has a period of which is about one-thousandth of the C/A Gold code bit period of , to act as an additional clock signal and resolve the uncertainty.

It allows a direct comparison of the L1 and L2 signals using the coded signal instead of the carrier wave. Formulate the matrix A as: The first three elements of each row of A are the components of a unit vector from the receiver to the indicated satellite.

As of 2006, even low-cost units commonly include Wide Area Augmentation System (WAAS) receivers. Many GPS receivers can relay position data to a PC or other device using the NMEA 0183 protocol, or the newer and less widely used NMEA 2000. references to these protocols have been compiled from public records, allowing open source tools like gpsd to read the protocol without violating intellectual property laws.

Government controls the export of some civilian receivers. Words 3 through 10 of subframes 2 and 3, contain the ephemeris data, giving the satellite s own precise orbit.

They are in a form for solution. Finally, GPS enables researchers to explore the Earth environment including the atmosphere, ionosphere and gravity field.

These traits make precise measurement and compensation of humidity errors more difficult than ionospheric effects. Changes in receiver altitude also change the amount of delay, due to the signal passing through less of the atmosphere at higher elevations. Both the C/A and P(Y) codes impart the precise time-of-day to the user. Since all of the satellite signals are modulated onto the same L1 carrier frequency, there is a need to separate the signals after demodulation.

CPGPS working to within 1% of perfect transition reduces this error to 3 centimeters (1 inch) of ambiguity. This suggests that an extremely accurate and expensive clock is required for the GPS receiver to work.

The standard deviation of the error in receiver position, , is computed by multiplying PDOP (Position Dilution Of Precision) by , the standard deviation of the user equivalent range errors. Short delay reflections are harder to filter out because they interfere with the true signal, causing effects almost indistinguishable from routine fluctuations in atmospheric delay. Multipath effects are much less severe in moving vehicles.

A figure, Two Sphere Surfaces Intersecting in a Circle, is shown below. The intersection of a third spherical surface with the first two will be its intersection with that circle; in most cases of practical interest, this means they intersect at two points. Each subframe contains 10 words of 30 bits with length 0.6 seconds each. Words 1 and 2 of every subframe have the same type of data.