GPS Satellite Signals
The SVs transmit two microwave carrier signals. The L1 frequency (1575.42 MHz) carries the navigation message and the SPS code signals. The L2 frequency (1227.60 MHz) is used to measure the ionospheric delay by PPS equipped receivers.
Three binary codes shift the L1 and/or L2 carrier phase.
- The C/A Code (Coarse Acquisition) modulates the L1 carrier phase. The C/A code is a repeating 1 MHz Pseudo Random Noise (PRN) Code. This noise-like code modulates the L1 carrier signal, "spreading" the spectrum over a 1 MHz bandwidth. The C/A code repeats every 1023 bits (one millisecond). There is a different C/A code PRN for each SV. GPS satellites are often identified by their PRN number, the unique identifier for each pseudo-random-noise code. The C/A code that modulates the L1 carrier is the basis for the civil SPS.
- The P-Code (Precise) modulates both the L1 and L2 carrier phases. The P-Code is a very long (seven days) 10 MHz PRN code. In the Anti-Spoofing (AS) mode of operation, the P-Code is encrypted into the Y-Code. The encrypted Y-Code requires a classified AS Module for each receiver channel and is for use only by authorized users with cryptographic keys. The P (Y)-Code is the basis for the PPS.
- The Navigation Message also modulates the L1-C/A code signal. The Navigation Message is a 50 Hz signal consisting of data bits that describe the GPS satellite orbits, clock corrections, and other system parameters
- The GPS Navigation Message consists of time-tagged data bits marking the time of transmission of each subframe at the time they are transmitted by the SV. A data bit frame consists of 1500 bits divided into five 300-bit subframes. A data frame is transmitted every thirty seconds. Three six-second subframes contain orbital and clock data. SV Clock corrections are sent in subframe one and precise SV orbital data sets (ephemeris data parameters) for the transmitting SV are sent in subframes two and three. Subframes four and five are used to transmit different pages of system data. An entire set of twenty-five frames (125 subframes) makes up the complete Navigation Message that is sent over a 12.5 minute period.
- Data frames (1500 bits) are sent every thirty seconds. Each frame consists of five subframes.
- Data bit subframes (300 bits transmitted over six seconds) contain parity bits that allow for data checking and limited error correction.
Position, and Time from GPS
- Code Phase Tracking (Navigation)
- The GPS receiver produces replicas of the C/A and/or P (Y)-Code. Each PRN code is a noise-like, but pre-determined, unique series of bits.
- The receiver produces the C/A code sequence for a specific SV with some form of a C/A code generator. Modern receivers usually store a complete set of precomputed C/A code chips in
- memory, but a hardware, shift register, implementation can also be used.
- Pseudo-Range Navigation
The position of the receiver is where the pseudo-ranges from a set of SVs intersect.
- Position is determined from multiple pseudo-range measurements at a single measurement epoch. The pseudo range measurements are used together with SV position estimates based on the precise orbital elements (the ephemeris data) sent by each SV. This orbital data allows the receiver to compute the SV positions in three dimensions at the instant that they sent their respective signals.
- Four satellites (normal navigation) can be used to determine three position dimensions and time. Position dimensions are computed by the receiver in Earth-Centered, Earth-Fixed X, Y, Z (ECEF XYZ) coordinates
- Receiver Position, Velocity, and Time
- Position in XYZ is converted within the receiver to geodetic latitude, longitude and height above the ellipsoid.
- Carrier Phase Tracking (Surveying)
Carrier-phase tracking of GPS signals has resulted in a revolution in land surveying. A line of sight along the ground is no longer necessary for precise positioning. Positions can be measured up to 30 km from reference point without intermediate points. This use of GPS requires specially equipped carrier tracking receivers.
The L1 and/or L2 carrier signals are used in carrier phase surveying. L1 carrier cycles have a wavelength of 19 centimeters. If tracked and measured these carrier signals can provide ranging measurements with relative accuracies of millimeters under special circumstances.
Tracking carrier phase signals provides no time of transmission information. The carrier signals, while modulated with time tagged binary codes, carry no time-tags that distinguish one cycle from another. The measurements used in carrier phase tracking are differences in carrier phase cycles and fractions of cycles over time. At least two receivers track carrier signals at the same time. Ionospheric delay differences at the two receivers must be small enough to insure that carrier phase cycles are properly accounted for. This usually requires that the two receivers be within about 30 km of each other.
Carrier phase is tracked at both receivers and the changes in tracked phase are recorded over time in both receivers.
- All carrier-phase tracking is differential, requiring both a reference and remote receiver tracking carrier phases at the same time.
- Unless the reference and remote receivers use L1-L2 differences to measure the ionospheric delay, they must be close enough to insure that the ionospheric delay difference is less than a carrier wavelength.
- Using L1-L2 ionospheric measurements and long measurement averaging periods, relative positions of fixed sites can be determined over baselines of hundreds of kilometers.
- Phase difference changes in the two receivers are reduced using software to differences in three position dimensions between the reference station and the remote receiver. High accuracy range difference measurements with sub-centimeter accuracy are possible. Problems result from the difficulty of tracking carrier signals in noise or while the receiver moves.
Phase difference changes in the two receivers are reduced using software to differences in three position dimensions between the reference station and the remote receiver. High accuracy range difference measurements with sub-centimeter accuracy are possible. Problems result from the difficulty of tracking carrier signals in noise or while the receiver moves.Two receivers and one SV over time results in single differenes.
GPS Error Sources
GPS errors are a combination of noise, bias, blunders.
- Noise errors are the combined effect of PRN code noise (around 1 meter) and noise within the receiver noise (around 1 meter).
Bias errors result from Selective Availability and other factors
- Selective Availability (SA)
- SA is the intentional degradation of the SPS signals by a time varying bias. SA is controlled by the DOD to limit accuracy for non-U. S. military and government users. The potential accuracy of the C/A code of around 30 meters is reduced to 100 meters (two standard deviations).
- The SA bias on each satellite signal is different, and so the resulting position solution is a function of the combined SA bias from each SV used in the navigation solution. Because SA is a changing bias with low frequency terms in excess of a few hours, position solutions or individual SV pseudo-ranges cannot be effectively averaged over periods shorter than a few hours. Differential corrections must be updated at a rate less than the correlation time of SA (and other bias errors).
- Other Bias Error sources;
- SV clock errors uncorrected by Control Segment can result in one meter errors.
- Ephemeris data errors: 1 meter
- Tropospheric delays: 1 meter. The troposphere is the lower part (ground level to from 8 to 13 km) of the atmosphere that experiences the changes in temperature, pressure, and humidity associated with weather changes. Complex models of tropospheric delay require estimates or measurements of these parameters.
- Unmodeled ionosphere delays: 10 meters. The ionosphere is the layer of the atmosphere from 50 to 500 km that consists of ionized air. The transmitted model can only remove about half of the possible 70 ns of delay leaving a ten meter un-modeled residual.
- Multipath: 0.5 meters. Multipath is caused by reflected signals from surfaces near the receiver that can either interfere with or be mistaken for the signal that follows the straight line path from the satellite. Multipath is difficult to detect and sometime hard to avoid.
- Selective Availability (SA)
Blunders can result in errors of hundred of kilometers.
- Control segment mistakes due to computer or human error can cause errors from one meter to hundreds of kilometers.
- User mistakes, including incorrect geodetic datum selection, can cause errors from 1 to hundreds of meters.
- Receiver errors from software or hardware failures can cause blunder errors of any size.
Noise and bias errors combine, resulting in typical ranging errors of around fifteen meters for each satellite used in the position solution
Differential GPS (DGPS) Techniques
The idea behind all differential positioning is to correct bias errors at one location with measured bias errors at a known position. A reference receiver, or base station, computes corrections for each satellite signal.
Because individual pseudo-ranges must be corrected prior to the formation of a navigation solution, DGPS implementations require software in the reference receiver that can track all SVs in view and form individual pseudo-range corrections for each SV. These corrections are passed to the remote, or rover, receiver which must be capable of applying these individual pseudo-range corrections to each SV used in the navigation solution. Applying a simple position correction from the reference receiver to the remote receiver has limited effect at useful ranges because both receivers would have to be using the same set of SVs in their navigation solutions and have identical GDOP terms (not possible at different locations) to be identically affected by bias errors.
Differential Code GPS (Navigation)
- Differential corrections may be used in real-time or later, with post-processing techniques.
- Real-time corrections can be transmitted by radio link. The U. S. Coast Guard maintains a network of differential monitors and transmits DGPS corrections over radiobeacons covering much of the U. S. coastline. DGPS corrections are often transmitted in a standard format specified by the Radio Technical Commission Marine (RTCM).
- Corrections can be recorded for post processing. Many public and private agencies record DGPS corrections for distribution by electronic means.
- Private DGPS services use leased FM sub-carrier broadcasts, satellite links, or private radio-beacons for real-time applications.
- To remove Selective Availability (and other bias errors), differential corrections should be computed at the reference station and applied at the remote receiver at an update rate that is less than the correlation time of SA. Suggested DGPS update rates are usually less than twenty seconds.
- DGPS removes common-mode errors, those errors common to both the reference and remote receivers (not multipath or receiver noise). Errors are more often common when receivers are close together (less than 100 km). Differential position accuracies of 1-10 meters are possible with DGPS based on C/A code SPS signals
- Differential corrections may be used in real-time or later, with post-processing techniques.
GPS Techniques and Project Costs
Receiver costs vary depending on capabilities. Small civil SPS receivers can be purchased for under $200, some can accept differential corrections. Receivers that can store files for post-processing with base station files cost more ($2000-5000). Receivers that can act as DGPS reference receivers (computing and providing correction data) and carrier phase tracking receivers (and two are often required) can cost many thousands of dollars ($5,000 to $40,000). Military PPS receivers may cost more or be difficult to obtain.
Other costs include the cost of multiple receivers when needed, post-processing software, and the cost of specially trained personnel.
Project tasks can often be categorized by required accuracies which will determine equipment cost.
- Low-cost, single-receiver SPS projects (100 meter accuracy)
- Medium-cost, differential SPS code Positioning (1-10 meter accuracy)
- High-cost, single-receiver PPS projects (20 meter accuracy)
- High-cost, differential carrier phase surveys (1 mm to 1 cm accuracy)
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