Differencing Modes and Their Error Characteristics

Error Source

Ionosphere Troposphere Satellite clock Receiver clock Broadcast ephemeris Ambiguity term

Noise level w.r.t. one-way observable

Single Difference

Reduced, depending on the baseline length Reduced, depending on the baseline length Eliminated Present

Reduced, depending on the baseline length Present

Increased by double difference

Reduced, depending on the baseline length Reduced, depending on the baseline length Eliminated Eliminated

Reduced, depending on the baseline length Present

Increased by 2

stochastic model describing the accuracy of the measurements and its statistical properties. A fundamental part of the stochastic model is a covariance matrix of observations, Z. The primary least-squares formula representing a general matrix form of a solution of a system of GPS observation equation is shown in Equation (9.4). Note that Equation (9.1) through Equation (9.3) (and in general, any GPS observation equation) are nonlinear; thus, they are linearized before processing through Equation (9.4):

where A is a design matrix containing the partial derivatives of the observable with respect to the unknown parameters, and y is the vector of observations minus "calculated observation" which is computed based on the approximated values of the parameters. For more details on the least-squares solution, see, for example, Strang and Borre (1997).

9.7.2 DGPS Services: An Overview

As explained earlier, the GPS error sources are spatially and temporally correlated for short to medium base-user separation. Thus, if the reference station and satellite coordinates are known (satellite location is known from broadcast ephemeris), the errors in the GPS measurements can be estimated at specified time intervals and made available to the nearby users through a wireless communication as differential corrections. These corrections can be used to remove the errors from the observables collected at the user's (unknown) location (Yunck et al., 1996). This mode of positioning uses DGPS services to mitigate the effects of the measurement errors at the user's location, leading to the increased positioning accuracy in real time. DGPS services are commonly provided by the government, industry, and professional organizations, and enable the users to use only one GPS receiver collecting pseudorange data, while still achieving superior accuracy as compared to the point-positioning mode. Naturally, in order to use a DGPS service, the user must be equipped with additional hardware capable of receiving and processing the differential corrections.

DGPS services normally involve some type of wireless transmission system. They may employ VHF or UHF systems for short ranges, low-frequency transmitters for medium ranges (beacons), or L-band or C-band geostationary satellites for coverage of entire continents, which is called Wide Area DGPS (WADGPS) or Global Satellite Based Augmentation System (GSBAS). WADGPS involves multiple GPS base stations with precisely known locations that track all GPS satellites in view. These data are sent to the master control station (see Figure 9.12) that estimates the errors in the GPS pseudoranges and forms a satellite uplink message that is transmitted to a geo-stationary satellite. This satellite, in turn, broadcasts the information to all users with specialized GPS receivers; the average correction latency is about 5 sec (

FIGURE 9.12 The Wide Area Augmentation System.

Real_Time_Aspects/TUAM1_Muellerschoen_1.pdf). The satellite uplink message contains GPS differential corrections and GPS satellite health status data. The positioning accuracy of WADGPS ranges from submeter to a few meters, depending on the provider, coverage, number of stations used, error modeling technique, and so forth. DGPS services routinely support the following applications: land survey, offshore positioning, precision agriculture, aerial photogrammetry and LiDAR (light detection and ranging), GIS and asset mapping, machine control, aircraft navigation, and intelligent vehicle highway system (IVHS).

The fundamental concept of WADGPS is the categorization of error sources in the GPS observables. By constructing a model for each error source (e.g., satellite clock, satellite ephemeris, ionospheric delay, and local errors, such as tropospheric delay, multipath, receiver noise, and hardware bias), the system creates a vector correction. This is the distinction between wide area and local area differential corrections. Local area augmentation systems transmit a scalar correction from the reference station to the user for each pseudorange measurement. In contrast, wide area systems transmit the error models to the user, which are then recombined to form a correction for each pseudorange measurement. The benefit of the vector correction is its improved ability to capture the spatial decorrelation of the error sources ( DGpS Services: examples

GSBAS, such as OmniSTAR™ ( and StarFire™ ( starfire/), are examples of commercial DGPS suppliers, providing worldwide coverage at the submeter to decimeter-level accuracy. For example, the StarFire™ solution represents an advance from the ground-based augmentation systems because it considers each of the GPS satellite signal error sources independently, instead of measuring a total (combined) error or atmospheric error only in the GPS pseudoranges. Examples of government-supported DGPS services include Federal Aviation Administration (FAA)-supported satellite-based Wide Area Augmentation System (WAAS), ground-based DGPS services, referred to as Local Area DGPS (LADGPS), such as U.S. Coast Guard and Canadian Coast Guard services, or FAA-supported Local Area Augmentation System (LAAS). An example of Internet-based WADGPS is the Global Differential GPS (IGDG) provided by NASA JPL, based on the NASA Global GPS Network (GGN) consisting of approximately sixty sites ( IGDG is designed for dual-frequency users and offers 10 cm horizontal and 20 cm vertical real-time positioning accuracy.

LAAS is installed at individual airports and is effective over just a short range, with accuracy of 1 m or less in all dimensions. The ground equipment includes four reference receivers, a LAAS ground facility, and a VHF data broadcast transmitter. This ground equipment is complemented by LAAS avionics installed on the aircraft. The GPS Reference Receivers and LAAS Ground Facility (or LGF) work together to measure errors in GPS-provided position. LAAS correction message is then sent to a VHF data broadcast (VDB) transmitter. The VDB broadcasts the LAAS signal throughout the LAAS coverage area to avionics in LAAS-equipped aircraft. The LAAS equipment in the aircraft uses the corrections provided on position, velocity, and time to guide the aircraft safely to the runway ( techops/navservices/nsss/Lass).

WAAS consists of a network of twenty-five ground reference stations and a number of geo-sta-tionary (Inmarsat) satellites broadcasting a signal in the GPS band (Figure 9.12), also providing additional ranging distances that are included in the user positioning solution. The WAAS signals contain information including differential corrections and GPS satellite health status. WAAS has been running 24 hours a day, 7 days a week since early 2000, providing high-integrity navigation signals for nonaviation users such as boaters, precision agriculture, crop dusters, surveyors, vehicle dispatchers and location services, cell phone 911 emergency services, hikers, and other personal recreation uses within the conterminous United States. WAAS was officially commissioned by the FAA for public aviation use on July 10, 2003. The published specifications of WAAS call for 7.6 m in the vertical direction, which corresponds to better than 5 m horizontal accuracy 95 percent of the time (for a single-frequency user receiver), but accuracies around 2 m horizontal RMS have already been demonstrated (;; Lachapelle et al., 2002). Enhanced, dual-frequency WAAS significantly increases the accuracy to approximately 30 to 70 cm in real time.

The GPS and WAAS signals are sent over the same frequency band, with the 50 bps (bits per second) data rate from the normal GPS satellites for information like ephemeris and almanacs, and 500 bps of the raw signal data rate from the WAAS satellite. The increased data rate for WAAS reduces the reliability of the WAAS data transmissions (increased bandwidth reduces SNR). The GPS signals are also slightly stronger than the WAAS signals from the geo-stationary satellites (

NAVCEN ( operates the U.S. Coast Guard Maritime Differential GPS (DGPS) Service, consisting of two control centers and over sixty remote broadcast sites, and the developing Nationwide DGPS Service (NDGPS). The Service broadcasts correction signals on marine radio beacon frequencies to improve the accuracy of and integrity to GPS-derived positions. The U.S. Coast Guard DGPS Service guarantees 10 m accuracy, while typical positional error of 1 to 3 m is achieved. October 2007 coverage is presented in Figure 9.13. DGPS Message Format

DGPS receivers support the major international standards for GPS and DGPS (RINEX, RTCM, and NMEA). RINEX (i.e., the Receiver Independent Exchange Format) is an ASCII format, established for an easy exchange of the GPS data collected by different GPS receivers. The format has been optimized for minimum space requirements independent from the number of different observation types of a specific receiver. Three primary types of RINEX files exist: observation data file, navigation message file, and meteorological data file ( html#rinex:_the_receiver_independent_exchange_format_version_2.10).

The most widely used international standards for DGPS message format were developed by the Radio Technical Commission for Maritime Services (RTCM), a committee that governs standards for passing data between different equipment used in the Marine Electronics industry. The RTCM Special Committee No. 104 established "Recommended Standards for Differential Navstar GPS Service," dated January 3, 1994, referred to as RTCM SC104, which is a standard format for sending differential"/>
FIGURE 9.13 U.S. differential Global Positioning System (DGPS) coverage. (Courtesy of DGPS System Management Branch, USCG Navigation Center;

correction data to a GPS receiver. The actual format is rather complex and lengthy, but it generally contains the following information: (1) the time of the measurement at the reference station, (2) observed range errors (corrections) for every satellite in view at that reference station, and (3) the range error rate for every satellite in view. RTCM SC104 version 2.0 (RTCM-2.0) format essentially deals with DGPS (code-only) corrections, and RTCM-2.1 incorporates several enhancements, especially for PDGPS (carrier phase) corrections (

The standard message types within RTCM-2.1 are message types 3, 5, 6, 7, 9, 15, and 16. A type 3 message contains information on the identity and surveyed position of the active reference DGPS station. Message type 5 notifies the user equipment suite that a satellite deemed unhealthy by its current navigation message is usable for DGPS navigation. The type 7 message provides information of its broadcasting DGPS station and the other two or three adjacent DGPS stations. The type 6 message is a filler message used only when the reference station has no other message to broadcast. The type 9 message has been selected for broadcasting pseudorange corrections. Two methods of transmitting the type 9 message are possible. The first method of broadcasting GPS pseudorange corrections is based upon "Three-Satellite Type 9 Messages," denoted as "type 9-3" messages. In this method, corrections for all satellites are assigned to either three satellite type 9 messages or to a remainder message of either one or two satellites. The transmission rate could be at either 100 or 200 bps. The second method of broadcasting pseudorange corrections is to broadcast individual type 9 messages for each satellite at a transmission rate of 50 bps. This message is referred to as the "Single Satellite Type 9 Message," denoted as the type 9-1 message. The type 15 message includes atmospheric parameters. The type 16 message can be utilized as a timely supplement to the notice to mariners or shipping, regarding information on the status of the local DGPS service which is not provided in other message types. Additionally, the type 16 message may provide limited information on service outages in adjacent coverage areas or planned outages for scheduled maintenance at any broadcast site. In order to keep data link loading to a minimum, type 16 messages contain only system information that is crucial to the safety of navigation. For more details on the RTCM format and message types, the reader is directed to

The recently updated standards, Version 3.0 RTCM [RTCM, 2004], consist primarily of messages designed to support real-time kinematic (RTK) operations for both GPS and GLONASS (see Section 9.11), including broadcasting of code and carrier phase observables, antenna parameters, and ancillary system parameters by the reference station to the user's location. Unlike the earlier version, this standard does not include tentative messages; it is designed to accommodate modifications to GPS and GLONASS (e.g., new L2C and L5 signals) and to the new systems that are under development (e.g., Galileo, see Section 9.11). In addition, augmentation systems that use geostationary satellites that provide ranging signals and operate in the same frequency bands are now in the implementation stages (RTCM, 2004). The primary reason for this update included the following shortcomings of the earlier versions: (1) parity scheme that uses words with 24 bits of data followed by 6 bits of parity was wasteful of bandwidth; (2) parity was not independent from word to word; (3) with so many bits devoted to parity, the actual integrity of the message was not as high as it should be; and (4) 30-bit words are awkward to handle. Version 3.0 is intended to correct these weaknesses.

Message types contained in the current Version 3.0 standard have been structured in several groups: (1) observations (GPS L1, GPS L1/L2, GLONASS L1, GLONASS L1/L2)—message type 1001-1004, 1009-1012; (2) station coordinates (antenna reference point coordinates and antenna height)—message type 1005-1006; (3) antenna description—message type 1007-1008; and (4) auxiliary operation information—message type 1013 (RTCM, 2004).

Aside from the differentially corrected position coordinates in NMEA (National Marine Electronics Association) format, DGPS receivers might also offer the possibility of storing all of the raw data and correction signals for postprocessing. The raw data at the receiver can generally be stored in either receiver-specific or standard RINEX format. NMEA is an industry association that sets data transmission standards (; and has developed specifications that define the interface between various pieces of marine electronic equipment, including a set of standard messages defining the possible outputs of a GPS receiver. The idea of NMEA is to send a line of data called a sentence that is totally self-contained and independent from other sentences. There are standard sentences for each device category, and there is also the ability to define proprietary sentences for use by the individual company. All of the standard sentences have a two-letter prefix that defines the device that uses that sentence type (e.g., for GPS receivers the prefix is GP), which is followed by a three-letter sequence that defines the sentence contents (

There are several GP sentences, each one containing some unique data associated with them. They are all in ASCII format and are in the form of comma delimited strings. The character string lengths vary from 30 to 100 characters and are output at the selected intervals. The most common string (or sentence) is called the GGA string that provides essential fix data containing the Time of the Fix, Latitude, Longitude, Height, Number of Satellites used in the fix, DOP, Differential Status, and the Age of the Correction. Other strings may contain Speed, Track, Date, and so forth. NMEA is available in virtually all GPS receivers and is the most commonly used data output format. It is also the format used in most software packages that interface to a GPS receiver.

Some other sentences that have applicability to GPS receivers are as follows:

• AAM—Waypoint Arrival Alarm

• BOD—Bearing Origin to Destination

• BWC—Bearing using Great Circle route

• GSA—Overall Satellite data

• GSV—Detailed Satellite data

• MSK—Send control for a beacon receiver

• MSS—Beacon receiver status information

• RMA—Recommended Loran data

• RMB—Recommended navigation data for GPS

• RMC—Recommended minimum data for GPS

• VTG—Vector track and Speed over the Ground

• WCV—Waypoint closure velocity (Velocity Made Good)

• WPL—Waypoint information

• XTE—Measured cross track error

• ZTG—Zulu (UTC) time and time to go (to destination)

The hardware interface for GPS units is designed to meet the NMEA requirements. They are also compatible with most computer serial ports using RS232 protocols; however, strictly speaking, the NMEA standard is not RS232, but rather EIA-422. The interface speed can generally be adjusted (set to 9600 or higher), but the NMEA standard is 4800 baud with 8 bits of data, no parity, and one stop bit (

9.7.3 Network-Based Real-Time Kinematic GPS (RTK GPS)

Another approach, gaining popularity in a number of countries, is to support the users through the local networks of Continuously Operating Reference Stations (CORS) that normally serve a range of applications, especially those requiring high accuracy in postprocessing or in real time (although the real-time support is still limited). Government agencies, such as NGS, Department of Transportation (DOT), or international organizations, such as IGS, deploy and operate these networks. All users typically have free access to the archived data that can be used as a reference (base data) in carrier phase or pseudorange data processing in relative mode. Alternatively, network-based positioning using carrier-phase observations with a single user receiver can be accomplished with the local specialized networks, which can estimate and transmit carrier phase correction (see, e.g., Cannon et al., 2001; Chen, 2000; Dai et al., 2001; Kim and Langley, 2000, Raquet, 1998; Rizos, 2002a; Vollath et al., 2000; Wanninger, 2002).

The long-range RTK technique (defined for 100 to 300 km or longer station separation) is the most challenging GPS data reduction method. As the base-rover separation increases, many distance-dependent biases, such as atmospheric or orbital errors, may become significant even in the relative mode, which complicates the ambiguity resolution process. This, in turn, may seriously corrupt the positioning results, unless these effects are properly accounted for. In general, the success of precise GPS positioning over long baselines depends on the ability to resolve the integer phase ambiguities when short observation time spans are required, which is especially relevant to RTK applications. The distance over which carrier-phase ambiguity can be resolved may be significantly increased by employing a multireference station approach. Over the past few years, the use of the reference station network approach has shown great promise in extending the interreceiver separation. The implementation of multiple reference stations in a permanent array offers several advantages over the standard single-baseline approach. It improves the accuracy of the mobile (user) receiver and makes the results less sensitive to the length of the baselines, at the same time acting as a "filter" for the lower-quality measurements coming occasionally from some stations. Consequently, the precision of the baseline, expressed as its estimated standard deviation, is improved. The most important contribution of the network solution, as compared to the single baseline case, is not, however, the improvement in precision, but rather the improved reliability and availability, as well as the opportunity to model the atmospheric errors (van der Marel, 1998). A commonly used base station separation in the network ranges between a few kilometers to a few hundreds of kilometers, depending on the applications served, coverage (network extent), and the required accuracy.

The network-based RTK concept can be summarized as follows: a network of permanent tracking stations uses GPS data to estimate the ionospheric and tropospheric corrections in real time and broadcasts this information to the users, who require accuracy better than DGPS. Thus, network-based positioning (either RTK or postprocessed) is a three-step procedure: (1) network solution (no user data is involved) to estimate the instantaneous ionospheric corrections and tropospheric delays (tropospheric total zenith delay, TZD) per station, (2) transmission of the corrections to the users (Internet, beacon, mobile phone), and (3) user positioning solution (in relative mode) using data from a single or multiple reference stations together with the atmospheric corrections derived in step (1). Naturally, if RTK mode is used, the user needs a data transmit from a reference station to form a double-difference carrier phase observable for positioning solution (Grejner-Brzezinska et al., 2005a, 2005b; Kashani et al., 2007; Wielgosz et al., 2004, 2005). This approach is similar to the virtual reference station (VRS) concept, but without the actual geometric relocation of the observation to the vicinity of the user receiver (van der Marel, 1998; Wanninger, 2002).

The VRS system uses observations from multiple reference stations to estimate the systematic errors in the data and to create a unique virtual reference station for each user's location. A synthetic data set (at the VRS location) is sent to the user located in the vicinity of VRS and is then used for relative positioning solution. The systematic errors modeled include ionosphere, troposphere, satellite orbit errors, and multipath; data are delivered to the rover in RTCM/CMR+ format. The following infrastructure is required for Trimble VRS™: dual-frequency GPS receivers, PCs, software, and communications links that are permanently or semipermanently stationed to provide continuous data logging, monitoring and data broadcast, rover receiver, rover interface, and office software that handles the data. The following are the basic processing steps (see Figure 9.14 and Figure 9.15):

• Reference station data streams back to server through LAN, Internet, or radio links

• Roving receiver sends an NMEA string back to the server using cellular modem

• VRS position is established for each user location

• Server uses VRS position to create corrected observables and broadcasts them to the rover

• Rover surveying in normal RTK mode but data are relative to the VRS

• User receiver logs files for postprocessing

FIGURE 9.14 Virtual reference station (VRS) data flow. (Courtesy Trimble Navigation Ltd.)

Reference Station

Raw Data

Reference Station t


GPS Network

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