Peter H. Dana
P. O. Box 1297 Georgetown, Texas 78627
The original Loran-C system was used primarily for marine navigation in a three transmitter, hyperbolic mode. Early receivers were designed to track a set of three transmitters consisting of a Master station and two Secondary stations (a chain) transmitting pulses at a common group repetition rate (GRI). The arrival times of the Secondary stations were measured with respect to the arrival time of the Master station to provide two time differences (TDs). The user located these hyperbolic lines of position (LOPs) on marine charts to obtain a position estimate.
Current Loran-C receivers track three or more transmitters to provide a position fix usually computed by the receiver and displayed as latitude and longitude. Some receivers contain accurate clocks, enabling them to use only two signals to provide position. Time and frequency receivers may need to track only one transmitted signal to control a timing pulse or oscillator signal with respect to the Loran-C system clocks. Some receivers operate in hostile interference environments while others are used in vehicles capable of high-dynamic maneuvers. Modern avionics receivers may track as many as eight transmitters from up to four different chains. Some use individual transmitted signals as pseudo-range measurements in combination with Global Positioning System (GPS) satellite measurements to provide interoperable navigation service. Differential Loran-C service is available in some areas, where system bias errors are broadcast to users requiring high accuracy position fixes.
As used today, effective coverage for the Loran-C system is a function of transmitter power, the position of the receiver with respect to the tracked transmitters, the 100 kHz propagation environment, the capabilities of the receiver, and the requirements of the user. Early coverage charts assumed a user community with single chain receivers operating in the hyperbolic mode and are not adequate descriptors of coverage for the new generation of Loran-C receivers and the variety of user requirements. GIS technologies can be used to model transmitters, propagation paths, interference sources, receiver capabilities, and unique user requirements in a flexible, interactive environment. Using the capabilities of GIS to manage, analyze, and display information in a single system, new coverage charts can be produced that can combine Loran-C modeling with other user information such as transportation routes, land use boundaries, fishing areas, or other interoperable navigation system service areas.
GIS software is available for a variety of platforms, from mainframes to personal computers. GIS prices range from a few hundred dollars for simple thematic mapping packages to hundreds of thousands of dollars for implementation of complete vehicle tracking and optimal routing dispatch systems for cities with populations in the millions.
Current users include private businesses as well as local, departmental, and national governmental agencies around the world. Applications include facilities management, natural resource inventory, land record maintenance, and site location analysis.
GIS software packages use a variety of approaches to the management of spatial information, but most model information as points, lines, and areas with associated attributes. While there are some successful raster-based GIS products, most are vector-based (with some capable of handling both). Modeling in GIS applications is often dependent on the way in which a specific GIS organizes data. Database management techniques range from simple spreadsheets to complex data structures. Relational databases and object-oriented methods are very different in their internal structure, but both methods have proven successful in similar applications.
One attribute of most GIS approaches is the use of a common coordinate system to represent information. In many GIS implementations real-world coordinates in the form of latitude and longitude are used, while in others an arbitrary graphic unit is used. Some systems model height and some can be configured to represent time as a fourth dimension. Data for GIS use must be georeferenced, or registered with the common coordinate system, to be useful. The accuracy of georeferencing has a significant impact on the validity of the GIS analysis to be performed. Some GIS packages can perform geocoding, an operation that matches attribute data in one data base with similar attributes in a georeferenced data base, resulting in automatic georeferencing of the original data base. The matching of customer addresses in one data base with the georeferenced street and street numbering representations in another data base is a common use of geocoding.
Data acquisition may be accomplished through the digitization of existing maps, keyboard entry of attribute data, or by the importation of existing data files. Many GIS packages allow for dynamic file sharing with data from spreadsheet or data base management packages. Data storage and management is an important task that may involve data transformations, preprocessing, error checking, and the manipulation of mass storage devices.
In most vector-based systems, points or nodes represent geographic entities with a single position in the common coordinate system. Utility poles, radio transmitters, and customer addresses are examples of point entities. Points are also used to represent those entities so small as to make their actual spatial extent insignificant at the scale required for GIS analysis. Points are also commonly used to represent area centroids, to arbitrarily locate an entity such as a label, or to position aggregate data within an area.
Lines, polylines, arcs, and spans are terms associated with groups of line segments that are used to represent transportation routes, pipelines, or other entities that link points within a GIS database.
Zones, polygons, and regions are GIS terms for groups of lines that enclose areas such as state boundaries, property lines, and soil type delineations. Complex polygons may contain islands consisting of other polygons or unmodeled areas.
Layers, tables, overlays, and coverages represent ensembles of information related by common attribute types. Layers are often thought of as similar to individual overhead transparencies that can be stacked to show spatial relationships between them. A layer containing soil-type regions can be paired with a layer containing vegetation zones for analysis and display by a GIS.
GIS analysis often requires many kinds of data manipulation. Most GIS packages allow for statistical operations such as regression and correlation; measurement capability for distance, direction, area, and perimeter computation; and geometric operations such as rotation, translation, and scaling. Other capabilities may include a high level macro-language or the ability to call user supplied functions written in some other software language.
At the heart of GIS modeling are geographic operators. A wide variety of operators is available in different GIS packages for spatial analysis. Spatial operators may include the ability to determine connectivity of line segments and the relationships of those line segments to common attributes. The ability to determine topology is also an important capability found in more sophisticated GIS packages.
Other geographic operators commonly available in GIS packages are intersection, point in polygon, area in area, and other expressions of interrelationships between geographic entities that can be used to select, reject, merge, or query spatial data bases. Many GIS packages provide line thinning and smoothing operators. Contouring and the graphic representation of three dimensional surfaces are desireable features.
One of the most powerful geographic operations is the creation of new entities from existing ones through proximity analysis. Buffering is the creation of a polygon around some existing entity or group of entities. The creation of a polygon that represents the area within ten kilometers of a hazardous materials transportation route is an example.
GIS mapping capabilities often include the ability to handle different earth shapes, geodetic datums, and map projections. These capabilities are required by many users for the digitization of existing maps, and for the production of useful output. The most useful GIS mapping systems support many different scanners, digitizers, plotters, printers, and video output devices.
By 1980, the Loran-C User Handbooks provided separate charts of coverage for each chain based on geometry, noise, and signal strength. These charts assumed a three station, Master-Secondary- Secondary receiver. Manual Secondary selection was based on both crossing angles and gradient, the change in position resulting from a change in TD . Increased use of Loran-C by ships, aircraft, and land- based vehicle tracking systems required additional coverage charts. The 1981 Specification of the Transmitted Loran-C Signal contained charts of GDOP contours for each triad in each chain allowing the navigator to select appropriate Master-Secondary pairs as the receiver location changed. Conventional two LOP, hyperbolic, single-chain navigation (triad navigation) was still assumed .
The increasing complexity of the Loran-C system and the increased use of Loran-C for avionics in the 1980s made more elaborate coverage generation methods necessary. The Federal Aviation Administration (FAA) sponsored a coverage generation software package, The Airport Screening Model . This program allowed the user to compute TDs, gradients, SNRs, and GDOP for a selected triad from a selected chain, using transmitter and chain data, ground conductivity estimates, and noise estimates. Written specifically for FAA prediction purposes, the program allowed predictions for specific locations and for traditional hyperbolic triad operation. The program was modified by the Transportation Systems Center for use in predicting potential coverage improvements in the United States . This new program incorporated receiver models and modern navigation techniques, including the use of TDs developed between Secondaries in a Master-independent mode. The output consisted of GDOP or SNR grids that were used to help plan the Mid-Continent chains.
In 1986 the U.S. Coast Guard produced a coverage generator, Coverage, written in Basic and implemented on HP9836C computers . This program generated coverage limit boundaries for output to plotters. Knowledgeable operator interaction was required to combine the result of SNR and GDOP computations. In 1989 a new coverage generator was produced by the Synetics Corporation and the U.S. Coast Guard for the U.S. Department of Transportation. This program was designed to run on IBM PC compatible computers and to be used by "an operator not knowledgeable in the field of Loran" . The program was based on techniques from the FAA Airport Screening Model. Changes included new atmospheric noise models, an implementation of mixed conductivity path phase delay prediction, mapping capabilities, and a boundary-following algorithm. The output of the program consisted of charts in a form similar to those provided in earlier User Handbooks. The use of triad geometry as a criteria continues in such publications as the newest User Handbook  and the FAA Advisory Circular 90-92, where the Loran- C oceanic and national air space coverage diagrams are based on three station hyperbolic positioning techniques .
The newest generation of coverage prediction programs has been developed by the Radio- Navigation Group at the University of Wales. The first of these programs was a menu-driven program that used an existing Computer-Aided-Design (CAD) package for output . The program modeled man-made interference sources that have long caused problems for Loran-C in Europe. This program was based on single triad navigation and used a three station GDOP model. The 1992 version of the Radio-Navigation Group program incorporated more sophisticated receiver models, including the ability to model cross-chain and master independent positioning modes . Future versions of this program will no doubt incorporate even more complex receiver modeling.
GIS packages can be used to acquire, manage, and store system data bases, conductivity maps, noise contours, and interference lists. Spatial analysis techniques using geographic operators can determine the impedance segments of a ray path, and mathematical operators can model field strength attenuation, ECD shifts, and GDOP.
GIS mapping capabilities can be used to digitize existing conductivity maps, noise contours, or service area maps. High quality output of coverage diagrams can be produced in the chart projection and local datum of the user.
Because the system runs under Microsoft Windows, any hardware system from a PC to a mainframe that supports Windows can serve as a MapInfo platform. Any input or output device supported by Windows can be used to digitize, plot, or print maps. MapInfo is also available in a Macintosh version and MapBasic scripts can be transferred between PCs and Macintosh computers.
MapInfo represents geographic entities as objects. Associated data is stored along with objects in tables, the MapInfo equivalent of GIS coverages or layers. Attribute information can be in character or numeric form. Objects include points, polylines, and regions. Geographic operators include Contains, Contains Entire, Contains Part, Within, Entirely Within, Partly Within, and Intersects. These operators, in conjunction with buffering, merging, joining, and a full array of structured query language (SQL) commands, allow the modeling of complex spatial relationships.
Many other GIS packages can be used to model Loran-C coverage. MapInfo was selected for its low cost, its availability, and the simplicity of use in the Windows environment.
For this case study noise values were computed from CCIR noise values  and stored as regions with noise value attributes in rms noise levels in decibels above one microvolt per meter in the NOISE table. No modeling of individual man-made interferers was included.
A new impedance table, SEGMENTS, is produced containing the line segments within a defined range limit of the grid. This is done using buffering commands and SQL selections.
This is accomplished by the use of a table of known positions outside of the land conductivity boundaries. These known points at sea, stored in the SEAPOINTS table, are assumed to have a conductivity of 5.0 mhos per meter. A line from each transmitter to the nearest of these points is computed. An SQL query determines the list of line segments intersected by this line. The same SQL statement orders the intersections by range from the known sea point.
Starting from the known conductivity level of the sea point, each intersection is examined and the level on each side of the intersection determined, until the conductivity level at the transmitter site is resolved. This transmitter site conductivity level is stored in the XMITRS table.
Using the computed conductivity level at the transmitter the program computes the topological relationships for each intersecting line segment, resolving the conductivity of each path segment. Given the list of ranges and conductivities stored in the SEGLIST table, any method, from full integral solutions to Millington's method, can be employed for ray path field strength attenuation.
This case study uses an average impedance method that has been used for prediction of both field strength and phase delay computations . Conductivity levels are converted to impedance values:
For each SEGLIST table, the effective path impedance is computed:
The resulting TOA variance is used as a weight in the position error computation:
A 100 meter coverage contour was produced for a single chain receiver operating on the 9940 chain. An SQL selection was performed on the contour table and the highway table, resulting in a new table containing the highways within the contour region. Another query computed the total length of the highways within the 100 meter, 2drms, coverage region [Figure 7].
Of particular significance is capability of GIS to model interoperable navigation systems. GIS techniques offers the potential for modeling differential GPS (DGPS) coverage and Loran-C concurrently, enabling independent users to experiment with DGPS beacon placement within existing and proposed Loran- C transmitter coverage. A fundamental advantage of GIS methods is the ability to use Loran-C coverage predictions in conjunction with other layers of spatial information. Rapid advances in GIS technologies will provide additional Loran-C coverage modeling capabilities in the future.
 U.S. Coast Guard. Loran-C User Handbook CG-462. Washington, DC: U.S. Department of Trans-portation. 1974.
 U.S. Coast Guard. Loran-C User Handbook COMDTINST MI6562.3. Washington, DC: U.S. Department of Transportation. 1980.
 U.S. Coast Guard. Specification of the Transmitted Loran-C Signal MI6562.4. Washington, DC: U.S. Department of Transportation. 1981.
 El-Arini, M. B. Airport Screening Model for Nonprecision Approaches Using Loran-C Navigation. McLean, VA: The Mitre Corporation. 1984.
 Bleau, Charles A. and Franklin MacKenzie. Model for Forecasting Loran-C Coverage. Proceedings of the Thirteenth Annual Technical Symposium. Bedford, MA: The Wild Goose Association. 1984.
 Last, David, Richard Farnsworth, and Mark Searle. A European Loran-C Coverage Prediction Model. Proceedings of the Nineteenth Annual Technical Symposium. Bedford, MA: The Wild Goose Association. 1990.
 Catlin, Jeff, Dean Foulis, Gary Noseworthy, and Gene Allard. The Automated Loran-C Coverage Diagram Generator. Proceedings of the Eighteenth Annual Technical Symposium. Bedford, MA: The Wild Goose Association. 1989.
 U.S. Coast Guard. Loran-C User Handbook COMDTPUB P16562.6. Washington, DC: U.S. Department of Transportation. 1992.
 Federal Aviation Administration. Advisory Circular 90-92. Washington, DC: U.S. Department of Transportation, General Services Section. 1993.
 Last, David, Mark Searle, and Richard Farnsworth. Coverage and Performance Predictions for the North-West European Loran-C System. Proceedings of the Twenty-First Annual Technical Symposium. Bedford, MA: The Wild Goose Association. 1992.
 FCC. FCC M3 Map Data File PB81-211567. Springfield, VA: National Technical Information Service. 1981.
 CCIR. World Distribution and Characteristics of Atmospheric Radio Noise, CCIR 322. Geneva: International Telecommunications Union, International Radio Consultative Committee. 1963.
 Penrod, Bruce, Richard Funderburk, and Peter Dana. Arrival of Loran-C Transmissions via GPS Common Mode/Common View Satellite Observations. Proceedings of the National Technical Meeting. Washington, DC: The Institute of Navigation. 1991.
 Kayton, Myron and Walter R. Fried, eds. Avionics Navigation Systems. New York: John Wiley & Sons. 1969.