## 1. Introduction

[2] A standard Global Positioning System (GPS) receiver processes L band radio signal pseudoranges from four or more GPS satellites to determine the receiver's position with a 1σ precision of about 5–10 m in real time. The receiver may also be equipped for radio reception of differential corrections to satellite pseudoranges from GPS reference receivers at known positions. Differential corrections supplied by a local area differential GPS (LDGPS) service, such as the U.S. Coast Guard (USCG) Maritime DGPS service, are supplied by the nearest reference receiver. A satellite differential correction is calculated by subtracting the associated pseudorange at the reference receiver from the known free-space range. This correction is then transmitted to the roaming receiver, where it is added to its corresponding measured pseudorange. The differential corrections tend to cancel out error biases (departures from actual free-space ranges and perfect timekeeping) that the reference and roaming receivers have in common. Pseudorange error biases are associated with the satellite clock residual error, satellite position error, ionosphere mismodeling, troposphere, and multipath and have approximate 1σ values of 2.0, 2.1, 4.0, 0.5, and 1.0 m, respectively, according to a standard error model [*Parkinson*, 1996]. The preceding list of error biases is usually in order of increasing spatial and temporal decorrelation tendency for increasing space-time separation between the roaming and reference receivers. Increasing this baseline separation decreases the effectiveness of differential corrections. We seek to restore this effectiveness by accounting for the difference in atmospheric delay contributions at the reference and roaming receiver positions. Although ionosphere error bias dominates the tropospheric error bias in magnitude, the tropospheric differences can be more significant than ionospheric differences because of their smaller decorrelation length scales and timescales [*Misra and Enge*, 2001].

[3] One can also purchase GPS receivers with access to a wide-area DGPS service (WADGPS), such as the U.S. Wide Area Augmentation System (WAAS). The WAAS system consists of 25 GPS reference receivers that are spread over the United States and Puerto Rico. These receivers correct their pseudoranges for tropospheric effects and transmit the constituent error biases for satellite clocks, satellite ephemeris, and ionospheric contributions to a central processing station. The station processes this data for use by WAAS-capable GPS receivers and uploads the information to geostationary satellites. WAAS GPS receivers download this information at the GPS L1 frequency and compute corrections to their pseudorange data, adding tropospheric corrections from a climatological model [*Collins et al.*, 1996]. DGPS is further discussed by *Misra and Enge* [2001].

[4] There are some potentially important issues with existing DGPS systems. One is coverage. In particular, ionospheric spatial and decorrelation lengths and times sometimes decrease beneath the resolution limits of the reference receiver distribution in the case of a WADGPS system. In the case of LADGPS, ionospheric conditions can differ substantially between reference and roaming receivers for large separations. Such instances that compromise the performance of a WADGPS system are shown to occur, especially at low and high latitudes, particularly during periods of high solar and magnetic activity [*Skone and Shrestha*, 2002; *Skone et al.*, 2003, 2004; *Yousuf and Skone*, 2005]. Unsettled tropospheric weather can also be a problem. In the case of LADGPS, knowledge of the ionospheric and tropospheric conditions at or near the reference and roaming receiver sites can be used to help correct these DGPS problems, especially if these data are used to update effective correction models. We test this approach on Virginia and Maryland data sets. If we find it to be effective at midlatitudes, we expect it would also be effective at low and high latitudes, except for the effect of irregularities and the sharp gradients that often are not included in models. In this case, there is probably no substitute for increasing the number of reference stations and observations.

[5] Another issue, particularly for WADGPS systems, is the approximation used to represent the ionospheric delay component of pseudorange, which is proportional to slant total electron content (TEC). Slant TEC, determined from two-frequency reference receiver data, is represented in a thin-shell approximation as the product of a geometrical obliquity factor and a vertical TEC value where the straight ray intersects the height of the electron density thin shell, called the ionospheric pierce point. This type of approximation and the associated interpolation of vertical TEC data at the pierce points have been found to be a problem at low latitudes [*Paul et al.*, 2005]. We attempt to avoid these approximations by processing the two-frequency data of GPS reference receivers to determine driving parameters [*Reilly and Singh*, 2004] of our Raytrace–Ionospheric conductivity and electron density–Bent–Gallagher (RIBG) ionospheric model [*Reilly*, 1993], which is then used with fast, straight ray-tracing computation through the RIBG height versus electron density profiles to determine ionospheric contributions. This type of approach, with interpolation of model-driving parameters at reference stations, should often improve the resolution capability and accuracy of a WADGPS GPS reference receiver network. For the troposphere we use weather station data for surface temperature, pressure, and relative humidity inputs to the Hopfield model; see equation (4.41) and the separate mapping functions for dry and wet delays given in the book by *Misra and Enge* [2001]. The Hopfield model is relatively accurate for the dry component, which accounts for about 90% of the tropospheric effect. The wet component, which is adequate by the Hopfield model, contributes the remaining amount.

[6] A third issue with DGPS systems is communication of the differential correction information to the roaming receiver. The roaming receiver's radio reception of differential corrections may sometimes be range limited or blocked by buildings or other obstructions. We avoid this difficulty by using the Internet to transmit differential corrections to the GPS roaming receiver.

[7] We investigate the effect of different ionospheric and tropospheric conditions at reference and roaming receivers and accordingly modify the DGPS corrections from the USCG LADGPS system, which then become what we call atmospheric DGPS (ADGPS) corrections. We process roaming GPS receiver data in section 2 for Alexandria and Fairfax in northern Virginia, as well as Driver in southeastern Virginia. The latter is also a reference station. These sites are separated by about 44, 67, and 228 km from the USCG GPS reference station in Annapolis, Maryland, respectively. Two-frequency data from the reference stations are processed [*Reilly and Singh*, 2004] to yield effective sunspot number drivers for RIBG, which are then used to compute the difference between ionospheric contributions to pseudoranges at roaming and reference receiver locations. Weather station data are used to compute differences in tropospheric contributions. We evaluate performance enhancement from using the ADGPS corrections. We also compare our results with WAAS GPS receiver results in Alexandria and Fairfax. Section 3 discusses results and proposes some ADGPS modifications for WADGPS and LADGPS systems.