: To perform the most precise relative positioning using GPS, it is necessary to resolve the carrier-phase integer cycle ambiguities. This process becomes increasingly difficult as the distance between the mobile and reference GPS receivers increases, due to the decorrelation of the GPS errors with distance, resulting in a practical limit on the distance over which ambiguity resolution can be performed when using a single reference receiver. This thesis proposes a novel method, called NetAdjust, which uses multiple reference receivers to reduce code and carrier-phase differential measurement errors and improve the ability to resolve carrier-phase ambiguities. The NetAdjust method is based upon an optimal linear minimum error variance estimator, and it "encapsulates" all of the network information into the measurements of a single reference receiver, so standard single-reference differential GPS processing algorithms can be used. The geometry of the reference receiver network is embedded within the error covariance matrix, and a functional form of this covariance matrix is described. The NetAdjust method was tested using two different GPS networks, an 11-receiver network covering a 400 km x 600 km region in southern Norway, and a 4-receiver network covering a 50 km x 150 km region at Holloman AFB in New Mexico. The results for L1 code, L1 phase, and widelane phase measurements are analyzed in the measurement domain and the position domain, showing improvements in RMS errors of up to 50% when using NetAdjust. Significant improvements in the ability to resolve carrier-phase ambiguities are also demonstrated for the Holloman and Norway test networks. Issues relating to development of an operational, real-time NetAdjust system are discussed. Also, a covariance analysis method is developed which can be used to predict NetAdjust effectiveness under various conditions and network configurations.

Development of a Method for Kinematic GPS Carrier-Phase Ambiguity Resolution Using Multiple Reference Receivers

T HE GPS satellite constellation is selected to satisfy many different conditions to provide worldwide three-dimensional navigation. The satellite constellation has been placed in an inclined orbit at 55 deg (formerly 63-deg inclination for earlier Block I satellites) to provide full Earth coverage, whereas a purely equatorial orbit cannot provide coverage above approximately 72° latitude at the GPS orbit altitude. The requirement for a minimum of four simultaneous pseudorange measurements with good geometry directly leads to a constellation of many satellites. A nongeosynchronous orbit was selected to permit the use of carrier phase/Doppler measurement profiles in addition to pseudorange measurements of code phase/delay. This objective was one of the reasons for the selection of the 12 sidereal hour orbit. This chapter discusses the operational satellite constellation of 24 satellites termed the GPS-24 (closely related to the previous Primary 21) constellation. The specific characteristics of this constellation are discussed in terms of the statistics of the numbers of satellites visible at different user latitudes and various elevation angles, the satellite ground tracks, and the signal Doppler shifts. The potential for the future augmentation of this GPS constellation by adding satellites in either the same planes or as geostationary satellites is also discussed. The chapter then continues with an analysis of the geometric dilution of precision (GDOP) and the related DOPs: PDOP, HDOP, VDOP, TDOP for position, horizontal, vertical, and time dilutions of precision. The bounds on the minimum value of these DOPs are analyzed for various numbers of satellites for both twoand three-dimensional problems with various constraints on elevation angle and user clock stability. Further discussion and development of the DOP concept is found in Chapter 11, this volume. The chapter concludes by describing the GDOP for the GPS-24 satellite constellation with a single satellite outage.

Satellite Constellation and Geometric Dilution of Precision

We discuss the accuracy of the ephemeris and clock corrections contained in the GPS navigation message.

Ephemeris and Clock Navigation Message Accuracy

The Global Positioning System (GPS) Block IIR satellites, which will replace the current Block II/IIA satellites, will have satellite-to-satellite communication capabilities that will allow intersatellite ranging between the Block IIR satellites. The cross-link pseudorange measurements will be used by onboard computers to update the stored navigation messages, which are based on trajectories predicted over an extended period of time, by ground-based processing of tracking data. During normal operations, the cross-link pseudorange measurements will provideimproved satellite states, which then can be broadcast to theusers. One oftheerrorsourcesin the updated navigation messages, which cannot be corrected by cross-link measurements, is found in the Earth orientation parameter (EOP) errors. As a consequence, as the age of the Earth rotation parameter increases, the performance of the autonomous navigation system will degrade. The effect of this error source on the Block II GPS autonomous navigation accuracy is described. This work is based on simulated cross-link pseudorange measurements. Realistic force, measurement, and reference frame models are used in the analysis to account for additional major error sources. Cross-link measurementsfora period of oneday, generated at the end ofeach of three different prediction intervals, are used to update the predicted trajectory. The estimated solutions then are compared to true solutions to evaluate the effect of prediction errors. With the current EOP prediction errors, the user range errors (URE), computed from improved trajectories and clock differences for a 90-day prediction, exceed 9 m, and for a 180-day prediction, they exceed 17 m. Finally, results of processing measurements from ground stations, instead of cross links, are discussed wherein the URE for the 180-day prediction case are shown to be about 3.1 m.

Autonomous navigation of global positioning system satellites using cross-link measurements

As the development of GPS continues, there will be an increasing need for a software-centered signal model. This model must accurately generate the observed pseudorange that would typically be encountered. The observed pseudorange varies from the true geometric range because of range measurement errors, which stem from a variety of hardware and environmental factors. In this paper, these errors are classified as either deterministic or random, and, where appropriate, their models are summarized. Of particular interest is the model for Selective Availability, which was derived from actual GPS data. The procedure for determination of this model, known as system identification theory, is briefly outlined. The synthesis of these error sources into the final signal model is given, along with simulation results.

A signal model for GPS

In early 1985, an improved ground Operational Control System (OCS) will maintain the navigation service. Primary among the OCS improvements over past GPS navigation systems is a global network of ground antennas (to upload satellite navigation data) and tracking/monitor stations. In addition, a refined Kalman filter will continuously estimate the Global Positioning System (GPS) satellite ephemerides and clock phases and frequencies. Although the user-GPS interface remains unaltered, the accuracy of the GPS navigation service is expected to improve by a factor of three.



Using real and simulated GPS pseudo range radiometric tracking data, The Aerospace Corporation has completed a detailed error analysis which shows that the satellite clock noise contributes more than 90 percent of the total satellite-to-user pseudo range error. If the number of OCS uploads is increased to three per day (as planned), then the accuracy of the navigation service is also expected to improve by nearly a factor of three because the clock-noise contribution to the range error increases linearly with time. Also, this analysis shows the consequence of satellite ephermeris uncertainties in the GPS navigation application.

R. Bowen

Papers

Global positioning system operational control system accuracies