Alfred Kleusberg

GPS for geodesy

Reference systems GPS satellite orbits propagation of the GPS signals GPS receivers and the observables GPS observation equations and positioning concepts GPS data processing strategies GPS quality control GPS carrier phase ambiguity fixing concepts active GPS control stations single-site GPS models short distance GPS models medium distance GPS measurements long distance kinematic GPS the GPS as a tool in global geodynamics atmospheric models from GPS the role of GPS in space geodesy.

GPS Observation Equations and Positioning Concepts

The purpose of this chapter is four-fold: First, it provides the connection between chapters 1 through 4 outlining the individual components of the Global Positioning System, and chapters 6 through 16 describing the models used in different geodetic applications of GPS. This connection is introduced through the observation equations for pseudorange and carrier phase measurements in section 5.2 GPS Observables, relating the measured quantities described in chapter 4 to geometrical and physical parameters of interest in a geodetic context. Typically, these equations will be non-linear with respect to some of the parameters, most notably with respect to the coordinates of the satellite and the receiver.

Applications of an orbiting gravity gradiometer

Considering present attempts to develop a gradiometer with an accuracy between 10−3E and 10−4E, two applications for such a device have been studied: (a) mapping the gravitational field of the Earth, and (b) estimating the geocentric distance of a satellite carrying the instrument. Given a certain power spectrum for the signal and 10−4E (rms) of white measurement noise, the results of an error analysis indicate that a six-month mission in polar orbit at a height of 200 km, with samples taken every three seconds, should provide data for estimating the spherical harmonic potential coefficients up to degree and order 300 with less than 50% error, and improve the coefficients through degree 30 by up to four orders of magnitude compared to existing models. A simulation study based on numerical orbit integrations suggests that a simple adjustment of the initial conditions based on gradiometer data could produce orbits where the geocentric distance is accurate to 10 cm or better, provided the orbits are 2000 km high and some improvement in the gravity field up to degree 30 is first achieved. In this sense, the gravity-mapping capability of the gradiometer complements its use in orbit refinement. This idea can be of use in determining orbits for satellite altimetry. Furthermore, by tracking the gradiometer-carrying spacecraft when it passes nearly above a terrestrial station, the geocentric distance of this station can also be estimated to about one decimeter accuracy. This principle could be used in combination with VLBI and other modern methods to set up a world-wide 3-D network of high accuracy.

Atmospheric Models from GPS

As discussed in earlier chapters of this monograph, atmospheric refractivity affects GPS measurements by introducing ionospheric and tropospheric delays. If not properly corrected or removed otherwise, these delays will cause position errors. This point of view treats the effects of atmospheric refraction on GPS measurements as a nuisance. The complementary point of view is that the refraction effects in GPS measurements contain useful information accumulated while passing through the atmosphere. In this scenario, the ionospheric and tropospheric delays are seen as remotely sensed data related to atmospheric parameters, with the possibility to recover some or all of these parameters through proper GPS data analysis.

Direct Determination of Angular Velocity Using GPS

Controlling a ship in a berthing operation is carried out mainly by the change of state, such as velocity and yaw rate (turn rate), although the value of the change of state is very small at berthing. Very high precision is, therefore, required to determine the velocity and angular velocity. A sensor that has an accuracy of ±0.02°/s (1 σ) is sought for determination of turn rate in a berthing system. Three-dimensional angular velocity can directly be determined, with 2 independent baselines of 3 GPS antennas, using instantaneous Doppler measurements or phase rate (temporal difference of phase) observations. This paper discusses the mathematical model for direct determination of angular velocity using GPS, and the comparison of the results of the angular velocity determination using the Doppler and phase rate. The precision of angular velocity determination is estimated using temporal difference of the attitude sensors (TSS and gyrocompass) on board a hydrographic sounding ship. The RMS values of the difference of yaw rate determination between the two systems were: ±0.16°/s using phase rate and ±0.31°/s using Doppler measurements with the separation of onboard antennas of ca. 1.34 m. 10 m baselines could satisfy the sensor requirements for angular velocity determination during berthing maneuvers.