Geometric Modeling of the ZSurface and ZCurve of GNSS Signals and Their Solution Techniques
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© 19802012 IEEE. This paper presents a novel geometric model to characterize the zerocrossing surface (zsurface) and its zcurve for signals emitted by a pair of Global Navigation Satellite System satellites (A, B). The zsurface is the surface of points which have zero difference in pseudorange to (A, B), and the zcurve is the intersection of zsurface with the earth's surface. As a form of time difference of arrival, modeling of the zsurface/ zcurve benefits from the elimination of common error terms (e.g., receiver clock offset) shared by the pair of pseudoranges, so that the resulting model can be used for design of advanced applications, such as timing and positioning integrity monitors and tools for geodetic and atmospheric measurements. The derivation of the zcurve starts with the shape modeling of the terrestrial service volume and the earth's surface. Then, an equipseudorange surface of (A, B)'s signals can be placed within these shape models. The zcurve can be derived as a boundary condition of the zsurface. The model can represent the morphing of zcurves with respect to the changes in satellite positions and signal propagation delays. As a result, the zmodels can be readily generalized into a ksurface and kcurve, where k represents the pseudorange difference between (A, B). Solutions for modeling and analysis of the z(k)surface/curve are based on a system of quadratic Cartesian equations. We propose an algebraic method to parameterize them in terms of geocentric latitude and longitude.
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Fu, G., Riedel, C., Holmes, T., & Liu, J.
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Earth Surface

Geometric Model

Global Navigation Satellite Systems (gnss)

Global Positioning System (gps)

Satellite

Signal Propagation

Time Difference Of Arrival (tdoa)
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