Analysis of Stochastic Properties of GPS Observables
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Date
2008-10
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University. Division of Geodetic Science
Abstract
Traditionally, data processing for GPS positioning requires modeling
considerations underlying the observations. The variance-covariance (v-c) matrix (as
part of the stochastic model) usually comprises only the variances of the individual
pseudo-range and carrier phase observations and generally disregards any possible
correlation among them. However, for high precision, optimal GPS positioning
estimators, it might be important to account for the possible correlation between the GPS
observables.
The objective of this research is based on two fundamental considerations; the
primary one is related to the stochastic analysis of the different types of GPS observables
in order to estimate and interpret the level of the measurement noise (based on singledifference
residuals). For this purpose, a static survey (zero baseline) was performed
with six pairs of geodetic-grade GPS receivers of different type and make. Based on
these data, the normalized autocorrelation, cross-correlation, power spectral density
functions and histograms were thoroughly examined.
The secondary consideration is related to the construction of an alternative v-c
matrix, which implements the major outcomes of the stochastic analysis (auto and crosscorrelation
functions), in order to test its impact in the positioning estimators (coordinates
determination) using precise GPS positioning.
The results presented in this thesis showed that the different types of geodeticgrade
GPS receivers analyzed here possess distinct noise characteristics. In other words,
the noise characteristics are receiver specific. Furthermore, correlation exists among the
different types of GPS observables (cross-correlation) and it varies between the receivers.
In terms of positioning estimators, an example for zero and short baseline (10 m)
measurements was analyzed. In both cases (zero and short baselines), the results
obtained using the traditional approach (diagonal v-c matrix) better compare to “true”
values as opposed to those using the alternative v-c matrix, which accounts for
correlation among the observables. This indicates, that the results obtained in this case
study may not always apply to survey data, and more research is needed to formulate a
more generic model.
Description
This report was prepared by Guadalupe Esteban Vazquez Becerra, a graduate student, Department of Civil and Environmental Engineering and Geodetic Science, under the supervision of Professor Dorota A. Grejner Brzezinska and Christopher Jekeli.
This Research was supported by the National Council for Science and Technology (CONACYT).
This report was also submitted to the Graduate School of The Ohio State University as a thesis in partial fulfillment of the requirements for the degree of Master of Science.
This Research was supported by the National Council for Science and Technology (CONACYT).
This report was also submitted to the Graduate School of The Ohio State University as a thesis in partial fulfillment of the requirements for the degree of Master of Science.