The accuracy of Global Positioning algorithms can be improved by incorporating observations from the satellites of multiple Global Navigation Satellite Systems (GNSS). To best utilize these observations, inter-system biases must be modeled. A unified observational model is proposed which accounts for these factors for an arbitrary number of GNSS. The Bayesian Information Criterion (BIC) may be imposed upon the unified model to balance data-fitting degree with model complexity among candidate models for a given satellite configuration scenario. A simple formulation is derived for the change to the Weighted Sum Squared Residuals (WSSR) outcome caused by modifying the least-squares design matrix to accomodate additional ISB parameters. The process of updating WSSR is shown to be $O(n^2)$, allowing a low-cost determination of the information entropy between any two candidate models. With this computationally cheap parameter selection process and a set of GNSS-heterogeneous observations, the form of the unified model with the highest expected accuracy may be efficiently selected, at a stage before matrix inversion is performed.

Library of Congress Subject Headings

Global Positioning System--Data processing

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


John Hamilton

Advisor/Committee Member

Bernard Brooks

Advisor/Committee Member

Hossein Shahmohamad


Physical copy available from RIT's Wallace Library at G109.5 .T65 2015


RIT – Main Campus

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