A Behavioral Framework for Wide-Area Differential GNSS

H.-S. Wang and S.-K. Wang (Taiwan)

Keywords

Global Navigation Satellite System (GNSS); BehavioralFramework; Structured Total LeastSquares; Dilution ofPrecision; Kernel Representation; Total LeastSquares.

Abstract

In this paper, we present a behavioral approach to solve wide-area Differential GNSS positioning problems as well as a way to represent the DOP (dilution of precision) of a moving object. The concept of behavioral modeling was first proposed by Jan C. Willems in a series of papers (J.C. Willems, "From time series to linear system part I, II, and III," Automatica Vol. 22, 1986.) as a generic tool for mathematical modeling of dynamical systems. In the proposed approach, a GNSS positioning problem is firstly described by a kernel representation and then the problem can be solved by a structured total least-squares (STLS) algorithm. STLS algorithm is a modified version of the traditional total least-squares (TLS) method. It can be shown that the STLS algorithm is able to provide better performance than the TLS algorithm for the problems that possess a particu-lar structure. In the case of the present paper, it is shown that the GNSS positioning problem has a Hankel structure (i.e., the geometric matrix of the pseudorange equation is Hankel), therefore the problem can be solved by an STLS algorithm subject to a Hankel structure.

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