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Linear observation model for PPP

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FundamentalsFundamentals
Title Linear observation model for PPP
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Advanced
Year of Publication 2011

According to the equations described in the combination of pairs of signals

Comb Pairs Sign Fig 1.png


Comb Pairs Sign Fig 2.png


Comb Pairs Sign Fig 3.PNG


the code and carrier measurements in the ionosphere-free combination are modelled as:


where is the unsmoothed code pseudorange measurement for the satellite in view and is the corresponding carrier measurement.

Following the same procedure as in Code Based Positioning (SPS), the linear observation model for the code and carrier measurements can be written as:


  • Prefit-residuals:



Note: The satellite clock offset includes the satellite clock relativistic correction due to the orbit eccentricity. The relativistic path range correction is included in the geometric range .The term is the nominal value for the tropospheric correction.

Notice that, and according to the equation


the tropospheric delay in the equation (2) can be decomposed into a nominal term and the deviation from this nominal . That is:


The mapping factor is an element of the design matrix (5) and the is a component of the parameters vector (6):


  • Design matrix



  • Vector parameters (to estimate)