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authorRefik Hadzialic2012-09-12 17:09:34 +0200
committerRefik Hadzialic2012-09-12 17:09:34 +0200
commit39cf255afbce6217a0368cd4c184c095019aa1a0 (patch)
tree3912857e35562b08cb8c6fc6dffe057e572d17ee
parentChanges and abstract in english needs german (diff)
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Appendix correction
-rw-r--r--vorlagen/thesis/maindoc.pdfbin8064792 -> 8064835 bytes
-rw-r--r--vorlagen/thesis/src/kapitel_A.tex17
2 files changed, 9 insertions, 8 deletions
diff --git a/vorlagen/thesis/maindoc.pdf b/vorlagen/thesis/maindoc.pdf
index 7e0ecee..b638b1a 100644
--- a/vorlagen/thesis/maindoc.pdf
+++ b/vorlagen/thesis/maindoc.pdf
Binary files differ
diff --git a/vorlagen/thesis/src/kapitel_A.tex b/vorlagen/thesis/src/kapitel_A.tex
index 6ce6cc0..6bc3dc4 100644
--- a/vorlagen/thesis/src/kapitel_A.tex
+++ b/vorlagen/thesis/src/kapitel_A.tex
@@ -909,7 +909,7 @@ has been subsituted with $\hat{r_i}$.
\dfrac{\partial f(\hat{x_u},\hat{y_u},\hat{z_u},\hat{t_u})}{\partial \hat{t_u}} = c
\end{array}
\end{equation}
-Then by substituting the equation terms from \eqref{eq:MultitaylorDeriv}, \eqref{eq:rhoSatsNewFun} and \eqref{eq:rhoSatsNewFunApprox}
+This is followed by substituting the equation terms from \eqref{eq:MultitaylorDeriv}, \eqref{eq:rhoSatsNewFun} and \eqref{eq:rhoSatsNewFunApprox}
into \eqref{eq:MultitaylorFour}, the resulting equation is given in \eqref{eq:MultitaylorDerivAfter}.
\begin{equation}
\label{eq:MultitaylorDerivAfter}
@@ -934,15 +934,15 @@ At this step, by solving equation \eqref{eq:MultitaylorFour}, the linearization
\end{equation}
By rearanging the equation \eqref{eq:MultitaylorDerivAfter} one derives equation \eqref{eq:MultitaylorDerivAfterRearange}.
And then by substituting the terms in \eqref{eq:SubsTerms1} and \eqref{eq:SubsTerms2} into \eqref{eq:MultitaylorDerivAfterRearange},
-the equation resembles the one given in \eqref{eq:userPosition}.
+the equation resembles the equation in \eqref{eq:userPosition}.
\begin{equation}
\label{eq:userPosition}
\Delta\rho_i = \alpha_{xi}\Delta x_u + \alpha_{yi}\Delta y_u + \alpha_{zi}\Delta z_u - c\Delta t_u
\end{equation}
There are four unknowns, $\Delta x_u$, $\Delta y_u$, $\Delta z_u$ and $\Delta t_u$, in equation \eqref{eq:userPosition}.
-By solving this set of linear equations, which shall result in finding $\Delta x_u$, $\Delta y_u$, $\Delta z_u$ and $\Delta t_u$,
-the GPS receiver position $(x_u, y_u, z_u)$ and clock offset $t_u$ is computed by replacing the
-same into equations in \eqref{eq:userCoordinates}. Equation \eqref{eq:userPosition} can be rewritten for four satellites
+By solving this set of linear equations, which shall result in finding of $\Delta x_u$, $\Delta y_u$, $\Delta z_u$ and $\Delta t_u$,
+the GPS receiver position is computed. The GPS receiver position $(x_u, y_u, z_u)$ and clock offset $t_u$ are obtained by substituting
+them into equations in \eqref{eq:userCoordinates}. Equation \eqref{eq:userPosition} can be rewritten for four satellites
in the matrix form as in \eqref{eq:userPositionMatrix}.
\begin{equation}
\label{eq:userPositionMatrix}
@@ -974,8 +974,9 @@ in the matrix form as in \eqref{eq:userPositionMatrix}.
-\Delta ct_u
\end{bmatrix}
\end{equation}
-Finally, by multiplying both left sides\footnote{Matrix multiplication is not communitative, $\mathbf{AB\neq BA}$.} of the equation \eqref{eq:userPositionMatrix}
-with the inverse term of $\boldsymbol{\alpha}$, it yields the result of the unknown terms, as given in equation \eqref{eq:userPositionMatrixFinal}.
+Finally, by multiplying both left sides\footnote{Matrix multiplication is not communitative, $\mathbf{AB\neq BA}$.}
+of the equation \eqref{eq:userPositionMatrix} with the inverse term of $\boldsymbol{\alpha}$, it yields the result
+of the unknown terms, as given in equation \eqref{eq:userPositionMatrixFinal}.
\begin{equation}
\label{eq:userPositionMatrixInverseMult}
\boldsymbol{\alpha}^{-1}\Delta\boldsymbol{\rho} = \boldsymbol{\alpha}^{-1}\boldsymbol{\alpha} \Delta \boldsymbol{x}
@@ -989,7 +990,7 @@ to the just derived position values, that is, $\hat{x_u}=x_u$, $\hat{y_u}=y_u$,
$\hat{t_u}=t_u$. This process is repeated until the approximated positions converge to their final
values. It is not necessarily required that the initial positions are very accurate
and the results are usually obtained by 4-5 itterations \citep{pseudorangeError}.
-Risks exist that the solutions shall still be corrupted but there are different error avoiding
+Risks exist that the solution may be still be corrupted but there are different error avoiding
mechanisms to solve these problems, like minimizing the error contribution using more than four satellite
measurements \citep{pseudorangeError} \citep[Chapter 7]{understandGPS}.