30 lines
1.2 KiB
Markdown
30 lines
1.2 KiB
Markdown
# Code-Based Positioning
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Code Based Positioning is based on solving the geometric problem of using at least 4 pseudorange measurements from satellites,
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resulting in
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$$
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R^j - D^j \simeq \sqrt{(x^j-x)^2 + (y^j-y)^2 + (z^j-z)^2} + c\delta t
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$$
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$$
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j = 1,2,...,n (n\geq 4)
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$$
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It uses the continuosly broadcast signals by satellites to calculate time-of-flight to the receiver's position,
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and then estimating the distance to each of them.
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It is implemented as the standard positioning service.
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# Phase-Based Positioning
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If higher accuracy is needed, phase-based positioning is used, which is implemented in Precise Point Positioning (PPP).
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It provides a significantly higher accuracy with centimetre-level positioning but incurs higher computational costs
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as more corrections have to be applied
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and requires tracking continuity.
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As the name suggests, both code and phase observations are used.
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Code and carrier measuremens are modeled as:
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$$
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R^j_C = \rho^j + c(\delta t - \delta t^j) + Tr^j + M^j_C + \epsilon^j_C
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$$
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$$
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\Phi^j_C = \rho^j + c(\delta t - \delta t^j) + Tr^j + \lambda^j_C + B^j_C + m^j_C +\epsilon^j_C
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$$
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Where $R^j$ is the unsmoothed pseudorange measurment for the $j$th satellite and $\Phi^j$ is the corresponding carrier measurement.
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