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Update The clock synchronization problem authored by Brian Histe's avatar Brian Histe
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The-clock-synchronization-problem.md
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...@@ -5,6 +5,7 @@ Clock synchronization with GNSS involves comparing the time kept by a GNSS recei ...@@ -5,6 +5,7 @@ Clock synchronization with GNSS involves comparing the time kept by a GNSS recei
# **1st synchronization problem: the distance calculation is very sensitive to clock errors** # **1st synchronization problem: the distance calculation is very sensitive to clock errors**
Indeed, if we calculate the time a signal makes to go from the satellites to the receptor, in an ideal world, we only would have to use the fact that ![lagrida_latex_editor__72_](uploads/e6e11d7df889518818c8123f954700d7/lagrida_latex_editor__72_.png). Indeed, if we calculate the time a signal makes to go from the satellites to the receptor, in an ideal world, we only would have to use the fact that ![lagrida_latex_editor__72_](uploads/e6e11d7df889518818c8123f954700d7/lagrida_latex_editor__72_.png).
With : With :
- ![lagrida_latex_editor__69_](uploads/5c926f7e6aac01d7485d65355efeb0b6/lagrida_latex_editor__69_.png) the distance between the satellite and the user, - ![lagrida_latex_editor__69_](uploads/5c926f7e6aac01d7485d65355efeb0b6/lagrida_latex_editor__69_.png) the distance between the satellite and the user,
- ![lagrida_latex_editor__70_](uploads/f347b61d1739c4711ddf9b5d8e232a3a/lagrida_latex_editor__70_.png) the speed of light, - ![lagrida_latex_editor__70_](uploads/f347b61d1739c4711ddf9b5d8e232a3a/lagrida_latex_editor__70_.png) the speed of light,
...@@ -12,7 +13,7 @@ With : ...@@ -12,7 +13,7 @@ With :
As time is multiplied by the speed of light, distance is very sensible to time mistake. As time is multiplied by the speed of light, distance is very sensible to time mistake.
Without any other mistake, time can be written ![lagrida_latex_editor__73_](uploads/1c3f0af394ac5ae992313930157c854a/lagrida_latex_editor__73_.png) with ![lagrida_latex_editor__74_](uploads/7ad505e13cf61943281e9f62418e7e26/lagrida_latex_editor__74_.png) the propagation time, ![lagrida_latex_editor__83_](uploads/9cc25f573f404c68b5001c37c22023f8/lagrida_latex_editor__83_.png) the bias of the receptor, ![lagrida_latex_editor__76_](uploads/a4480fac0d264f77733a7bb0458e0ca1/lagrida_latex_editor__76_.png) the bias of the satellite. Without any other mistake being taken into account, transmission time between the satellite and the user can be written ![lagrida_latex_editor__73_](uploads/1c3f0af394ac5ae992313930157c854a/lagrida_latex_editor__73_.png) with ![lagrida_latex_editor__74_](uploads/7ad505e13cf61943281e9f62418e7e26/lagrida_latex_editor__74_.png) the propagation time, ![lagrida_latex_editor__83_](uploads/9cc25f573f404c68b5001c37c22023f8/lagrida_latex_editor__83_.png) the bias of the receptor, ![lagrida_latex_editor__76_](uploads/a4480fac0d264f77733a7bb0458e0ca1/lagrida_latex_editor__76_.png) the bias of the satellite.
And the pseudo-distance between the satellite and the receptor ![lagrida_latex_editor__87_](uploads/cee25cb5eb25a1e4c0cc7d59f536673f/lagrida_latex_editor__87_.png) And the pseudo-distance between the satellite and the receptor ![lagrida_latex_editor__87_](uploads/cee25cb5eb25a1e4c0cc7d59f536673f/lagrida_latex_editor__87_.png)
......