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--- doc:lps:tdoa:principles [2018-11-05 17:35]
kristoffer
+++ doc:lps:tdoa:principles [2020-05-12 14:02] (current)
kimberly
@@ Line 1: / Line 1: @@
+<WRAP center round important 60%>
+This page has deprecated and moved to the new documentation framework of the main Bitcraze website. Please go to [[https://www.bitcraze.io/documentation/system/]]
+</WRAP>
 ====== Loco Positioning TDoA principles ======
@@ Line 75: / Line 79: @@
 ===== Geometry =====
-TODO
+The geometrical properties of TDoA limits the space where the position can be estimated with a reasonable accuracy.
+Consider an example set up where we have three anchors, A0, A1 and A2. This example is in 2D to make it easier to visualize, but the same principles are valid for 3D.
+In the first image the Crazyflie (Tag) is located at (0.0, -0.5). The lines where the TDoA is constant are drawn in the figure and the position is where the lines cross.
+For instance, the TDoA between anchors A0 and A1 is 0.44 (a bit closer to A0 than A1), this means that the Tag could be anywhere on the blue line. The yellow line
+shows possible positions based on the TDoA value between A0 and A2, while the green line is for TDoA between A1 and A2.
+{{:doc:lps:tdoa:in_convex_hull.jpeg?600|}}
+In the second image the Tag is further away, at (3.5, -0.3). Note how the lines showing the possible positions are close to parallel in the intersection point, making it
+harder to estimate a correct possition.
+{{:doc:lps:tdoa:outside_convex_hull.jpeg?600|}}
+The red lines shows the convex hull of the system, basically the space defined by the anchors. A good rule of thumb is that the accuracy of the estimated position is good withing
+the convex hull but deteriorates quickly when moving away outside.
+The measured TDoA values in a real system contains errors and all the TDoA curves will never cross in one single point. The estimated position used in a Tag is instead a point that is "as close as possible" to all the curves, a point where the total error is minimized.
+Read more about TDoA at:
+  * https://en.wikipedia.org/wiki/Multilateration
+  * http://mikehamer.info/assets/papers/Ledergerber,%20Hamer,%20DAndrea%20-%20IROS%202015.pdf

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