10.1 One-Dimensional Spherical Simplex Sigma Points
Consider the one-dimensional case (nx = 1) with three arbitrary points along a line at points (c0, c1, c2) = (0, q1, − q2), as shown in Figure 2.4. Inserting these points into the moment equations yields the set of equations
Noting that the vector points must be equidistant from the origin, making q2 = q1, from (10.5) it follows immediately that
(10.7)
From (10.4) we obtain
(10.8)
Now from (10.6)
(10.9)
Thus, for the 1D case, the sigma points are defined by
(10.10)
with the weights
(10.11)
(10.12)
(10.13)
Remembering ...
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