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

(10.4) equation

(10.5) equation

(10.6) equation

Noting that the vector points must be equidistant from the origin, making q2 = q1, from (10.5) it follows immediately that

(10.7) equation

From (10.4) we obtain

(10.8) equation

Now from (10.6)

(10.9) equation

Thus, for the 1D case, the sigma points are defined by

(10.10) equation

with the weights

(10.11) equation

(10.12) equation

(10.13)

Remembering ...

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