Bayesian Estimation and Tracking: A Practical Guide

10.1 One-Dimensional Spherical Simplex Sigma Points

Consider the one-dimensional case (n_x = 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)

(10.5)

(10.6)

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 ...