Bayesian Estimation and Tracking: A Practical Guide

10.2 Two-Dimensional Spherical Simplex Sigma Points

For the two-dimensional case, consider the vector points at the vertices of the simplex shown in Figure 10.1. In this equilateral triangle, all sides and angles are equal and all integration points are equidistant from the point at the origin. For this 2D case, the vector integration points are the set (c₀, c₁, c₂, c₃) = . Here, s₃ is a scale factor that will be determined below.

Figure 10.1 Depiction of a two-dimensional simplex with four vector integration points.

Once again, the moment equations (10.1)–(10.3) must be satisfied. Thus, from (10.1) it follows that

(10.17)

and (10.2) results in

(10.18)

(10.19)

Finally, (10.3) leads to

(10.20)

which reduces to the set of equations

(10.21)

(10.22)

From (10.18) it follows that

(10.23)