Chapter 10

The Sigma Point Class: The Spherical Simplex Kalman Filter

For the UKF, with the exception of the integration point at the origin, the vector integration points used for the moment integrations (9.9)–(9.11) are symmetrical about 0, equidistant from the origin, and fall on the axes of an n_{x}-dimensional Cartesian coordinate system. For the spherical simplex Kalman filter, we replace the requirement for symmetry about the origin with a requirement that all vector points be equidistant from the origin and from each other, thus lying at the vertices of an n_{x}-dimensional simplex (see Figure 2.4). This integration rule was first proposed by Julier [10Julier].

Let the integration (sigma) points be redefined as All of these simplex vector points c_{j} must satisfy the moment equations (9.9)–(9.11), repeated here for clarity