Bayesian Estimation and Tracking: A Practical Guide

2.2 Vector Point Generators

In the discussions on sigma point Kalman filters (Chapters 8–12), we will make use of a simplifying notation for the generation of the vector sigma points that are used for multidimensional numerical integration.

We define the n-dimensional vector generator function

(2.21)

where 0 ≤ u_i ≤ u_j if i ≤ j [2, 3]. In this notation, specifies the dimension of the vector points generated by u and it is understood that u_i represents ±u_i. Such a generator will be denoted as either

(2.22)

or

(2.23)

where , with the zero coordinates suppressed for convenience. This notation represents the set of k multidimensional vector points that can be generated from u by permutations and changing the sign of some coordinates.

In Part II, we will be considering rules for multidimensional integration of Gaussian-weighted integrals. Our numerical solutions will involve the evaluation of nonlinear functions at sets of vector points that consist of a constant times a set of vector points ...