The Sigma Point Class: The Gauss–Hermite Kalman Filter
Practical methods for one-dimensional Gauss–Hermite integration has its origins in the work of Wilf , as noted in the Numerical Recipes book , and the short but excellent paper by Ball . Unlike the methods addressed in the preceding chapters, Gauss–Hermite integration is a quadrature method that uses orthogonal polynomials instead of simple polynomials.
Consider the general multidimensional integral (5.60), rewritten here in more explicit form
Changing variables to remove the factor of 1/2 from the exponent, let
Thus, (11.1) becomes