11.3 Multidimensional Gauss–Hermite Kalman Filter
Constructing multidimensional orthogonal polynomial integration rules can be a difficult task if one first attempts to construct interpolative multidimensional polynomials. The simplest method of constructing multidimensional cubature rules is to form product rules from one-dimensional integration rules. Consider first a two-dimensional case where 
and we expand 
as the double sum
where 
and 
are defined by (11.50) and 
and 
are defined by (11.49). The double sum in (11.69) can be converted into the single sum indexed over 
by forming the ...
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