11.2 One-Dimensional Gauss–Hermite Kalman Filter

For one dimension, (11.4) becomes

(11.52) equation

where

(11.53) equation

or

(11.54) equation

Using (11.49) in (11.54) yields the one-dimensional Gauss–Hermite sigma points

(11.55) equation

In addition, we can write

(11.56) equation

and (11.52) now becomes

(11.57) equation

and finally, because the integral over the density function equals one, (11.57) reduces to

(11.58) equation

Using (11.58), the one-dimensional state prediction equation (5.51) now becomes

(11.59) equation

where

(11.60) equation

with

(11.61) equation

For the one-dimensional ...

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