8.1 One-Dimensional Finite Difference Kalman Filter
8.1.1 One-Dimensional Finite Difference State Prediction
The scalar derivation for the EKF state prediction equation in terms of was given in (7.10)), repeated here for clarity
As noted previously, this is accurate to third order in c.
Replacing the second-order derivative with its finite difference approximation from (2.47), (8.1) becomes
(8.2)
Gathering terms, this can be rewritten as
Let
so that
(8.5)
and define the finite difference evaluation points as
where
(8.7)
See Section 2.2 for an explanation of the notation . Using (8.4) and (8.6), (8.3) becomes
Replacing the continuous c defined in (7.3) with ...
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