
Mixture Kalman Filters and Beyond 557
where h
map
(x
k
), depends only on the position component of the state, i.e., ,
the nonlinear part of the model. Furthermore, w
n
k
≡ 0 (i.e., , no process noise
enters directly on the nonlinear part), w
l
k
= w
k
, and e
k
is the same a s in the
original problem formulation.
A more accura te measurement noise model would also consider secondary
reflections (e.g., from the tree canopies), resulting in a bi-modal Gaussian
mixture representation. This could provide further structure to the problem.
This application has been studied extensively in [5, 31].
26.7 Approximate Rao-Blackwellized Nonlinear
Filtering
The implementation