Wh. Fleming et Wm. Mceneaney, A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering, SIAM J CON, 38(3), 2000, pp. 683-710
The Hamilton-Jacobi-Bellman (HJB) equation associated with the robust/H-inf
inity filter (as well as the Mortensen filter) is considered. These filters
employ a model where the disturbances have finite power. The HJB equation
for the filter information state is a first-order equation with a term that
is quadratic in the gradient. Yet the solution operator is linear in the m
ax-plus algebra. This property is exploited by the development of a numeric
al algorithm where the effect of the solution operator on a set of basis fu
nctions is computed off-line. The precomputed solutions are stored as vecto
rs of coefficients of the basis functions. These coefficients are then used
directly in the real-time computations.