A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering

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.