Minimax quadratic filtering of uncertain linear stochastic systems with partial fourth-order information

A minimax filtering problem for a class of uncertain linear stochastic syst ems is studied. Uncertainties involving fourth-order moments of the noise d istribution and of the initial state are considered. Under the hypothesis t hat the second-order statistics are known (hence the linear filter is avail able) the quadratic minimax filter is found. Moreover, it is shown that the minimax filter gives a worst case error variance even less than the exact error variance of the linear filter. Numerical simulations show that this i mprovement is meaningful also in cases of "great uncertainty" regarding the higher order statistics.