An important issue in nonlinear dynamics is the optimal estimation and detection of the partially observed states of a system at low signal‐to‐noise ratios. In this paper, we will outline a Bayesian‐based approach that allows for the optimal determination of the state probability density function in time as a function of the observations. This leads to optimal detector designs based on the notion of generalized innovation sequences. Here, the density functions are defined over a computational grid which is designed to capture the phase space dynamics of the nonlinear system. Partial measurements are used to update the projected system state and density function. Estimation and detection decisions are based on the propagated density functions. ©1996 American Institute of Physics.