Methods for estimating a conditional probability distribution for signal states of a non-linear random dynamic process. The filter is based on multiple particles, each defined by a state space model similar to the dynamic process. Each particle is updated on the basis of a control input derived by proportional gain feedback on an innovation process. The innovation process is the difference between an increment in an observed quantity measured by one or more sensors and an average of a function of the particles. The particle filter of the invention may also be applied to filtering problems with data association uncertainty where multiple measurements are obtained, of which at most one originates from a specified target.