We present new finite-dimensional filters for estimating the state of Markov jump-linear systems, given noisy measurements of the Markov chain. Discrete-time as well as continuous-time models are considered. A robust version of the continuous-time filters is used to derive a discretization which links the continuous and discrete-time results. Simulations compare the robust discretization with direct numerical solutions of the filtering equations. The new filters have applications in the passive tracking of maneuvering targets.