The problem of estimating the position, velocity, and acceleration of an agile target from imperfect position measurements is addressed in this paper. A discrete sliding mode observer (DSMO) is used that can handle measurement inaccuracies apart from unmeasured disturbance inputs. The target acceleration input acts as an unmeasured disturbance input to the observer. The parameters of DSMO are derived considering the worst case measurement error and unmeasured disturbance inputs. The selected parameters guarantee the convergence of the error dynamics into the boundary layer and finite state estimation error within the boundary layer. A numerical simulation study is presented for the state estimation of a sinusoidally maneuvering target. Experimental results are presented for the state estimation of a target unmanned ground vehicle (UGV), with position information obtained from a camera mounted on an unmanned air vehicle (UAV).