This paper introduces a new concept for tracking closely spaced targets in Cartesian space based on position measurements corrupted with additive Gaussian noise. The basic idea is to select a special state representation that eliminates the target identity and avoids the explicit evaluation of association probabilities. One major advantage of this approach is that the resulting likelihood function for this special problem is unimodal. Hence, it is especially suitable for closely spaced targets. The resulting estimation problem can be tackled with a standard nonlinear estimator. In this work, we focus on two targets in two-dimensional Cartesian space. The Cartesian coordinates of the targets are represented by means of extreme values, i.e., minima and maxima. Simulation results demonstrate the feasibility of the new approach.