When the primary measurement sensor is passive in nature--by which we mean that it does not directly measure range or range rate--there are well-documented challenges for target state estimation. Most estimation schemes rely on variations of the Extended Kalman Filter (EKF), which, in certain situations, suffer from divergence and/or covariance collapse. For this and other reasons, we believe that the Kalman filter is fundamentally ill-suited to the problems that are inherent in target state estimation using passive sensors. As an alternative, we propose a bounded-error (or set-membership) approach to the target state estimation problem. Such estimators are nearly as old as the Kalman filter, but have enjoyed much less attention. In this study we develop a practical estimator that bounds the target states, and apply it to the two-dimensional case of a submarine tracking a surface vessel, which is commonly referred to as Target Motion Analysis (TMA). The estimator is robust in the sense that the true target state does not escape the determined bounds; and the estimator is not unduly pessimistic in the sense that the bounds are not wider than the situation dictates. The estimator is--as is the problem itself--nonlinear and geometric in nature. In part, the simplicity of the estimator is maintained by using redundant states to parameterize the target's velocity. These redundant states also simplify the incorporation of other measurements that are frequently available to the system. The estimator's performance is assessed in a series of simulations and the results are analyzed. Extensions of the algorithm are considered.