The current development of ultra-wide band localization systems focuses on reducing the number of infrastructure nodes (anchors). In certain areas and applications the full three-dimensional position is not necessary and thus constraining the solution brings an opportunity to use fewer anchors. In this work soft-constraining of lateral and vertical position component for time difference of arrival positioning in a corridor-like scenario is presented. Implementation in extended and unscented Kalman filter solvers is described. The test in real environment suggests that the constraints enable reliable along-track position estimation even with two or three anchors in sight, the accuracy is better than 30 cm (RMS). Moreover, the soft nature of constraint allow for uncertainty in the constraint definition.