A trajectory is a polygonal line consisting of the positions that a moving object occupies as time passes, and as such, it can be derived by periodically sampling the positions of the object. In this manner, and due to the proliferation of location-sensing devices, it has been possible to create large datasets of trajectories. Using these datasets it is possible to derive much information about the movement patterns of the objects. However, trajectory data is uncertain, and this can negatively impact the accuracy of data mining algorithms used to obtain the movement patterns of objects. One of the sources of trajectory uncertainty is the error inherent to GPS measurements, and another source relates to the fact that in practice many trajectories have sampling points that are on average too far in time, so it is difficult to determine its movement between points. In this paper, we propose a technique called TrajEstU that estimates the trajectory of a moving object in an unconstrained space. The algorithm is applied when there is uncertainty in trajectories due to measurement errors and/or low sampling rates. Experiments show that TrajEstU achieves up to 98% accuracy on real life and synthetic trajectory datasets.