The Tactile Internet (TI) aims to expand seamless interaction over the Internet by providing a new form of interaction through touch by providing haptic feedback. To realize this, the TI is limited by a round-trip latency of 1-10 ms, meaning that the TI is limited by a physical distance of 1500 km. A workaround to this requirement is the introduction of local simulations. To keep track of moving objects in these simulations, a stable tracking algorithm is needed. This algorithm is provided in the form of a particle filter. The TI requires high tracking accuracy from this algorithm, but to achieve that the algorithm becomes computationally expensive. If the movement of the to-be-tracked object is known a priori, however, the particle filter can be adapted to focus only on that movement, neglecting the other directions. This increases tracking accuracy with an equal amount of samples, thus requiring a lower amount of samples to achieve the same accuracy, reducing computational power. This paper explores how to achieve this adaptation and analyses the increase in accuracy. By adapting the filter, the tracking accuracy is significantly increased, even with a lower number of samples. This results in gaining a speedup with a factor of about $36$, while having similar tracking accuracy.