Tracking a moving object like a ship, vehicle, aircraft or even an animal or human is challenging especially when given only noisy observations of the path. To successfully track such an object the method used needs to infer the unknown information, for example the acceleration, from noisy position data. Here we present such a method based on a shadowing filter algorithm. In comparison with other filters such as Kalman and Particle filters the shadowing filter solves the tracking problem based on deterministic dynamics instead of statistics. The algorithm presented shows how to track rigid bodies having an unknown moment of inertia and we validate the performance of the filter and explore how the two important parameters of the filter impact on its performance.