Thepartially observableMarkovdecision process (POMDP) provides ageneral framework for modeling an agent's decision process with state uncertainty, and online planning plays a pivotal role in solving it. A belief is a distribution of states representing state uncertainty. Methods forlarge-scale POMDP problems rely on the same idea of sampling both states and observations.

Localisation in GPS-denied environments is challenging and many existing solutions have infrastructural and on-site calibration requirements. This paper tackles these challenges by proposing a localisation system that is infrastructure-free and does not require on-site calibration, using a single active PTZ camera to detect, track and localise a circular LED marker. We propose to use a CNN trained using only synthetic images to detect the LED marker as an ellipse and show that our approach is more robust than using traditional ellipse detection without requiring tuning of parameters for feature extraction. We also propose to leverage the predicted elliptical angle as a measure of uncertainty of the CNN's predictions and show how it can be used in a filter to improve marker range estimation and 3D localisation. We evaluate our system's performance through localisation of a UAV in real-world flight experiments and show that it can outperform alternative methods for localisation in GPS-denied environments. We also demonstrate our system's performance in indoor and outdoor environments.

Over the last years, particle filters have been applied with great success to a variety of state estimation problems. We present a statistical approach to increasing the efficiency of particle filters by adapting the size of sample sets on-the-fly. The key idea of the KLD-sampling method is to bound the approximation error introduced by the sample-based representation of the particle filter. The name KLD-sampling is due to the fact that we measure the approximation error by the Kullback-Leibler distance. Our adaptation approach chooses a small number of samples if the density is focused on a small part of the state space, and it chooses a large number of samples if the state uncertainty is high.