Fingerprinting based localisation systems rely on taking a radio map of the environment and determine the position of the device by comparing this map to its current measurements. Therefore the performance of any such system heavily relies on the accuracy of this comparison. Typically two problems arise: first, access points can be missed in a scanning cycle both during the fingerprinting phase as well as during the localisation phase and second, if different devices are used for fingerprinting and for localisation their received signal strengths might not be the same due to differing antenna attenuation. A successful comparison function has to cope with both of these issues yielding repeatable high likelihoods for measurements taken in the same location while at the same time providing sufficiently high discrimination for measurements taken in different locations. In this paper we will propose such a likelihood observation function based on rigorous assumptions. Like most approaches we will compare RSSI values based on squared Euclidean distance of the log energies, which is essentially a Gaussian assumption on the distribution of the measurement error justifiable by arguments like maximum entropy or the law of large numbers acting on multiple additive error sources. However, this naive approach suffers from the varying dimensionality of the log-energy space caused by missing access points in the measurement. In order to overcome this in a rigorous manner we propose to model the access point pickup probabilities using Gibbs distributions enabling the introduction of rigorously motivated penalties for these dimension mismatches. As a further extension of the likelihood observation function we also propose to make it invariant to differences in antenna attenuation by estimating these explicitly from the log-energy observations and using the minimised squared observation residuals as invariant distance measure instead. We will discuss the properties of this improved likelihood observation function and compare its performance in a particle filter based WiFi localisation system.

WiFi localisation has become very popular in recent years. Most widely used are fingerprinting based techniques where a map of received signal strengths is used to infer the position based on comparing the current signal strength measurement to this map. Most research focuses on this inference itself and on the creation of accurate fingerprinting maps. In this paper we will not address those issues in depth but focus on analysing the fingerprint maps themselves in more detail. By looking closely into the maximum likelihood estimation for the position we will derive its expected uncertainty and show that it can be calculated for every possible position in advance from the fingerprint maps alone. This allows to derive an expected localisation accuracy map of the environment that can be used to assess and optimise the WiFi design based on localisation accuracy needs rather than relying on given access point placements solely based on coverage or signal-to-noise criteria.

When rotating a pinhole camera, images are related by the infinite homography KRK-1, which is algebraically a conjugate rotation. Although being a very common image transformation, e.g. important for self-calibration or panoramic image mosaicing, it is not completely understood yet. We show that a conjugate rotation has 7 degrees of freedom (as opposed to 8 for a general homography) and give a minimal parameterization. To estimate the conjugate rotation, authors traditionally made use of point correspondences, which can be seen as local zero order Taylor approximations to the image transformation. Recently however, affine feature correspondences have become increasingly popular. We observe that each such affine correspondence now provides a local first order Taylor approximation, which has not been exploited in the context of geometry estimation before. Using those two novel concepts above, we finally show that it is possible to estimate a conjugate rotation from a single affine feature correspondence under the assumption of square pixels and zero skew. As a byproduct, the proposed algorithm directly yields rotation, focal length and principal point.

Recently real-time active 3D range cameras based on time-of-flight technology (PMD) have become available. Those cameras can be considered as a competing technique for stereo-vision based surface reconstruction. Since those systems directly yield accurate 3d measurements, they can be used for benchmarking vision based approaches, especially in highly dynamic environments. Therefore, a comparative study of the two approaches is relevant. In this work the achievable accuracy of the two techniques, PMD and stereo, is compared on the basis of patch-let estimation. As patchlet we define an oriented small planar 3d patch with associated surface normal. Least-squares estimation schemes for estimating patchlets from PMD range images as well as from a pair of stereo images are derived. It is shown, how the achivable accuracy can be estimated for both systems. Experiments under optimal conditions for both systems are performed and the achievable accuracies are compared. It has been found that the PMD system outperformed the stereo system in terms of achievable accuracy for distance measurements, while the estimation of normal direction is comparable for both systems.