Towards Precise Localisation : Subsample Methods, Efficient Estimation and Merging of Maps

Abstract: Over the last couple of years audio and radio sensors have become cheaper and more common in our everyday life. Such sensors can be used to form a network, from which one can obtain distance measures by correlating the different received signals. One example of such distance measures is time-difference of arrival measurements (TDoA), which can be used to estimate the positions of the senders and receivers. The result is a 3D map of the environment, similar to what you get from doing structure from motion (SfM) with images. If a new sensor appears, the map can in turn be used to determine the position of that sensor, i.e. for localisation. In this thesis we present three studies that take us towards precise localisation. Paper I involves finding exact — on a subsample level — TDoA measurements. These types of subsample refinements give a higher precision, but are sensitive to noise. We present an explicit expression for the variance of the TDoA estimate and study the impact that noise in the signals have. In Paper III TDoA measurements are used to estimate sender and receiver positions in an efficient way. We present a new initialisation approach followed by a scheme for performing local optimisation for TDoA data with constant offset, i.e. when the sound events are repetitive with some constant period. The sender and receiver positions together constitute a map of the environment and such maps are studied in Paper II. Assuming that we have a number of different map representations of the same environment — coming from either sound, radio or image data — we present an algorithm for how to merge these representations into one map, in an efficient way using only a small memory footprint representation. The final map has a higher precision and the method can also be used to detect changes that have occurred between the creation of the different map representations. Thus, altogether, we present a number of improvements of the localisation process. We perform analysis as well as experimental evaluation of each of these improvements.