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

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

Metallicity of M dwarfs III. Planet-metallicity and planet-stellar mass correlations of the HARPS GTO M dwarf sample

Aims. The aim of this work is the study of the planet-metallicity and the planet-stellar mass correlations for M dwarfs from the HARPS GTO M dwarf subsample Methods. We use a new method that takes advantage of the HARPS high-resolution spectra to increase the precision of metallicity, using previous photometric calibrations of [Fe/H] and effective temperature as starting values. Results. In this work we use our new calibration (rms = 0.08 dex) to study the planet-metallicity relation of our sample. The well-known correlation for Giant planet FGKM hosts with metallicity is present. Regarding Neptunians and smaller hosts no correlation is found but there is a hint that an anti-correlation with [Fe/H] may exist. We combined our sample with the California Planet Survey late-K and M-type dwarf sample to increase our statistics but found no new trends. We fitted a power law to the frequency histogram of the Jovian hosts for our sample and for the combined sample, f_p = C10^\alpha[Fe/H], using two different approaches: a direct bin fitting and a bayesian fitting procedure. We obtained a value for C between 0.02 and 0.04 and for \alpha between 1.26 and 2.94. Regarding stellar mass, an hypothetical correlation with planets was discovered, but was found to be the result of a detection bias.Comment: Accepted for publication in A&A. 18 pages, 11 Figures, 12 Table

The impact of uncertainty in satellite data on the assessment of flood inundation models

The performance of flood inundation models is often assessed using satellite observed data; however these data have inherent uncertainty. In this study we assess the impact of this uncertainty when calibrating a flood inundation model (LISFLOOD-FP) for a flood event in December 2006 on the River Dee, North Wales, UK. The flood extent is delineated from an ERS-2 SAR image of the event using an active contour model (snake), and water levels at the flood margin calculated through intersection of the shoreline vector with LiDAR topographic data. Gauged water levels are used to create a reference water surface slope for comparison with the satellite-derived water levels. Residuals between the satellite observed data points and those from the reference line are spatially clustered into groups of similar values. We show that model calibration achieved using pattern matching of observed and predicted flood extent is negatively influenced by this spatial dependency in the data. By contrast, model calibration using water elevations produces realistic calibrated optimum friction parameters even when spatial dependency is present. To test the impact of removing spatial dependency a new method of evaluating flood inundation model performance is developed by using multiple random subsamples of the water surface elevation data points. By testing for spatial dependency using Moran’s I, multiple subsamples of water elevations that have no significant spatial dependency are selected. The model is then calibrated against these data and the results averaged. This gives a near identical result to calibration using spatially dependent data, but has the advantage of being a statistically robust assessment of model performance in which we can have more confidence. Moreover, by using the variations found in the subsamples of the observed data it is possible to assess the effects of observational uncertainty on the assessment of flooding risk

The Limit of Finite-Sample Size and a Problem with Subsampling

This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a nuisance parameter or the parameter of interest. The paper shows that subsample, b_nAsymptotic size, b

Consistent testing for stochastic dominance: a subsampling approach

We propose a procedure for estimating the critical values of the extended Kolmogorov- Smirnov tests of First and Second Order Stochastic Dominance in the general K-prospect case. We allow for the observations to be serially dependent and, for the …rst time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent and powerful against some N¡1=2 local alternatives. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably.