Precise positioning in urban canyons : applied to the localisation of buried assets

The last decades have seen the applications related to Global Positioning Systems (GPS) flourishing in various and unrelated ways such as car navigation, electronic advertisement, military defense (e.g. missile tracking) ... etc. The increasing consumers interest in positioning market is also due to the recent coupling of mobile phone and GPS technologies which is deemed to kick-off the location based services market (LBS). The LBS market are electronic services for providing information that has been created, compiled, selected or filtered taking into consideration the current locations of the users or those of other persons or mobile objects. Analysts foresee that these services will open a new era of mass consumption market where all positioning technologies will play a key role. The level of positioning accuracy (e.g. 1 cm or 1 m) will be a service that the user may order from his mobile phone, laptop or other devices. In this background, the aim of the conducted research is to locate accurately buried pipes in built up areas using GPS and other positioning technologies. This work should be considered as an attempt to solve the general problem: positioning accurately everywhere and every time. Thus, the research work undertaken at the University of Nottingham Institute of Engineering Surveying and Space Geodesy (IESSG) focused on the integration of GPS with other existing technologies (e.g. signal from cellular networks). Algorithms are developed and then tested through simulations. The results showed that the integration of the GPS and GSM technologies may provide a position accuracy of a user no better than 20 m. The main issue is the lack of synchronisation between the two technologies. In a second part, a network of ground-based transceivers called LOCATA is introduced and studied in detail with statistics on the residual of the signal (e.g. multipath, fading) and the time series of the rover's position. Results were averaged on various environments (e.g. downs, urban canyons). The overall results showed that it is possible to locate the LOCATA rover better than 5 cm in 3D and better than 2 cm in 2D in both urban and open field scenarios. However some unwanted phenomena (interferences) were found which degraded the performances of this new technology (from a few centimetres to tens of centimetres). Finally, the LOCATA prototype was studied beyond its actual capabilities (at the time of writing this thesis) via simulations of the coupling with GPS technology. Results were extracted from a simulator and the statistics calculated from the data collected in the previous chapters. It gave a proof that the LOCATA-GPS technology may achieve the centimetre level in the urban canyons (in 3D)

GPS Vertical Land Motion Corrections to Sea-Level Rise Estimates in the Pacific Northwest

We construct coastal Pacific Northwest profiles of vertical land motion (VLM) known to bias long-term tide-gauge measurements of sea-level rise (SLR) and use them to estimate absolute sea-level rise with respect to Earth’s center of mass. Multidecade GPS measurements at 47 coastal stations along the Cascadia subduction zone show VLM varies regionally but smoothly along the Pacific coast and inland Puget Sound with rates ranging from +4.9 to –1.2 mm/yr. Puget Sound VLM is characterized by uniform subsidence at relatively slow rates of +0.1 to –0.3 mm/yr. Uplift rates of 4.5 mm/yr persist along the western Olympic Peninsula of northwestern Washington State and decrease southward becoming nearly 0 mm/yr south of central coastal Washington through Cape Blanco, Oregon. South of Cape Blanco, uplift increases to 1–2 mm/yr, peaks at 4 mm/yr near Crescent City, California, and returns to zero at Cape Mendocino, California. Using various stochastic noise models, we estimate long-term (~50–100 yr) relative sea-level rise rates at 18 coastal Cascadia tide gauges and correct them for VLM. Uncorrected SLR rates are scattered, ranging between –2 mm/yr and + 5 mm/yr with mean 0:52±1:59 mm/yr, whereas correcting for VLM increases the mean value to 1.99 mm/yr and reduces the uncertainty to ±1:18 mm/yr, commensurate with, but approximately 17% higher than, twentieth century global mean

The Generalized Method of Wavelet Moments with Exogenous Inputs: a Fast Approach for the Analysis of GNSS Position Time Series

The Global Navigation Satellite System (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow studying global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogeneous variable: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used Maximum Likelihood Estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach has important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations quickly becomes computationally prohibitive. Compared to standard methods, the processing time of the GMWMX is over $1000$ times faster and allows the estimation of large scale problems within minutes on a standard computer. We validate the performances of our method via Monte-Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power-law or Mat\'ern processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.Comment: 30 pages, 11 figures, 3 table

Estimation of offsets in GPS time-series and application to the detection of earthquake deformation in the far-field

Extracting geophysical signals from Global Positioning System (GPS) coordinate time-series is a well-established practice that has led to great insights into how the Earth deforms. Often small discontinuities are found in such time-series and are traceable to either broad-scale deformation (i.e. earthquakes) or discontinuities due to equipment changes and/or failures. Estimating these offsets accurately enables the identification of coseismic deformation estimates in the former case, and the removal of unwanted signals in the latter case which then allows tectonic rates to be estimated more accurately. We develop a method to estimate accurately discontinuities in time series of GPS positions at specified epochs, based on a so-called ‘offset series’. The offset series are obtained by varying the amount of GPS data before and after an event while estimating the offset. Two methods, a mean and a weighted mean method, are then investigated to produce the estimated discontinuity from the offset series. The mean method estimates coseismic offsets without making assumptions about geophysical processes that may be present in the data (i.e. tectonic rate, seasonal variations), whereas the weighted mean method includes estimating coseismic offsets with a model of these processes. We investigate which approach is the most appropriate given certain lengths of available data and noise within the time-series themselves. For the Sumatra–Andaman event, with 4.5 yr of pre-event data, we show that between 2 and 3 yr of post-event data are required to produce accurate offset estimates with the weighted mean method. With less data, the mean method should be used, but the uncertainties of the estimated discontinuity are larger

Spatial Variations of Stochastic Noise Properties in GPS Time Series

The noise in position time series of 568 GPS (Global Position System) stations across North America with an observation span of ten years has been investigated using solutions from two processing centers, namely, the Pacific Northwest Geodetic Array (PANGA) and New Mexico Tech (NMT). It is well known that in the frequency domain, the noise exhibits a power-law behavior with a spectral index of around −1. By fitting various noise models to the observations and selecting the most likely one, we demonstrate that the spectral index in some regions flattens to zero at long periods while in other regions it is closer to −2. This has a significant impact on the estimated linear rate since flattening of the power spectral density roughly halves the uncertainty of the estimated tectonic rate while random walk doubles it. Our noise model selection is based on the highest log-likelihood value, and the Akaike and Bayesian Information Criteria to reduce the probability of over selecting noise models with many parameters. Finally, the noise in position time series also depends on the stability of the monument on which the GPS antenna is installed. We corroborate previous results that deep-drilled brace monuments produce smaller uncertainties than concrete piers. However, if at each site the optimal noise model is used, the differences become smaller due to the fact that many concrete piers are located in tectonic/seismic quiet areas. Thus, for the predicted performance of a new GPS network, not only the type of monument but also the noise properties of the region need to be taken into account

Sea Level Rise Estimation on the Pacific Coast from Southern California to Vancouver Island

Previous studies have estimated the sea level rise (SLR) at various locations on the west coast of the USA and Vancouver Island in Canada. Here, we construct an entire SLR profile from Vancouver Island in the Pacific Northwest to San Diego in Southern California. First, we process global navigation satellite system (GNSS) measurements at 405 stations blanketing the whole coast to generate a profile of vertical land motion (VLM) known to bias century-long tide gauge (TG) measurements recording relative SLR (RSLR). We are then able to estimate the absolute SLR (ASLR) by correcting the SLR with the VLM. Our study emphasizes the relationship between the various tectonic movements (i.e., the Cascadia subduction zone, the San Andreas strike-slip fault system) along the Pacific coast which renders it difficult to accurately estimate the SLR. That is why we precisely model the stochastic noise of both GNSS and tide gauge time series using a combination of various models and information criterions (ICs). We also use the latest altimetry products and sea surface height (SSH) to compare it with ASLR at the same location as the TGs. This study supports previous analysis that the power law + white noise and generalized Gauss–Markov + white noise models are the best stochastic noise models for the GNSS time series. The new coastal profile confirms the large variability of VLM estimates in the Pacific Northwest around the Cascadia subduction zone in agreement with previous studies, and a similar result when the San Andreas fault comes onshore in Central California (San Francisco Bay). Negative RSLR values are mostly located in the Pacific Northwest (Vancouver Island and Olympic Peninsula). We also observe a much bigger variation (about 90–150%) of the ASLR in the Pacific Northwest which is predominantly due to glacial isostatic adjustment (GIA). Moreover, the comparison between the ASLR and the SSH estimates shows similarities in the center of the studied area (South Washington, Oregon planes, and some parts of Southern California) where the tectonic activity does not significantly influence the TG measurements. Finally, the twentieth-century satellite geocentric ocean height rates show a global mean of 1.5 to 1.9 mm/yr. Our estimates based on ASLR and SSH are within this interval

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author has introduced the notion of energy spaces included in the Schwartz space S-(R). In this model, the key is to look at which ones of these subspaces are reduced to {0} with the help of energy operators ( and generalized energy operators). It leads to define additional solutions for a nominated PDE. Beyond that, this work intends to develop the concept of multiplicity of solutions for a linear PDE through the study of these energy spaces (i.e. emptiness). The main concept is that the PDE is viewed as a generator of solutions rather than the classical way of solving the given equation with a known form of the solutions together with boundary conditions. The theory is applied to the wave equation with the special case of the evanescent waves. The work ends with a discussion on another concept, the duplication of solutions and some applications in a closed cavity

Precise positioning in urban canyons : applied to the localisation of buried assets

The last decades have seen the applications related to Global Positioning Systems (GPS) flourishing in various and unrelated ways such as car navigation, electronic advertisement, military defense (e.g. missile tracking) ... etc. The increasing consumers interest in positioning market is also due to the recent coupling of mobile phone and GPS technologies which is deemed to kick-off the location based services market (LBS). The LBS market are electronic services for providing information that has been created, compiled, selected or filtered taking into consideration the current locations of the users or those of other persons or mobile objects. Analysts foresee that these services will open a new era of mass consumption market where all positioning technologies will play a key role. The level of positioning accuracy (e.g. 1 cm or 1 m) will be a service that the user may order from his mobile phone, laptop or other devices. In this background, the aim of the conducted research is to locate accurately buried pipes in built up areas using GPS and other positioning technologies. This work should be considered as an attempt to solve the general problem: positioning accurately everywhere and every time. Thus, the research work undertaken at the University of Nottingham Institute of Engineering Surveying and Space Geodesy (IESSG) focused on the integration of GPS with other existing technologies (e.g. signal from cellular networks). Algorithms are developed and then tested through simulations. The results showed that the integration of the GPS and GSM technologies may provide a position accuracy of a user no better than 20 m. The main issue is the lack of synchronisation between the two technologies. In a second part, a network of ground-based transceivers called LOCATA is introduced and studied in detail with statistics on the residual of the signal (e.g. multipath, fading) and the time series of the rover's position. Results were averaged on various environments (e.g. downs, urban canyons). The overall results showed that it is possible to locate the LOCATA rover better than 5 cm in 3D and better than 2 cm in 2D in both urban and open field scenarios. However some unwanted phenomena (interferences) were found which degraded the performances of this new technology (from a few centimetres to tens of centimetres). Finally, the LOCATA prototype was studied beyond its actual capabilities (at the time of writing this thesis) via simulations of the coupling with GPS technology. Results were extracted from a simulator and the statistics calculated from the data collected in the previous chapters. It gave a proof that the LOCATA-GPS technology may achieve the centimetre level in the urban canyons (in 3D)

Covariance matrix analysis for higher order fractional Brownian motion time series

Fractional Brownian motion (fBm) is an important mathematical model for describing a range of phenomena and processes. The properties of discrete time fBm (dfBm) when m equals 1 and 2 have been reported in the literature. This paper focuses on analysis of auto-covariance matrix of the m-th order (m \u3e 2) of a dfBm process and the error associated with the approximation of a large dimensional auto-covariance matrix. Applying matrix theory and analysis, we also generalize the asymptotic properties of the eigenvalues of the auto-covariance matrix. Based on the analysis, two theorems and one lemma are proposed and their proofs are provided. Your goal is to simulate, as closely as possible, the usual appearance of typeset papers. This document provides an example of the desired layout and contains information regarding desktop publishing format, type sizes, and type faces