Parametric Estimation of Harmonically Related Sinusoids

Mud-pulse telemetry is a method used for measurement-while-drilling (MWD)in the oil industry. The telemetry signals are corrupted by spurious mud pump noise consisting of a large number of harmonically related sinusoids. In order to denoise the signal, the noise parameters have to be tracked accurately in real time. There are well established parametric estimation techniques for determining various parameters of independent sinusoids. The iterative methods based on the linear prediction properties of the sinusoids provide a computationally e±cient way of solving the non linear optimization problem presented by these methods. However, owing to the large number of these sinusoids, incorporating the harmonic relationship in the problem becomes important. This thesis is aimed at solving the problem of estimating parameters of harmonically related sinusoids. We examine the efficacy of IQML algorithm in estimating the parameters of the telemetry signal for varying SNRs and data lengths. The IQML algorithm proves quite robust and successfully tracks both stationary and slowly varying frequency signals. Later, we propose an algorithm for fundamental frequency estimation which relies on the initial harmonic frequency estimate. The results of tests performed on synthetic data that imitates real field data are presented. The analysis of the simulation results shows that the proposed method manages to remove noise causing sinusoids in the telemetry signal to a great extent. The low computational complexity of the algorithm also makes for an easy implementation on field where computational power is limited

An empirical behavioral model of liquidity and volatility

We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are validated against real data. Our empirical studies of order flow uncover several interesting regularities in the way trading orders are placed and cancelled. The resulting simple model of order flow is used to simulate price formation under a continuous double auction, and the statistical properties of the resulting simulated sequence of prices are compared to those of real data. The model is constructed using one stock (AZN) and tested on 24 other stocks. For low volatility, small tick size stocks (called Group I) the predictions are very good, but for stocks outside Group I they are not good. For Group I, the model predicts the correct magnitude and functional form of the distribution of the volatility and the bid-ask spread, without adjusting any parameters based on prices. This suggests that at least for Group I stocks, the volatility and heavy tails of prices are related to market microstructure effects, and supports the hypothesis that, at least on short time scales, the large fluctuations of absolute returns are well described by a power law with an exponent that varies from stock to stock

A statistical framework for recovering intensity mapping autocorrelations from crosscorrelations

Intensity mapping experiments will soon have surveyed large swathes of the sky, providing information about the underlying matter distribution of the early universe. The resulting maps can be used to recover statistical information, such as the power spectrum, about the measured spectral lines (for example, HI, [CII], and [OIII]). However precise power spectrum measurements, such as the 21 cm autocorrelation, continue to be challenged by the presence of bright foregrounds and non-trivial systematics. By crosscorrelating different data sets, it may be possible to mitigate the effects of both foreground uncertainty and uncorrelated instrumental systematics. Beyond their own merit, crosscorrelations could also be used to recover autocorrelation information. Such a technique was proposed in Beane et al. (2019) for recovering the 21 cm power spectrum. Generalizing their result, we develop a statistical framework for combining multiple crosscorrelation signals in order to infer information about the corresponding autocorrelations. We do this first within the Least Squares Estimator (LSE) framework, and show how one can derive their estimator, along with several alternative estimators. We also investigate the posterior distribution of recovered autocorrelation and associated model parameters. We find that for certain noise regimes and cosmological signal modeling assumptions this procedure is effective at recovering autospectra from a set of crosscorrelations. Finally, we showcase our framework in the context of several near-future line intensity mapping experiments.Comment: 18 pages, 13 figures, to be submitted to MNRA

Low-frequency gravitational-wave science with eLISA/NGO

We review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultracompact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISA's high signal-to-noise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.Comment: 20 pages, 8 figures, proceedings of the 9th Amaldi Conference on Gravitational Waves. Final journal version. For a longer exposition of the eLISA science case, see http://arxiv.org/abs/1201.362

Passive mode-locking theory for conventional and colliding-pulse lasers

Imperial Users onl

A state space approach to chemical plant fault detection

Imperial Users onl

A statistical model of internet traffic.

PhDWe present a method to extract a time series (Number of Active Requests (NAR)) from web cache logs which serves as a transport level measurement of internet traffic. This series also reflects the performance or Quality of Service of a web cache. Using time series modelling, we interpret the properties of this kind of internet traffic and its effect on the performance perceived by the cache user. Our preliminary analysis of NAR concludes that this dataset is suggestive of a long-memory self-similar process but is not heavy-tailed. Having carried out more in-depth analysis, we propose a three stage modelling process of the time series: (i) a power transformation to normalise the data, (ii) a polynomial fit to approximate the general trend and (iii) a modelling of the residuals from the polynomial fit. We analyse the polynomial and show that the residual dataset may be modelled as a FARIMA(p, d, q) process. Finally, we use Canonical Variate Analysis to determine the most significant defining properties of our measurements and draw conclusions to categorise the differences in traffic properties between the various caches studied. We show that the strongest illustration of differences between the caches is shown by the short memory parameters of the FARIMA fit. We compare the differences revealed between our studied caches and draw conclusions on them. Several programs have been written in Perl and S programming languages for this analysis including totalqd.pl for NAR calculation, fullanalysis for general statistical analysis of the data and armamodel for FARIMA modelling