Matrix Pencil method as a signal processing technique performance and application on power systems signals

Master'sMASTER OF ENGINEERIN

A wide area system for power transmission security enhancement using a process systems approach

Imperial Users onl

The use of late time response for stand off onbody concealed weapon detection

A new system for remote detection of onbody concealed weapons such as knives and handheld guns at standoff distances presented in this thesis. The system was designed, simulated, constructed and tested in the laboratory. The detection system uses an Ultrawide Band (UWB) antenna to bombard the target with a UWB electromagnetic pulse. This incident pulse induces electrical currents in the surface of an object such as a knife, which given appropriate conditions these currents generate an electromagnetic backscatter radiation. The radiated waves are detected using another UWB antenna to obtain the Late Time Response (LTR) signature of the detected object. The LTR signature was analysed using the Continuous Wavelet Transform (CWT) in order to assess the nature and the geometry of the object. The thesis presents the work which divided into two related areas. The first involved the design, simulation, fabrication, and testing of an Ultra-wide Band (UWB) antenna with operating bandwidth of 0.25 – 3.0 GHz and specific characteristics. Simulated and measured results show that the designed antenna achieves the design objectives which are, flat gain, a VSWR of around unity and distortion less transmitted narrow pulse. The operating bandwidth was chosen to cover the fundamental Complex Natural Resonance (CNR) modes of most firearms and to give a fine enough time resolution. The second area covered by this thesis presents a new approach for extract target signature based on the Continuous Wavelet Transform (CWT) applied to the scattering response of onbody concealed weapons. A series of experiments were conducted to test the operation of the detection system which involved onbody and offbody objects such as, knives, handheld guns, and a number of metallic wires of various dimensions. Practical and simulation results were in good agreement demonstrating the success of the approach of using the CWT in analyzing the LTR signature which is used for the first time in this work. Spectral response for every target could be seen as a distribution in which the energy level and life-time depended on the target material and geometry. The spectral density provides very powerful information concerning target unique signature

Applying Dynamic Mode Decomposition to Interconnected Systems for Forecasting and System Identification

Dynamic Mode Decomposition (DMD) describes a family of dynamical systems analysis approaches that approximate complex, likely non-linear behaviors with a low-rank linear operator. DMD has traditionally been used in a systems-identification context and was originally developed as a method of modeling fluid flows using the Koopman Operator. In contrast to these original applications, this work explores DMD's ability to produce high-fidelity forecasts using small training sets in an effort to flexibly model two complex, real-world systems. In particular, a novel, iterative implementation of DMD is tested and validated on 18 years of trading price data for constituent companies of the S\&P 500 and on 2 years of per-capita COVID-19 case counts throughout the continental US. The novel combination of DMD with blocked time-series cross-validation described in this work was found to consistently produce forecasts with an average MAPE of approximately 0.1 (in the case of the financial model) and RMSE of approximately 0.2 cases per 1000 citizens (for the COVID-19 model). In addition to reliably predicting the complex behaviors characteristic of real-world systems, this approach was leveraged to identify robust, distinct dynamical trends and construct networks which provided insights into central system elements. This work has illustrated the utility of applying DMD in an iterative approach facilitates forecasting accuracy across a variety of systems without compromising its ability to uncover fundamental characteristics of these underlying systems

Bayesian super-resolution with application to radar target recognition

This thesis is concerned with methods to facilitate automatic target recognition using images generated from a group of associated radar systems. Target recognition algorithms require access to a database of previously recorded or synthesized radar images for the targets of interest, or a database of features based on those images. However, the resolution of a new image acquired under non-ideal conditions may not be as good as that of the images used to generate the database. Therefore it is proposed to use super-resolution techniques to match the resolution of new images with the resolution of database images. A comprehensive review of the literature is given for super-resolution when used either on its own, or in conjunction with target recognition. A new superresolution algorithm is developed that is based on numerical Markov chain Monte Carlo Bayesian statistics. This algorithm allows uncertainty in the superresolved image to be taken into account in the target recognition process. It is shown that the Bayesian approach improves the probability of correct target classification over standard super-resolution techniques. The new super-resolution algorithm is demonstrated using a simple synthetically generated data set and is compared to other similar algorithms. A variety of effects that degrade super-resolution performance, such as defocus, are analyzed and techniques to compensate for these are presented. Performance of the super-resolution algorithm is then tested as part of a Bayesian target recognition framework using measured radar data

Exact and approximate Strang-Fix conditions to reconstruct signals with finite rate of innovation from samples taken with arbitrary kernels

In the last few years, several new methods have been developed for the sampling and exact reconstruction of specific classes of non-bandlimited signals known as signals with finite rate of innovation (FRI). This is achieved by using adequate sampling kernels and reconstruction schemes. An example of valid kernels, which we use throughout the thesis, is given by the family of exponential reproducing functions. These satisfy the generalised Strang-Fix conditions, which ensure that proper linear combinations of the kernel with its shifted versions reproduce polynomials or exponentials exactly. The first contribution of the thesis is to analyse the behaviour of these kernels in the case of noisy measurements in order to provide clear guidelines on how to choose the exponential reproducing kernel that leads to the most stable reconstruction when estimating FRI signals from noisy samples. We then depart from the situation in which we can choose the sampling kernel and develop a new strategy that is universal in that it works with any kernel. We do so by noting that meeting the exact exponential reproduction condition is too stringent a constraint. We thus allow for a controlled error in the reproduction formula in order to use the exponential reproduction idea with arbitrary kernels and develop a universal reconstruction method which is stable and robust to noise. Numerical results validate the various contributions of the thesis and in particular show that the approximate exponential reproduction strategy leads to more stable and accurate reconstruction results than those obtained when using the exact recovery methods.Open Acces

Parametric spectral analysis: scale and shift

We introduce the paradigm of dilation and translation for use in the spectral analysis of complex-valued univariate or multivariate data. The new procedure stems from a search on how to solve ambiguity problems in this analysis, such as aliasing because of too coarsely sampled data, or collisions in projected data, which may be solved by a translation of the sampling locations. In Section 2 both dilation and translation are first presented for the classical one-dimensional exponential analysis. In the subsequent Sections 3--7 the paradigm is extended to more functions, among which the trigonometric functions cosine, sine, the hyperbolic cosine and sine functions, the Chebyshev and spread polynomials, the sinc, gamma and Gaussian function, and several multivariate versions of all of the above. Each of these function classes needs a tailored approach, making optimal use of the properties of the base function used in the considered sparse interpolation problem. With each of the extensions a structured linear matrix pencil is associated, immediately leading to a computational scheme for the spectral analysis, involving a generalized eigenvalue problem and several structured linear systems. In Section 8 we illustrate the new methods in several examples: fixed width Gaussian distribution fitting, sparse cardinal sine or sinc interpolation, and lacunary or supersparse Chebyshev polynomial interpolation