A stochastic model for natural feature representation

This paper presents a robust stochastic model for the incorporation of natural features within data fusion algorithms. The representation combines Isomap, a non-linear manifold learning algorithm, with Expectation Maximization, a statistical learning scheme. The representation is computed offline and results in a non-linear, non-Gaussian likelihood model relating visual observations such as color and texture to the underlying visual states. The likelihood model can be used online to instantiate likelihoods corresponding to observed visual features in real-time. The likelihoods are expressed as a Gaussian Mixture Model so as to permit convenient integration within existing nonlinear filtering algorithms. The resulting compactness of the representation is especially suitable to decentralized sensor networks. Real visual data consisting of natural imagery acquired from an Unmanned Aerial Vehicle is used to demonstrate the versatility of the feature representation.

Self excitation in equity indices

A "self-exciting" market is one in which the probability of observing a crash increases in response to the occurrence of a crash. It essentially describes cases where the initial crash serves to weaken the system to some extent, making subsequent crashes more likely. This thesis investigates if equity markets possess this property. A self-exciting extension of the well-known jump-based Bates (1996) model is used as the workhorse model for this thesis, and a particle-filtering algorithm is used to facilitate estimation by means of maximum likelihood. The estimation method is developed so that option prices are easily included in the dataset, leading to higher quality estimates. Equilibrium arguments are used to price the risks associated with the time-varying crash probability, and in turn to motivate a risk-neutral system for use in option pricing. The option pricing function for the model is obtained via the application of widely-used Fourier techniques. An application to S&P500 index returns and a panel of S&P500 index option prices reveals evidence of self excitation.

Filter and control performance bounds in the presence of model uncertainties with aerospace applications

This thesis establishes performance properties for approximate filters and controllers that are designed on the basis of approximate dynamic system representations. These performance properties provide a theoretical justification for the widespread application of approximate filters and controllers in the common situation where system models are not known with complete certainty. This research also provides useful tools for approximate filter designs, which are applied to hybrid filtering of uncertain nonlinear systems. As a contribution towards applications, this thesis also investigates air traffic separation control in the presence of measurement uncertainties.

Parameter estimation of thrust models of uninhabited airborne systems

This paper presents a method for the estimation of thrust model parameters of uninhabited airborne systems using specific flight tests. Particular tests are proposed to simplify the estimation. The proposed estimation method is based on three steps. The first step uses a regression model in which the thrust is assumed constant. This allows us to obtain biased initial estimates of the aerodynamic coeficients of the surge model. In the second step, a robust nonlinear state estimator is implemented using the initial parameter estimates, and the model is augmented by considering the thrust as random walk. In the third step, the estimate of the thrust obtained by the observer is used to fit a polynomial model in terms of the propeller advanced ratio. We consider a numerical example based on Monte-Carlo simulations to quantify the sampling properties of the proposed estimator given realistic flight conditions.

Design of a nonlinear excitation controller using inverse filtering for transient stability enhancement

This paper proposes a nonlinear excitation controller to improve transient stability, oscillation damping and voltage regulation of the power system. The energy function of the predicted system states is used to obtain the desired flux for the next time step, which in turn is used to obtain a supplementary control input using an inverse filtering method. The inverse filtering technique enables the system to provide an additional input for the excitation system, which forces the system to track the desired flux. Synchronous generator flux saturation model is used in this paper. A single machine infinite bus (SMIB) test system is used to demonstrate the efficacy of the proposed control method using time-domain simulations. The robustness of the controller is assessed under different operating conditions.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

Wide-area damping control for inter-area oscillations using inverse filtering technique

In this study, a non-linear excitation controller using inverse filtering is proposed to damp inter-area oscillations. The proposed controller is based on determining generator flux value for the next sampling time which is obtained by maximising reduction rate of kinetic energy of the system after the fault. The desired flux for the next time interval is obtained using wide-area measurements and the equivalent area rotor angles and velocities are predicted using a non-linear Kalman filter. A supplementary control input for the excitation system, using inverse filtering approach, to track the desired flux is implemented. The inverse filtering approach ensures that the non-linearity introduced because of saturation is well compensated. The efficacy of the proposed controller with and without communication time delay is evaluated on different IEEE benchmark systems including Kundur's two area, Western System Coordinating Council three-area and 16-machine, 68-bus test systems.