30 April 2004
Implemented robust regressio technology in portfolio optimization. Constructed optimized portfolio based on robust regression estimations. Compared the portfolio performance with optimized portfolio which is based on ordinary least square estimation.
Iterative Memoryless Non-linear Estimators of Correlation for Complex-Valued Gaussian Processes that Exhibit Robustness to Impulsive NoiseTamburello, Philip Michael 04 February 2016 (has links)
The autocorrelation function is a commonly used tool in statistical time series analysis. Under the assumption of Gaussianity, the sample autocorrelation function is the standard method used to estimate this function given a finite number of observations. Non-Gaussian, impulsive observation noise following probability density functions with thick tails, which often occurs in practice, can bias this estimator, rendering classical time series analysis methods ineffective. This work examines the robustness of two estimators of correlation based on memoryless nonlinear functions of observations, the Phase-Phase Correlator (PPC) and the Median- of-Ratios Estimator (MRE), which are applicable to complex-valued Gaussian random pro- cesses. These estimators are very fast and easy to implement in current processors. We show that these estimators are robust from a bias perspective when complex-valued Gaussian pro- cesses are contaminated with impulsive noise at the expense of statistical efficiency at the assumed Gaussian distribution. Additionally, iterative versions of these estimators named the IMRE and IPPC are developed, realizing an improved bias performance over their non- iterative counterparts and the well-known robust Schweppe-type Generalized M-estimator utilizing a Huber cost function (SHGM). An impulsive noise suppression technique is developed using basis pursuit and a priori atom weighting derived from the newly developed iterative estimators. This new technique is proposed as an alternative to the robust filter cleaner, a Kalman filter-like approach that relies on linear prediction residuals to identity and replace corrupted observations. It does not have the same initialization issues as the robust filter cleaner. Robust spectral estimation methods are developed using these new estimators and impulsive noise suppression techniques. Results are obtained for synthetic complex-valued Guassian processes and real-world digital television signals collected using a software defined radio. / Ph. D.
Karlgaard, Christopher David
12 August 2010
The development of navigation filters that make use of robust estimation techniques is important due to the sensitivity of the typical minimum L2 norm techniques, such as the Kalman filter, to deviations in the assumed underlying probability distribution. In particular, those distributions with thicker tails than the Gaussian distribution can give rise to erratic filter performance and inconsistency of results. This dissertation discusses the development of an adaptive discrete-time robust nonlinear filtering technique based on a recursive form of Huber's mixed minimum L1/L2 norm approach to estimation, which is robust with respect to deviations from the assumed Gaussian error probability distributions inherent to the Kalman filter. This mixed norm approach is applied to a type of Sigma-Point Kalman filter, known as the Divided Difference Filter, which can capture second-order effects of nonlinearities in the system and measurement dynamics. Additionally, if these assumed parameters of the distribution differ greatly from the true parameters, then the filter can exhibit large errors and possibly divergence in nonlinear problems. This behavior is possible even if the true error distributions are Gaussian. To remedy these problems, adaptive filtering techniques have been introduced in order to automatically tune the Kalman filter by estimating the measurement and process noise covariances, however these techniques can also be highly sensitive to the nature of the underlying error distributions. The Huber-based formulations of the filtering problem also make some assumptions regarding the distribution, namely the approach considers a class of contaminated densities in the neighborhood of the Gaussian density. Essentially the method assumes that the statistics of the main Gaussian density are known, as well as the ratio or percentage of the contamination. The technique can be improved upon by the introduction of a method to adaptively estimate the noise statistics along with the state and state error covariance matrix. One technique in common use for adaptively estimating the noise statistics in real-time filtering applications is known as covariance matching. The covariance matching technique is an intuitively appealing approach in which the measurement noise and process noise covariances are determined in such a way that the true residual covariance matches the theoretically predicted covariance. The true residual covariance is approximated in real time using the sample covariance, over some finite buffer of stored residuals. The drawback to this approach is that the presence of outliers and non-Gaussianity can create problems of robustness with the use of the covariance matching technique. Therefore some additional steps must be taken to identify the outliers before forming the covariance estimates. In this dissertation, an adaptive scheme is proposed whereby the filter can estimate the process noise and measurement noise covariance matrices along with the state estimate and state estimate error covariance matrix. The adaptation technique adopts a robust approach to estimating these covariances that can resist the effects of outliers. The particular outlier identification method employed in this paper is based on quantities known as projection statistics, which utilize the sample median and median absolute deviation, and as a result are highly effective technique for multivariate outlier identification. These projection statistics are then employed as weights in the covariance matching procedure in order to reduce the influence of the outliers. The hybrid robust/adaptive nonlinear filtering methods introduced in this dissertation are applied to the problem of 6-DOF rendezvous navigation in elliptical orbit. The full nonlinear equations of relative motion are formulated in spherical coordinates centered on the target orbit. A relatively simple control law based on feedback linearization is used to track a desired rendezvous trajectory. The attitude dynamics are parameterized using Modified Rodrigues Parameters, which are advantageous for both control law development and estimation since they constitute a minimal 3-parameter attitude description. A switching technique which exploits the stereographic projection properties of the MRP coordinate is utilized to avoid singularities which inevitably arise in minimal attitude descriptions. This dissertation also introduces the proper covariance transformations associated with the singularity avoidance switching technique. An attitude control law based on backstepping is employed to track the target vehicle. A sensor suite consisting of a generic lidar or optical sensor, an Inertial Measurement Unit, consisting of accelerometers and gyroscopes, a star tracker, and a horizon sensor are utilized to provide measurement data to the navigation filters so that the chaser vehicle can estimate its relative state during the rendezvous maneuver. Several filters are implemented for comparison, including the Extended Kalman Filter, First and Second-Order Divided Difference Filters and Huber-based generalizations of these filters that include adaptive techniques for estimating the noise covariances. Monte-Carlo simulations are presented which include both Gaussian and non-Gaussian errors, including mismatches in the assumed noise covariances in the navigation filters in order to illustrate the benefits of the robust/adaptive nonlinear filters. Additionally, computational burdens of the various filters is compared. / Ph. D.
05 May 2019
The covariance estimation is one of the most critical tasks in multivariate statistical analysis. In many applications, reliable estimation of the covariance matrix, or scatter matrix in general, is required. The performance of the classical maximum likelihood method relies a great deal on the validity of the model assumption. Since the assumptions are often approximately correct, many robust statistical methods have been proposed to be robust against the deviation from the model assumptions. M-estimator is an important class of robust estimator of the scatter matrix. The properties of these robust estimators under high dimensional setting, which means the number of dimensions has the same order of magnitude as the number of observations, is desirable. To study these, random matrix theory is a very important tool. With high dimensional properties of robust estimators, we introduced a new method for blind spectrum sensing in cognitive radio networks.
Cho, Jung Jin
15 May 2009
Smart devices with multiple on-board sensors, networked through wired or wireless links, are distributed in physical systems and environments. Broad applications of such sensor networks include manufacturing quality control and wireless sensor systems. In the operation of sensor systems, robust methods for retrieving reliable information from sensor systems are crucial in the presence of potential sensor failures. Existence of sensor redundancy is one of the main drivers for the robustness or fault tolerance capability of a sensor system. The redundancy degree of sensors plays two important roles pertaining to the robustness of a sensor network. First, the redundancy degree provides proper parameter values for robust estimator; second, we can calculate the fault tolerance capability of a sensor network from the redundancy degree. Given this importance of the redundancy degree, this dissertation presents efficient algorithms based on matroid theory to compute the redundancy degree of a clustered sensor network. In the efficient algorithms, a cluster pattern of a sensor network allows us to decompose a large sensor network into smaller sub-systems, from which the redundancy degree can be found more efficiently. Finally, the robustness analysis as well as its algorithm procedure is illustrated using examples of a multi-station assembly process and calibration of wireless sensor networks.
30 September 2004
Robustness of a system has been defined in various ways and a lot of work has been done to model the system robustness , but quantifying or measuring robustness has always been very difficult. In this research we consider a simple system of a linear estimator and then attempt to model the system performance and robustness in a geometrical manner which admits an analysis using the differential geometric concepts of slope and curvature. We try to compare two different types of curvatures, namely the curvature along the maximum slope of a surface and the square-root of the absolute value of sectional curvature of a surface, and observe the values to see if both of them can alternately be used in the process of understanding or measuring system robustness. In this process we have worked on two different examples and taken readings for many points to find if there is any consistency in the two curvatures.
Estimation robuste en population finie et infinie / Robust estimation in finite and infinite populationFavre-Martinoz, Cyril 13 October 2015 (has links)
Les travaux de recherche développés dans cette thèse portent sur l'estimation robuste dans un contexte de population finie et infinie. Cette thèse comporte cinq chapitres, une introduction et une conclusion. Le chapitre 2 passe en revue la littérature portant sur plusieurs sujets tels que : l'inférence en population finie, l'estimation pour des petits domaines, l'estimation robuste dans un contexte de populations finies mais également de populations infinies. Dans le chapitre 3, le problème du choix du seuil dans le cas des estimateurs winzorisés est abordé. Nous avons montré que ces estimateurs appartiennent à une classe plus large, ce qui a permis de déterminer la valeur du seuil qui minimise le plus grand biais conditionnel estimé de l'échantillon (en valeur absolue) par rapport à l'estimateur winzorisé. Sous certaines conditions, nous avons montré que le seuil optimal existe et qu'il est unique dans certaines situations. Nous avons également proposé une méthode de calage permettant d'assurer la cohérence externe, qui est un problème très important en pratique. Les résultats d'une étude par simulation montrent que la méthode proposée fonctionne très bien en termes de biais et d'efficacité relative. Dans le chapitre 4, nous avons généralisé les résultats obtenus par Beaumont, Haziza et Ruiz-Gazen (2013, Biometrika) au cas de l'échantillonnage à deux-phases avec application au problème de la non-réponse totale. À notre connaissance, c'est le premier article portant sur l'estimation robuste en présence de données manquantes. Nous avons développé une version robuste des estimateurs par double dilatation et des estimateurs de calage. Dans le chapitre 5, nous nous sommes intéressés à l'estimation robuste dans un contexte de statistique classique (ou de populations infinies). Nous avons proposé une alternative robuste à la moyenne empirique. En particulier, nous avons développé une expression approximative de l'erreur quadratique moyenne pour des distributions appartenant aux domaines d'attraction de Gumbel et à celui de Frechet, ce qui nous a permis de comparer l'efficacité de l'estimateur proposé à celle de l'estimateur winzorisé une fois proposé par Rivest (1994, Biometrika). Dans le chapitre 6, nous avons traité du problème de l'estimation robuste dans un contexte d'estimation pour petits domaines, qui est un sujet qui a suscité beaucoup d'intérêt dans les dernières années. Nous avons proposé une approche unifiée d'estimation robuste à la présence de valeurs influentes dans le cas d'un modèle linéaire mixte généralisé. Lorsque le modèle sous-jacent est un modèle linéaire mixte, la méthode proposée est équivalente à la méthode de Dongmo Jiongo, Haziza et Duchesne (2013, Biometrika). Nous avons effectué des simulations dans le cas d'une variable d'intérêt continue, d'une variable binaire et d'une variable de comptage et avons montré empiriquement que la méthode proposée a de bonnes propriétés en termes d'erreur quadratique moyenne. / The main topic of this thesis is the robust estimation in finite or infinite population. The thesis is divided in five chapters, an introduction and a conclusion. The chapter 2 is a literature review focus on several topics as: inference in finite population, small area estimation, robust estimation in finite and infinite population. In chapter 3, we deal with the winsorization, which is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. We consider a method of determining the constant which involves minimizing the sample's largest estimated conditional bias. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties. In chapter 4, we extend the results of Beaumont et al. (2013) to the case of two-phase sampling designs. We extend the concept of conditional bias attached to a unit with respect to both phases and propose a robust version of the double expansion estimator. Our results can be naturally extended to the case of unit nonresponse, since the set of respondents often being viewed as a second phase sample. A robust version of calibration estimators, based on auxiliary information available at both phases, is also constructed. In chapter 5, we focus on the estimation of the population mean of a skewed population. We propose a robust version of the empirical mean, develop some mean square error approximations for the max-domain of attraction of Gumbel and Fréchet, and compare the efficiency of the proposed estimator to the one-winsorized estimator proposed by Rivest (1994, Biometrika). We also extend the result to the case of a regression coefficient for a linear model. In chapter 6, we focus on the robust estimation for small areas. We first propose a robust predictor in a general model-based framework with the use of generalized linear models and then we propose a unified framework for robust small area prediction in the context of generalized LMMs. We conduct a Monte Carlo study in the case where the variable of interest is continuous, binary or count data and we show empirically that the estimator derived from the proposed method have good bias and relative efficiency properties.
This thesis is about a robust filtering method known as the interval Kalman filter (IKF), an extension of the Kalman filter (KF) to the domain of interval mathematics. The key limitation of the KF is that it requires precise knowledge of the system dynamics and associated stochastic processes. In many cases however, system models are at best, only approximately known. To overcome this limitation, the idea is to describe the uncertain model coefficients in terms of bounded intervals, and operate the filter within the framework of interval arithmetic. In trying to do so, practical difficulties arise, such as the large overestimation of the resulting set estimates owing to the over conservatism of interval arithmetic. This thesis proposes and demonstrates a novel and effective way to limit such overestimation for the IKF, making it feasible and practical to implement. The theory developed is of general application, but is applied in this work to the heading estimation of the Springer unmanned surface vehicle, which up to now relied solely on the estimates from a traditional KF. However, the IKF itself simply provides the range of possible vehicle headings. In practice, the autonomous steering system requires a single, point-valued estimate of the heading. In order to address this requirement, an innovative approach based on the use of machine learning methods to select an adequate point-valued estimate has been developed. In doing so, the so called weighted IKF (wIKF) estimate provides a single heading estimate that is robust to bounded model uncertainty. In addition, in order to exploit low-cost sensor redundancy, a multi-sensor data fusion algorithm compatible with the wIKF estimates and which additionally provides sensor fault tolerance has been developed. All these techniques have been implemented on the Springer platform and verified experimentally in a series of full-scale trials, presented in the last chapter of the thesis. The outcomes demonstrate that the methods are both feasible and practicable, and that they are far more effective in providing accurate estimates of the vehicle’s heading than the conventional KF when there is uncertainty in the system model and/or sensor failure occurs.
Malady, Amy Colleen
25 May 2011
Cyclostationarity feature-based (C-FB) detection and classification is a large field of research that has promising applications to intelligent receiver design. Cyclostationarity FB classification and detection algorithms have been applied to a breadth of wireless communication signals — analog and digital alike. This thesis reports on an investigation of existing methods of extracting cyclostationarity features and then presents a novel robust solution that reduces SNR requirements, removes the pre-processing task of estimating occupied signal bandwidth, and can achieve classification rates comparable to those achieved by the traditional method while based on only 1/10 of the observation time. Additionally, this thesis documents the development of a novel low order consideration of the cyclostationarity present in Continuous Phase Modulation (CPM) signals, which is more practical than using higher order cyclostationarity. Results are presented — through MATLAB simulation — that demonstrate the improvements enjoyed by FB classifiers and detectors when using robust methods of estimating cyclostationarity. Additionally, a MATLAB simulation of a CPM C-FB detector confirms that low order C-FB detection of CPM signals is possible. Finally, suggestions for further research and contribution are made at the conclusion of the thesis. / Master of Science
Automated Detection of Surface Defects on Barked Hardwood Logs and Stems Using 3-D Laser Scanned DataThomas, Liya 15 November 2006 (has links)
This dissertation presents an automated detection algorithm that identifies severe external defects on the surfaces of barked hardwood logs and stems. The defects detected are at least 0.5 inch in height and at least 3 inches in diameter, which are severe, medium to large in size, and have external surface rises. Hundreds of real log defect samples were measured, photographed, and categorized to summarize the main defect features and to build a defect knowledge base. Three-dimensional laser-scanned range data capture the external log shapes and portray bark pattern, defective knobs, and depressions. The log data are extremely noisy, have missing data, and include severe outliers induced by loose bark that dangles from the log trunk. Because the circle model is nonlinear and presents both additive and non-additive errors, a new robust generalized M-estimator has been developed that is different from the ones proposed in the statistical literature for linear regression. Circle fitting is performed by standardizing the residuals via scale estimates calculated by means of projection statistics and incorporated in the Huber objective function to bound the influence of the outliers in the estimates. The projection statistics are based on 2-D radial-vector coordinates instead of the row vectors of the Jacobian matrix as proposed in the statistical literature dealing with linear regression. This approach proves effective in that it makes the GM-estimator to be influence bounded and thereby, robust against outliers. Severe defects are identified through the analysis of 3-D log data using decision rules obtained from analyzing the knowledge base. Contour curves are generated from radial distances, which are determined by robust 2-D circle fitting to the log-data cross sections. The algorithm detected 63 from a total of 68 severe defects. There were 10 non-defective regions falsely identified as defects. When these were calculated as areas, the algorithm locates 97.6% of the defect area, and falsely identifies 1.5% of the total clear area as defective. / Ph. D.
Page generated in 0.1495 seconds