On the application of a hybrid ellipsoidal-rectangular interval arithmetic algorithm to interval Kalman filtering for state estimation of uncertain systems

Modelling uncertainty is a key limitation to the applicability of the classical Kalman filter for state estimation of dynamic systems. For such systems with bounded modelling uncertainty, the interval Kalman filter (IKF) is a direct extension of the former to interval systems. However, its usage is not yet widespread owing to the over-conservatism of interval arithmetic bounds. In this paper, the IKF equations are adapted to use an ellipsoidal arithmetic that, in some cases, provides tighter bounds than direct, rectangular interval arithmetic. In order for the IKF to be useful, it must be able to provide reasonable enclosures under all circumstances. To this end, a hybrid ellipsoidal-rectangular enclosure algorithm is proposed, and its robustness is evidenced by its application to two characteristically different systems for which it provides stable estimate bounds, whereas the rectangular and ellipsoidal approaches fail to accomplish this in either one or the other case

Application of artificial neural networks to weighted interval Kalman filtering

The interval Kalman filter is a variant of the traditional Kalman filter for systems with bounded parametric uncertainty. For such systems, modelled in terms of intervals, the interval Kalman filter provides estimates of the system state also in the form of intervals, guaranteed to contain the Kalman filter estimates of all point-valued systems contained in the interval model. However, for practical purposes, a single, point-valued estimate of the system state is often required. This point value can be seen as a weighted average of the interval bounds provided by the interval Kalman filter. This article proposes a methodology based on the application of artificial neural networks by which an adequate weight can be computed at each time step, whereby the weighted average of the interval bounds approximates the optimal estimate or estimate which would be obtained using a Kalman filter if no parametric uncertainty was present in the system model, even when this is not the case. The practical applicability and robustness of the method are demonstrated through its application to the navigation of an uninhabited surface vehicle. © IMechE 2014

On quaternion based parametrization of orientation in computer vision and robotics

The problem of orientation parameterization for applications in computer vision and robotics is examined in detail herein. The necessary intuition and formulas are provided for direct practical use in any existing algorithm that seeks to minimize a cost function in an iterative fashion. Two distinct schemes of parameterization are analyzed: The first scheme concerns the traditional axis-angle approach, while the second employs stereographic projection from unit quaternion sphere to the 3D real projective space. Performance measurements are taken and a comparison is made between the two approaches. Results suggests that there exist several benefits in the use of stereographic projection that include rational expressions in the rotation matrix derivatives, improved accuracy, robustness to random starting points and accelerated convergence

Linkage analysis merging replicate phenotypes: an application to three quantitative phenotypes in two African samples

We report two approaches for linkage analysis of data consisting of replicate phenotypes. The first approach is specifically designed for the unusual (in human data) replicate structure of the Genetic Analysis Workshop 17 pedigree data. The second approach consists of a standard linkage analysis that, although not specifically tailored to data consisting of replicate genotypes, was envisioned as providing a sounding board against which our novel approach could be assessed. Both approaches are applied to the analysis of three quantitative phenotypes (Q1, Q2, and Q4) in two sets of African families. All analyses were carried out blind to the generating model (i.e., the “answers”). Using both methods, we found numerous significant linkage signals for Q1, although population colocalization was absent for most of these signals. The linkage analysis of Q2 and Q4 failed to reveal any strong linkage signals

DNA methylotype analysis in colorectal cancer

The methylation status of a gene promoter is considered to be an important mechanism for the development of many tumors, including colorectal cancer. Recent studies have shown that specific patterns of DNA methylation across multiple CpG loci in some human tumors are more informative than the detection of one single CpG locus in tumor genomes. In the present study, multiple CpG methylations of three genes (CDKN2A, DPYD and MLH1) were detected in DNA samples from patients with colorectal cancer using Pyrosequencing(®) technology. The bisulfite-converted DNA was amplified with a nested PCR and five or six CpG loci of each gene were assessed to determine DNA methylotype. Our data showed that 10/49 (20.4%), 6/48 (12.5%) and 14/49 (28.6%) of tumors were methylated with a DNA methylation level >0.2 in CDKN2A, DPYD and MLH1, respectively. Our study indicated a similar DNA methylation level across the multiple CpG loci for all three genes in the methylated tumor DNA samples, demonstrating a dichotomous trait in DNA methylation. The tumor DNA samples had unique DNA methylation patterns, which were high-degree and multiple-site methylation, but the normal DNA samples had no or a low-degree and dispersed single-site methylation. In addition, an inverse correlation in those methylated tumors was observed between DNA methylation and RNA expression for MLH1 (R(S)=−0.62, P=0.003), but not for CDKN2A and DPYD. In conclusion, distinctive DNA methylotypes exist in colorectal cancer and may depict a distinct biology in apparently homogeneous tumors

Automatic classification of field-collected dinoflagellates by artificial neural network

Automatic taxonomic categorisation of 23 species of dinoflagellates was demonstrated using field-collected specimens. These dinoflagellates have been responsible for the majority of toxic and noxious phytoplankton blooms which have occurred in the coastal waters of the European Union in recent years and make severe impact on the aquaculture industry. The performance by human 'expert' ecologists/taxonomists in identifying these species was compared to that achieved by 2 artificial neural network classifiers (multilayer perceptron and radial basis function networks) and 2 other statistical techniques, k-Nearest Neighbour and Quadratic Discriminant Analysis. The neural network classifiers outperform the classical statistical techniques. Over extended trials, the human experts averaged 85% while the radial basis network achieved a best performance of 83%, the multilayer perceptron 66%, k-Nearest Neighbour 60%, and the Quadratic Discriminant Analysis 56%

Application of a Self-Similar Pressure Profile to Sunyaev-Zel'dovich Effect Data from Galaxy Clusters

We investigate the utility of a new, self-similar pressure profile for fitting Sunyaev-Zel'dovich (SZ) effect observations of galaxy clusters. Current SZ imaging instruments - such as the Sunyaev-Zel'dovich Array (SZA) - are capable of probing clusters over a large range in physical scale. A model is therefore required that can accurately describe a cluster's pressure profile over a broad range of radii, from the core of the cluster out to a significant fraction of the virial radius. In the analysis presented here, we fit a radial pressure profile derived from simulations and detailed X-ray analysis of relaxed clusters to SZA observations of three clusters with exceptionally high quality X-ray data: A1835, A1914, and CL J1226.9+3332. From the joint analysis of the SZ and X-ray data, we derive physical properties such as gas mass, total mass, gas fraction and the intrinsic, integrated Compton y-parameter. We find that parameters derived from the joint fit to the SZ and X-ray data agree well with a detailed, independent X-ray-only analysis of the same clusters. In particular, we find that, when combined with X-ray imaging data, this new pressure profile yields an independent electron radial temperature profile that is in good agreement with spectroscopic X-ray measurements.Comment: 28 pages, 6 figures, accepted by ApJ for publication (probably April 2009

A Robust Navigation Technique for Integration in the Guidance and Control of an Uninhabited Surface Vehicle

In this paper, we propose a novel robust navigational approach to be integrated with the guidance and control systems of an uninhabitedsurface vehicle Springer. A weighted Interval Kalman Filter (wIKF) in used for waypoint tracking, and has been compared with that of one that uses a conventional Kalman Filter (KF) navigational design. The conventional KF fails to predict correctly the vehicle’s heading when there is unmodelled uncertainty of the sensing equipment, and thus would negatively affect the performance of subsequent navigation, guidance and control (NGC). While the proposed method using a wIKF technique enhances robustness with respect to erroneous modelling, and thus secures better accuracy and efficiency in completing a mission