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

Radio Sources from a 31 GHz Sky Survey with the Sunyaev-Zel'dovich Array

We present the first sample of 31-GHz selected sources to flux levels of 1 mJy. From late 2005 to mid 2007, the Sunyaev-Zel'dovich Array (SZA) observed 7.7 square degrees of the sky at 31 GHz to a median rms of 0.18 mJy/beam. We identify 209 sources at greater than 5 sigma significance in the 31 GHz maps, ranging in flux from 0.7 mJy to ~200 mJy. Archival NVSS data at 1.4 GHz and observations at 5 GHz with the Very Large Array are used to characterize the sources. We determine the maximum-likelihood integrated source count to be N(>S) = (27.2 +- 2.5) deg^-2 x (S_mJy)^(-1.18 +- 0.12) over the flux range 0.7 - 15 mJy. This result is significantly higher than predictions based on 1.4-GHz selected samples, a discrepancy which can be explained by a small shift in the spectral index distribution for faint 1.4-GHz sources. From comparison with previous measurements of sources within the central arcminute of massive clusters, we derive an overdensity of 6.8 +- 4.4, relative to field sources.Comment: 13 pages, 5 figure

Towards automating underwater measurement of fish length: a comparison of semi-automatic and manual stereo–video measurements

Underwater stereo–video systems are widely used for counting and measuring fish in aquaculture, fisheries, and conservation management. Length measurements are generated from stereo–video recordings by a software operator using a mouse to locate the head and tail of a fish in synchronized pairs of images. This data can be used to compare spatial and temporal changes in the mean length and biomass or frequency distributions of populations of fishes. Since the early 1990s stereo–video has also been used for measuring the lengths of fish in aquaculture for quota and farm management. However, the costs of the equipment, software, the time, and salary costs involved in post processing imagery manually and the subsequent delays in the availability of length information inhibit the adoption of this technology. We present a semi-automatic method for capturing stereo–video measurements to estimate the lengths of fish. We compare the time taken to make measurements of the same fish measured manually from stereo–video imagery to that measured semi-automatically. Using imagery recorded during transfers of Southern Bluefin Tuna (SBT) from tow cages to grow out cages, we demonstrate that the semi-automatic algorithm developed can obtain fork length measurements with an error of less than 1% of the true length and with at least a sixfold reduction in operator time in comparison to manual measurements. Of the 22 138 SBT recorded we were able to measure 52.6% (11 647) manually and 11.8% (2614) semi-automatically. For seven of the eight cage transfers recorde,d there were no statistical differences in the mean length, weight, or length frequency between manual and semi-automatic measurements. When the data were pooled across the eight cage transfers, there was no statistical difference in mean length or weight between the stereo–video-based manual and semi-automated measurements. Hence, the presented semi-automatic system can be deployed to significantly reduce the cost involved in adoption of stereo–video technology

A Millimeter-wave Galactic Plane Survey with the BICEP Polarimeter

In order to study inflationary cosmology and the Milky Way Galaxy's composition and magnetic field structure, Stokes I, Q, and U maps of the Galactic plane covering the Galactic longitude range 260° < ℓ < 340° in three atmospheric transmission windows centered on 100, 150, and 220 GHz are presented. The maps sample an optical depth 1 ≾ AV ≾ 30, and are consistent with previous characterizations of the Galactic millimeter-wave frequency spectrum and the large-scale magnetic field structure permeating the interstellar medium. The polarization angles in all three bands are generally perpendicular to those measured by starlight polarimetry as expected and show changes in the structure of the Galactic magnetic field on the scale of 60°. The frequency spectrum of degree-scale Galactic emission is plotted between 23 and 220 GHz (including WMAP data) and is fit to a two-component (synchrotron and dust) model showing that the higher frequency BICEP data are necessary to tightly constrain the amplitude and spectral index of Galactic dust. Polarized emission is detected over the entire region within two degrees of the Galactic plane, indicating the large-scale magnetic field is oriented parallel to the plane of the Galaxy. A trend of decreasing polarization fraction with increasing total intensity is observed, ruling out the simplest model of a constant Galactic magnetic field orientation along the line of sight in the Galactic plane. A generally increasing trend of polarization fraction with electromagnetic frequency is found, varying from 0.5%-1.5% at frequencies below 50 GHz to 2.5%-3.5% above 90 GHz. The effort to extend the capabilities of BICEP by installing 220 GHz band hardware is described along with analysis of the new band

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

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

Atmospheric phase correction using CARMA-PACS: high angular resolution observations of the FU Orionis star PP 13S*

We present 0".15 resolution observations of the 227 GHz continuum emission from the circumstellar disk around the FU Orionis star PP 13S*. The data were obtained with the Combined Array for Research in Millimeter-wave Astronomy (CARMA) Paired Antenna Calibration System (C-PACS), which measures and corrects the atmospheric delay fluctuations on the longest baselines of the array in order to improve the sensitivity and angular resolution of the observations. A description of the C-PACS technique and the data reduction procedures are presented. C-PACS was applied to CARMA observations of PP 13S*, which led to a factor of 1.6 increase in the observed peak flux of the source, a 36% reduction in the noise of the image, and a 52% decrease in the measured size of the source major axis. The calibrated complex visibilities were fitted with a theoretical disk model to constrain the disk surface density. The total disk mass from the best-fit model corresponds to 0.06 M_⊙, which is larger than the median mass of a disk around a classical T Tauri star. The disk is optically thick at a wavelength of 1.3 mm for orbital radii less than 48 AU. At larger radii, the inferred surface density of the PP 13S* disk is an order of magnitude lower than that needed to develop a gravitational instability

A Millimeter-Wave Galactic Plane Survey With The BICEP Polarimeter

In addition to its potential to probe the Inflationary cosmological paradigm, millimeter-wave polarimetry is a powerful tool for studying the Milky Way galaxy's composition and magnetic field structure. Towards this end, presented here are Stokes I, Q, and U maps of the Galactic plane from the millimeter-wave polarimeter BICEP covering the Galactic longitude range 260 - 340 degrees in three atmospheric transmission windows centered on 100, 150, and 220 GHz. The maps sample an optical depth 1 < AV < 30, and are consistent with previous characterizations of the Galactic millimeter-wave frequency spectrum and the large-scale magnetic field structure permeating the interstellar medium. Polarized emission is detected over the entire region within two degrees of the Galactic plane and indicates that the large-scale magnetic field is oriented parallel to the plane of the Galaxy. An observed trend of decreasing polarization fraction with increasing total intensity rules out the simplest model of a constant Galactic magnetic field throughout the Galaxy. Including WMAP data in the analysis, the degree-scale frequency spectrum of Galactic polarization fraction is plotted between 23 and 220 GHz for the first time. A generally increasing trend of polarization fraction with electromagnetic frequency is found, which varies from 0.5%-1.5%at frequencies below 50 GHz to 2.5%-3.5%above 90 GHz. The BICEP and WMAP data are fit to a two-component (synchrotron and dust) model showing that the higher frequency BICEP data are necessary to tightly constrain the amplitude and spectral index of Galactic dust. Furthermore, the dust amplitude predicted by this two-component fit is consistent with model predictions of dust emission in the BICEP bands