Enabling Robust State Estimation through Measurement Error Covariance Adaptation

Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and non-cooperative environments. When dealing with novel and non-cooperative environments, little is known a priori about the measurement error uncertainty, thus, there is a requirement that the uncertainty models of the localization algorithm be adaptive. Within this paper, we propose the batch covariance estimation technique, which enables robust state estimation through the iterative adaptation of the measurement uncertainty model. The adaptation of the measurement uncertainty model is granted through non-parametric clustering of the residuals, which enables the characterization of the measurement uncertainty via a Gaussian mixture model. The provided Gaussian mixture model can be utilized within any non-linear least squares optimization algorithm by approximately characterizing each observation with the sufficient statistics of the assigned cluster (i.e., each observation's uncertainty model is updated based upon the assignment provided by the non-parametric clustering algorithm). The proposed algorithm is verified on several GNSS collected data sets, where it is shown that the proposed technique exhibits some advantages when compared to other robust estimation techniques when confronted with degraded data quality.Comment: 14 pages, 13 figures, Submitted to IEEE Transactions on Aerospace And Electronic System

Uncertainty Model Estimation in an Augmented Data Space for Robust State Estimation

The requirement to generate robust robotic platforms is a critical enabling step to allow such platforms to permeate safety-critical applications (i.e., the localization of autonomous platforms in urban environments). One of the primary components of such a robotic platform is the state estimation engine, which enables the platform to reason about itself and the environment based upon sensor readings. When such sensor readings are degraded traditional state estimation approaches are known to breakdown. To overcome this issue, several robust state estimation frameworks have been proposed. One such method is the batch covariance estimation (BCE) framework. The BCE approach enables robust state estimation by iteratively updating the measurement error uncertainty model through the fitting of a Gaussian mixture model (GMM) to the measurement residuals. This paper extends upon the BCE approach by arguing that the uncertainty estimation process should be augmented to include metadata (e.g., the signal strength of the associated GNSS observation). The modification of the uncertainty estimation process to an augmented data space is significant because it increases the likelihood of a unique partitioning in the measurement residual domain and thus provides the ability to more accurately characterize the measurement uncertainty model. The proposed batch covariance estimation over an augmented data-space (BCE-AD) is experimentally validated on collected data where it is shown that a significant increase in state estimation accuracy can be granted compared to previously proposed robust estimation techniques.Comment: 6 pages, 5 figures, Correspondence submitted to the IEEE Transactions on Aerospace and Electronic System

Robust Incremental State Estimation through Covariance Adaptation

Recent advances in the fields of robotics and automation have spurred significant interest in robust state estimation. To enable robust state estimation, several methodologies have been proposed. One such technique, which has shown promising performance, is the concept of iteratively estimating a Gaussian Mixture Model (GMM), based upon the state estimation residuals, to characterize the measurement uncertainty model. Through this iterative process, the measurement uncertainty model is more accurately characterized, which enables robust state estimation through the appropriate de-weighting of erroneous observations. This approach, however, has traditionally required a batch estimation framework to enable the estimation of the measurement uncertainty model, which is not advantageous to robotic applications. In this paper, we propose an efficient, incremental extension to the measurement uncertainty model estimation paradigm. The incremental covariance estimation (ICE) approach, as detailed within this paper, is evaluated on several collected data sets, where it is shown to provide a significant increase in localization accuracy when compared to other state-of-the-art robust, incremental estimation algorithms.Comment: 8 pages, 4 figures, 2 tables, submitted to IEEE Robotics and Automation Letter

Evidence for the Magnetoionic Nature of Oblique VHF Reflections from Midlatitude Sporadic-E Layers

Mid-latitude sporadic-E (Es) is an intermittent phenomenon of the lower E region of the ionosphere. Es clouds are thin, transient, and patchy layers of intense ionization, with ionization densities which can be much higher than in the background ionosphere. Oblique reflection of radio signals in the very high frequency (VHF) range is regularly supported, but the mechanism for it has never been clearly established—specular reflection, scattering, and magnetoionic double refraction have all been suggested. This article proposes using the polarization behaviour of signals reflected from intense midlatitude sporadic-E clouds as an indicator of the true reflection mechanism. Results are presented from a measurement campaign in the summer of 2018, which gathered a large amount of data at a receiving station in the UK using 50 MHz amateur radio beacons as signal sources. In all cases the signals received were elliptically polarized, despite being transmitted with linear polarization; there were also indications that polarization behaviour varied systematically with the orientation of the path to the geomagnetic field. This represents, for all the examples recorded, clear evidence that signals were reflected from midlatitude Es by magnetoionic double refraction

The ``Nernst Theorem'' and Black Hole Thermodynamics

The Nernst formulation of the third law of ordinary thermodynamics (often referred to as the ``Nernst theorem'') asserts that the entropy, $S$, of a system must go to zero (or a ``universal constant'') as its temperature, $T$, goes to zero. This assertion is commonly considered to be a fundamental law of thermodynamics. As such, it seems to spoil the otherwise perfect analogy between the ordinary laws of thermodynamics and the laws of black hole mechanics, since rotating black holes in general relativity do not satisfy the analog of the ``Nernst theorem''. The main purpose of this paper is to attempt to lay to rest the ``Nernst theorem'' as a law of thermodynamics. We consider a boson (or fermion) ideal gas with its total angular momentum, $J$, as an additional state parameter, and we analyze the conditions on the single particle density of states, $g(\epsilon,j)$, needed for the Nernst formulation of the third law to hold. (Here, $\epsilon$ and $j$ denote the single particle energy and angular momentum.) Although it is shown that the Nernst formulation of the third law does indeed hold under a wide range of conditions, some simple classes of examples of densities of states which violate the ``Nernst theorem'' are given. In particular, at zero temperature, a boson (or fermion) gas confined to a circular string (whose energy is proportional to its length) not only violates the ``Nernst theorem'' also but reproduces some other thermodynamic properties of an extremal rotating black hole.Comment: 20 pages, plain LaTeX fil

Investigating the physical properties of transiting hot Jupiters with the 1.5-m Kuiper Telescope

We present new photometric data of 11 hot Jupiter transiting exoplanets (CoRoT-12b, HAT-P-5b, HAT-P-12b, HAT-P-33b, HAT-P-37b, WASP-2b, WASP-24b, WASP-60b, WASP-80b, WASP-103b, XO-3b) in order to update their planetary parameters and to constrain information about their atmospheres. These observations of CoRoT-12b, HAT-P-37b and WASP-60b are the first follow-up data since their discovery. Additionally, the first near-UV transits of WASP-80b and WASP-103b are presented. We compare the results of our analysis with previous work to search for transit timing variations (TTVs) and a wavelength dependence in the transit depth. TTVs may be evidence of a third body in the system and variations in planetary radius with wavelength can help constrain the properties of the exoplanet's atmosphere. For WASP-103b and XO-3b, we find a possible variation in the transit depths that may be evidence of scattering in their atmospheres. The B-band transit depth of HAT-P-37b is found to be smaller than its near-IR transit depth and such a variation may indicate TiO/VO absorption. These variations are detected from 2-4.6$\sigma$, so follow-up observations are needed to confirm these results. Additionally, a flat spectrum across optical wavelengths is found for 5 of the planets (HAT-P-5b, HAT-P-12b, WASP-2b, WASP-24b, WASP-80b), suggestive that clouds may be present in their atmospheres. We calculate a refined orbital period and ephemeris for all the targets, which will help with future observations. No TTVs are seen in our analysis with the exception of WASP-80b and follow-up observations are needed to confirm this possible detection.Comment: 18 pages, 7 figures, 9 Tables. Light Curves available online. Accepted to MNRAS (2017 August 25

Circularly Symmetric Apodization via Starshaped Masks

Recently, we introduced a class of shaped pupil masks, called spiderweb masks, that produce point spread functions having annular dark zones. With such masks, a single image can be used to probe a star for extrasolar planets. In this paper, we introduce a new class of shaped pupil masks that also provide annular dark zones. We call these masks starshaped masks. Given any circularly symmetric apodization function, we show how to construct a corresponding starshaped mask that has the same point-spread function (out to any given outer working distance) as obtained by the apodization.Comment: Paper also at: http://www.orfe.princeton.edu/~rvdb/tex/starshape/ms.pdf Updated to clarify misleading statements regarding total throughput for apodizations and their corresponding starshaped mask

On the Glueball Spectrum of Pure Yang-Mills Theory in 2+1 Dimensions

We present details of the analytic computation of the spectrum of lowest spin glueballs in pure Yang-Mills theory in 2+1 dimensions. The new ingredient is provided by the conjectured new non-trivial expression for the (quasi)Gaussian part of the ground state wave-functional. We show that this wave-functional can be derived by solving the Schrodinger equation under certain assumptions. The mass spectrum of the theory is determined by the zeros of Bessel functions, and the agreement with available lattice data is excellent.Comment: 43 pages, 3 figures, LaTeX; version to appear in Physical Review

Supersymmetry Breaking and Dilaton Stabilization in String Gas Cosmology

In this Note we study supersymmetry breaking via gaugino condensation in string gas cosmology. We show that the same gaugino condensate which is introduced to stabilize the dilaton breaks supersymmetry. We study the constraints on the scale of supersymmetry breaking which this mechanism leads to.Comment: 11 page

Kinematic and kinetic differences between military patients with patellar tendinopathy and asymptomatic controls during single leg squats

© 2019 Background: Knee valgus alignment has been associated with lower-limb musculoskeletal injury. This case-control study aims to: assess biomechanical differences between patients with patellar tendinopathy and healthy controls. Methods: 43 military participants (21 cases, 22 controls) were recorded using 3D-motion capture performing progressively demanding, small knee bend, single leg and single leg decline squats. Planned a priori analysis of peak: hip adduction, knee flexion, pelvic tilt, pelvic obliquity and trunk flexion was conducted using MANOVA. Kinematic and kinetic data were graphed with bootstrapped t-tests and 95% CI's normalised to the squat cycle. ANOVA and correlations in SPSS were used for exploratory analysis. Findings: On their symptomatic side cases squatted to less depth (−6.62° p 0.05). Cases experienced more pain on testing on decline board (ES = 0.69, p 0.05), correlated with extensor knee moment. Interpretation: Knee valgus alignment is a plausible risk factor for patellar tendinopathy. Conclusions relating to causation are limited by the cross-sectional study design. Increasing squat depth, use of a declined surface and isolating the eccentric phase enable progression of loading prescription guided by pain