Angular Uncertainty Research Articles

Estimating trajectories of meteors: an observational Monte Carlo approach – II. Results

ABSTRACT In the first paper of this series, we examined existing methods of optical meteor trajectory estimation and developed a novel method which simultaneously uses both the geometry and the dynamics of meteors to constrain their trajectories. We also developed a simulator which uses an ablation model to generate realistic synthetic meteor trajectories which we use to test meteor trajectory solvers. In this second paper, we perform simulation validation to estimate radiant and velocity accuracy, which may be achieved by various meteor observation systems as applied to several meteor showers. For low-resolution all-sky systems, where the meteor deceleration is generally not measurable, the multi-parameter fit method assuming a constant velocity better reproduces the radiant and speed of synthetic meteors. For moderate field of view systems, our novel method performs the best at all convergence angles, while multi-parameter fit methods generally produce larger speed errors. For high-resolution, narrow field of view systems, we find our new method of trajectory estimation reproduces radiant and speed more accurately than all other methods tested. The ablation properties of meteoroids are commonly found to be the limiting factor in velocity accuracy. We show that the true radiant dispersion of meteor showers can be reliably measured with moderate field of view (or more precise) systems provided appropriate methods of meteor trajectory estimation are employed. Finally, we compare estimated and real angular radiant uncertainty and show that for the solvers tested the real radiant error is on average underestimated by a factor of two.

On the Angular Resolution Limit uncertainty under compound Gaussian noise

The Angular Resolution Limit (ARL) is a fundamental statistical metric to quantify our ability to resolve two closely-spaced narrowband far-field complex sources. This statistical quantity, is defined as the minimal angular deviation between the two sources to be separated for a prefixed detection-based performance. In this work, we assume that the sources of interest are corrupted by a compound-Gaussian noise. In the standard literature, denoting with δ the true distance between the two sources, the derivation of the ARL is based on the statistical distribution of the Generalized Likelihood Ratio Test (GLRT) for a binary test where there is only one source under the null hypothesis (i.e., δ=0) and two sources under the alternative hypothesis δ ≠ 0. In literature, the true angular distance (TAD) is generally considered as an unknown deterministic parameter, then a maximum likelihood-based estimation of δ is exploited in the GLRT. In this paper, breaking away from existing contributions, we suppose that the TAD is a random variable, Gaussian distributed, meaning that δ∼N(δ0,σδ2). The TAD uncertainty can have many causes as for instance moving sources or/and platform, antenna calibration error, etc. In this work, a generic and flexible (but common) statistical model of the uncertain knowledge of the TAD is preferred instead of a too much specified error model. The degree of randomness (or uncertainty) is quantified by the ratio ξ=δ02/σδ2. The standard framework of the GLRT is no longer feasible for our problem formulation. To cope with the compound Gaussian noise modeling and the random model of the TAD, a powerful upper bound from information/geometry theory is exploited in this work. More precisely, a new expected Chernoff Upper Bound (CUB) on the minimal error probability is introduced. Based on the analysis of this upper bound, we show that the expected-CUB is highly dependent on the degree of uncertainty, ξ. As a by-product, the optimal s-value in the Chernoff divergence for which the expected-CUB is the tightest upper bound is analytically studied and the role of the mean value δ0 in the ARL context is analyzed.

Effect of CZT system characteristics on Compton scatter event recovery.

Improving 511 keV photon detection sensitivity is a common goal for positron emission tomography system designers. One attractive approach to increase sensitivity is recovering events that are normally rejected. The kinematics of Compton scattering can be used to recover the line of response through direction difference angle (DDA). The uncertainty of DDA is determined by the energy and spatial resolution of a system. In this work, we evaluated the performance of small animal CZT-based positron emission tomography systems with energy resolution of 1%, 4%, and 6% and different spatial resolution based on prior work for guiding new design efforts. Designs with energy resolution limited by counting statistics and by electronic noise were considered. The influence of modifying the conventional energy window and uncertainty of DDA was investigated. For a system with 4% energy resolution and limited by electronic noise, the figure of merit of noise equivalent count increases by 65% as the lower energy bound increases from 471 keV to 493 keV. If the system-wide energy resolution becomes worse than 4% of the full width half maximum at 511 keV, going to a pixel size finer than 1 mm has very limited effect in reducing total angular uncertainty. For a system with 1% energy resolution, as the spatial resolution improves from 1 mm to 0.5 mm, the contrast-to-noise ratio increases by 9%.

Impact and mitigation of angular uncertainties in Bragg coherent x-ray diffraction imaging

Bragg coherent diffraction imaging (BCDI) is a powerful technique to explore the local strain state and morphology of microscale crystals. The method can potentially reach nanometer-scale spatial resolution thanks to the advances in synchrotron design that dramatically increase coherent flux. However, there are experimental bottlenecks that may limit the image reconstruction quality from future high signal-to-noise ratio measurements. In this work we show that angular uncertainty of the sample orientation with respect to a fixed incoming beam is one example of such a factor, and we present a method to mitigate the resulting artifacts. On the basis of an alternative formulation of the forward problem, we design a phase retrieval algorithm which enables the simultaneous reconstruction of the object and determination of the exact angular position corresponding to each diffraction pattern in the data set. We have tested the algorithm performance on simulated data for different degrees of angular uncertainty and signal-to-noise ratio.

Dynamic output feedback sliding mode control for spacecraft hovering without velocity measurements

In consideration of target angular velocity uncertainty and external disturbance, a modified dynamic output feedback sliding mode control (DOFSMC) method is proposed for spacecraft autonomous hovering system without velocity measurements. As a stepping-stone, an additional dynamic compensator is introduced into the design of sliding surface, then an augmented system is reconstructed with the system uncertainty and external disturbance. Based on the linear matrix inequality (LMI), a sufficient condition is given, which guarantees the disturbance attenuation performance of sliding mode dynamics. By introducing an auxiliary variable, a modified version of adaptive sliding mode control (ASMC) law is designed, and the finite-time stability of sliding variable is established by the Lyapunov stability theory. Compared with other results, the proposed method is less conservative and can decrease the generated control input force significantly. Finally, two simulation examples are performed to validate the effectiveness of the proposed method.

Robust Control Allocation in Attitude Fault-Tolerant Control for Combined Spacecraft Under Measurement Uncertainty

Attitude control of combined service-target system in the post-capture phase has received great attention. A new attitude dynamics of the combined spacecraft with reaction wheels has been established in the author's former work, however, the measurement uncertainty in attitude and angular velocity and uncertainty in the reconfiguration matrix of reaction wheels have not been considered, which may cause huge impact on the system performance. In this paper, a novel combination of disturbance-observer-based dynamic surface control under measurement uncertainty and robust control allocation due to uncertain mass center is investigated for attitude stabilization of the combined spacecraft. Firstly, considering measurement uncertainty, inertia uncertainty, actuator fault and actuator saturation, a new attitude dynamics of combined spacecraft is established. Then, a virtual controller is designed and all the states in the closed-loop system converge to a small neighborhood of zero, where the lumped disturbance is compensated by two stable nonlinear disturbance observers and adverse effect of actuator saturation is addressed by a stable compensator. Finally, in consideration of uncertain location of mass center in the reconfiguration matrix, a LMI-based robust control allocation is employed to deal with the problem of distributing the three axis torques over the reaction wheels. Numerical simulations are presented to illustrate the effectiveness of the proposed method.

Detection of a flaring blazar coincident with an IceCube high-energy neutrino

In September 22, 2017, IceCube released a public alert announcing the detection of a 290 TeV neutrino track event with an angular uncertainty of one square degree (90% containment). A multi-messenger follow-up campaign was initiated resulting in the detection of a GeV gamma-ray flare by the Fermi Large Area Telescope positionally consistent with the location of the known Bl Lac object, TXS 0506+056 , located only 0.1 degrees from the best-fit neutrino position. The probability of finding a GeV gamma-ray flare in coincidence with a high-energy neutrino event assuming a correlation of the neutrino flux with the gamma-ray energy flux in the energy band between 1 and 100 GeV was calculated to be 3σ (after trials correction). Following the detection of the flaring blazar the imaging air Cherenkov telescope MAGIC detected the source for the first time in the > 100 GeV gamma-ray band. The activity of the source was confirmed in X-ray, optical and radio wavelength. Several groups have developed lepto-hadronic models which succeed to explain the multi-messenger spectral energy distribution.

Ground vehicle target signature identification with cognitive automotive radar using 24–25 and 76–77 GHz bands

The authors present cognitive automotive radar (CARr) as a significant capability to the sensing technology suite of autonomous driving vehicles. CARr is a closed-loop intelligent radar system utilising the automotive frequency bands of 24–25 and 76–77 GHz for the purposes of ground vehicle target signature identification. The authors consider specific cases of ground vehicle recognition and ground vehicle class identification in the presence of aspect angle uncertainty using forward-looking automotive radar. The transmit-adaptive waveforms are based from signal-to-noise ratio and mutual information optimisation metrics. In this study, two new adaptive waveform techniques with the flexibility to accommodate angular uncertainty probability distributions are introduced. The classification performance of these new waveforms is compared against the receive-adaptive wideband pulsed and other transmit-adaptive waveforms in the presence of angular uncertainties characterised by the uniform and truncated normal distributions. To ensure the validity of results, high-fidelity electromagnetic simulated radar cross-section signatures generated from scaled-to-true-physical-size ground vehicle computer-aided design models are utilised.

A multiwavelength view of BL Lacs neutrino candidates

The discovery of high-energy astrophysical neutrinos by IceCube kicked off a new line of research to identify the electromagnetic counterparts producing these neutrinos. Among the extragalactic sources, active galactic nuclei (AGN), and in particular Blazars, are promising candidate neutrino emitters. Their structure, with a relativistic jet pointing to the Earth, offers a natural accelerator of particles and for this reason a perfect birthplace of high energy neutrinos. A good characterisation of the spectral energy distribution (SED) of these sources can improve the understanding of the physical composition of the source and the emission processes involved. Starting from our previous works in which we assumed a correlation between the $\gamma$-ray and the neutrino flux of the BL Lacs of the 2FHL catalogue (detected by Fermi above 50GeV), we select those BL Lac in spatial correlation with the IceCube events. We obtain a sample of 7 sources and we start an observational campaign to have a better characterisation of the synchrotron peak. During the analysis of the data a new source has been added because of its position inside the angular uncertainty of a muon track event detected by IceCube. This source, namely TXS0506+056, was in a high-state during the neutrino event and we will consider it as benchmark to check the proprieties of the other sources of the sample during the related neutrino detection. We obtain a better characterisation of the SED for the sources of our sample. A prospective extreme Blazar, a very peculiar low synchrotron peak (LSP) source with a large separation of the two peaks and a \textit{twin} of TXS0506+056 come up. We also provide the $\gamma$-ray light curve to check the trend of the sources around the neutrino detection but no clears patterns are in common among the sources.

Diffraction-Limited Plenoptic Imaging with Correlated Light.

Traditional optical imaging faces an unavoidable trade-off between resolution and depth of field (DOF). To increase resolution, high numerical apertures (NAs) are needed, but the associated large angular uncertainty results in a limited range of depths that can be put in sharp focus. Plenoptic imaging was introduced a few years ago to remedy this trade-off. To this aim, plenoptic imaging reconstructs the path of light rays from the lens to the sensor. However, the improvement offered by standard plenoptic imaging is practical and not fundamental: The increased DOF leads to a proportional reduction of the resolution well above the diffraction limit imposed by the lens NA. In this Letter, we demonstrate that correlation measurements enable pushing plenoptic imaging to its fundamental limits of both resolution and DOF. Namely, we demonstrate maintaining the imaging resolution at the diffraction limit while increasing the depth of field by a factor of 7. Our results represent the theoretical and experimental basis for the effective development of promising applications of plenoptic imaging.

Empirical Bolometric Fluxes and Angular Diameters of 1.6 Million Tycho-2 Stars and Radii of 350,000 Stars with Gaia DR1 Parallaxes

Abstract We present bolometric fluxes and angular diameters for over 1.6 million stars in the Tycho-2 catalog, determined using previously determined empirical color-temperature and color-flux relations. We vet these relations via full fits to the full broadband spectral energy distributions for a subset of benchmark stars and perform quality checks against the large set of stars for which spectroscopically determined parameters are available from LAMOST, RAVE, and/or APOGEE. We then estimate radii for the 355,502 Tycho-2 stars in our sample whose Gaia DR1 parallaxes are precise to . For these stars, we achieve effective temperature, bolometric flux, and angular diameter uncertainties of the order of 1%–2% and radius uncertainties of order 8%, and we explore the effect that imposing spectroscopic effective temperature priors has on these uncertainties. These stellar parameters are shown to be reliable for stars with ≲ 7000 K. The over half a million bolometric fluxes and angular diameters presented here will serve as an immediate trove of empirical stellar radii with the Gaia second data release, at which point effective temperature uncertainties will dominate the radius uncertainties. Already, dwarf, subgiant, and giant populations are readily identifiable in our purely empirical luminosity-effective temperature (theoretical) Hertzsprung–Russell diagrams.

Design and optimization of the electrostatic input module for the ISTTOK Tokamak HIBD cylindrical energy analyzer

The Heavy Ion Beam Diagnostic of the ISTTOK Tokamak is based on the injection of a single ionized primary beam (Xe+, Cs+) of energy 20–25 keV and on the collection of all doubly ionized ions emerging from the primary beam due to the impact ionization with the plasma electrons. In the present configuration three local plasma parameters can be retrieved: plasma density (ne), electron temperature (Te), and poloidal magnetic field (Bp). A new detection system is being design in order to determine the plasma potential (Vp) profile via the secondary ions energy measurements. To that end an improved 90̂ cylindrical electrostatic analyzer (CEA) has been designed and optimized to measure the energy of the secondary ions. This paper reports on the design optimization of the input stage of the new detection arrangement to guide and shape 4 secondary beams into the entrance of the CEA. It is composed of a set of four electrostatic cylindrical plates followed by four pairs of steering plates and a multiple aperture Einzel-like electrostatic lens, consisting of four planar vertical electrodes containing four passing slits. Individual secondary beams with dimension of 8 mm × 2.5 mm were obtained without overlapping between the four beams from different slits. By changing the incident beam energy from 20 keV to 20.2 keV (in order to simulate a local plasma potential value of +200 V), without adjusting bias voltage of the input system, results in a vertical beam shift of 1 mm which can be recovered by changing the voltage on the parallel plate arrangement by 40 V. The flexibility and tolerance of the optic system was tested successfully for the expected angular uncertainty of the beam by +/−0.5̂ at the input module entrance and with the expected energy spread of the beam corresponding to different plasma positions inside the tokamak.

Robust Planning for a Patient Treated in Decubitus Position with Proton Pencil Beam Scanning Radiotherapy

A challenging case was reported for a patient treated in decubitus position with proton pencil beam scanning. A regular robust plan with the consideration of the uncertainties of translational alignment and range accuracy cannot ensure the target coverage as revealed in two verification computed tomography (CT) scans during the first week of the treatment. The irreproducibility of daily alignment and anatomical variations in such a position is mainly due to patient’s roll. To mitigate the interfractional effect on the target coverage, a novel robust optimization against the patient’s angular setup uncertainties was implemented to improve the plan quality by introducing two artificial CT image sets by rolling the planning CT three degrees in both clockwise and counter-clockwise directions and adding them into robust optimization scenarios, which was shown to be an effective and simple way to mitigate target dose degradation with respect to interfractional variations. This method can be easily generalized and applied to other situations where angular variations in patient’s setup can introduce large dosimetric effects. It is recommended that angularly robust optimization method should be integrated into the treatment planning system as an option particularly for patient’s treatment subject to large angular variations, such as the one in the decubitus position reported here.

Self-calibration technique for on-machine spindle-mounted vision systems

On-machine measuring (OMM) systems are being more and more applied in machine tools in order to measure workpieces on the machine itself. Many of these systems are directly mounted in the machine spindle, so the measuring uncertainty is affected by clamping positioning and orientation variations, especially when integrating optical systems based on machine vision. This paper presents a self-calibration technique for vision systems by using redundant information of on machine measurements, avoiding extra mechanical anchoring or calibration means. It has been applied to a vision system with the angular placement uncertainty of a tool holder coupling being the main uncertainty contributor. A milling machine pilot case has been selected for demonstration, showing an effective self-calibration capability both in laboratory and industrial conditions.

Double-Layered CZT Compton Imager

In this paper, we propose a double-layered cadmium zinc telluride Compton camera using the weighted list-mode maximum likelihood expectation maximization (MLEM) method. We performed a Monte Carlo simulation of the performance. The detection system comprised two detector arrays arranged in parallel. Each array consisted of $6 \times 6$ crystals with a 7.5 mm pixel pitch. The dimension of a single crystal was $6 \times 6 \times 15$ mm. For Compton imaging, the 137Cs activity was set to 78 kBq and the acquisition time was set to 2 hours. By applying the weighted MLEM method, the events with small angular uncertainty were more emphasized than those with large angular uncertainty. Each angular uncertainty was calculated based on the energy and geometry uncertainties of each event. We compared the traditional list-mode MLEM and the weighted list-mode MLEM for single and double detector arrays. The results showed that the combination of a double-layered imager with the weighted MLEM method represented the best image performance compared to other combinations. The sources at the offset positions were also simulated to estimate the directional dependency of the camera system.

Analysis of a Distributed Array System for Satellite Acquisition

Orbiting satellites and other spatial vehicles have complex trajectories that can usually be precisely approximated with analytical or numerical trajectory estimation algorithms. However, some scenarios, such as Launch and Early Orbit Phase (LEOP) or critical maneuvers, present greater angular uncertainty. During these, large dish antennas used for telemetry, tracking, & command (TT&C) may have too narrow a beamwidth to perform a reliable and fast acquisition. A novel acquisition aid system based on distributed array elements placed on the rim of the main antenna's reflector has been implemented and successfully tested with real satellite signals. This paper presents an analysis of the proposed solution, from a system engineering perspective, exposes several simulations carried out in MATLAB, which motivated some of the design criteria, and compares them with the actual results obtained in field campaigns, thus deriving the final figures of merit (FoM) of the system.

All-sky Search for Time-integrated Neutrino Emission from Astrophysical Sources with 7 yr of IceCube Data

Since the recent detection of an astrophysical flux of high energy neutrinos, the question of its origin has not yet fully been answered. Much of what is known about this flux comes from a small event sample of high neutrino purity, good energy resolution, but large angular uncertainties. In searches for point-like sources, on the other hand, the best performance is given by using large statistics and good angular reconstructions. Track-like muon events produced in neutrino interactions satisfy these requirements. We present here the results of searches for point-like sources with neutrinos using data acquired by the IceCube detector over seven years from 2008--2015. The discovery potential of the analysis in the northern sky is now significantly below $E_\nu^2d\phi/dE_\nu=10^{-12}\:\mathrm{TeV\,cm^{-2}\,s^{-1}}$, on average $38\%$ lower than the sensitivity of the previously published analysis of four years exposure. No significant clustering of neutrinos above background expectation was observed, and implications for prominent neutrino source candidates are discussed.

Probabilistic Mapping with Ultrasonic Distance Sensors

This paper proposes a probabilistic robotic mapping approach to merge ultrasonic distance readings by modelling them as Gaussian random variables and using scan matching to reduce uncertainty in mapping process. To account for the high angular uncertainty of ultrasonic distance sensors, both positive readings (detected objects) and negative readings (the lack of detection) are taken into account to update the measurements and create the updated environment map. To support this approach, the map consists simultaneously from two parts – free space scans are stored in occupancy grid and obstacle readings are represented as Gaussian variable feature set.

Janus particle-based microprobes: Determination of object orientation

Employing information extracted from their translational dynamics, colloidal particles have served extensively as micro-sized probes in in situ analytical techniques such as particle image velocimetry and microrheology. Janus particles, partially shadowed by metal caps appear directional when imaged with an optical microscope, and hence detectable rotational dynamics are introduced into an otherwise spherically symmetric system. Current tracking methods require high-resolution imaging, are time consuming, or focus on bulk light intensity variations. Here, we introduce two image analysis methods that identify the actual body center of gold-capped Janus particles (AuJPs), as well as distinguish the particle orientation within the space. Method I tracks the optical centroid, determines the particle’s in-plane tilting angle, and locates its actual body center (i.e., the Optical Centroid-Tilting Angle-Geometry, OCTAG procedure). Method: II tracks the diffraction ring center and the moon-phase center revealing in-plane orientation (i.e., the Ring-Phase Dual Optical Centroids, RPDOC procedure). With both methods we are able to successfully identify actual body centers and orientations of AuJPs with a resolution of 0.5 pixels and an angular uncertainty of sub−10°. It is thus possible to probe the local medium response on sub-micrometer length scales. The data analysis is applied to track dilute suspensions of AuJPs undergoing Brownian motion in a viscous glycerol-water mixture of volume ratio 1 or 2. Mean-square displacement (MSD) and angular mean-square displacement (AMSD) extracted from the experimental measurements are related to medium viscosities according to the Stokes-Einstein equation and the Perrin rotational diffusion, respectively. The viscosities calculated based on the diffusion coefficients determined from analysis of the translational and rotational dynamics of the microprobes differ by less than 6%. The 6% deviation observed is attributed to wall and gravitational effects. Results indicate that Janus particles can serve as novel probes in microrheology, and their asymmetric surface properties may potentially be used to investigate particle-medium interactions.

Design and experimental verification of novel six-degree-of freedom geometric error measurement system for linear stage

In this study, a novel and simple measurement system for simultaneously measuring the geometric errors in six-degree-of-freedom (6-DOF) for a moving linear stage of a machine tool is designed and validated. Compared to laser interferometer and laser Doppler systems, this new measurement system is less expensive and capable of multiple functions. The proposed measurement system comprises an optics module, composed of two reflectors and two cubic beam splitters; a sensing module, composed of three two-dimensional position sensitive detectors (PSDs); and a helium-neon (He-Ne) laser. Using skew-ray tracing and a first-order Taylor series expansion, the 6-DOF geometric errors of the moving linear stage, which include translation and rotation errors, are analyzed. A laboratory prototype system is built to verify the effectiveness and accuracy of the proposed measurement system. The experimental results show that the displacement uncertainty and the angular uncertainty of the proposed measurement system are less than 1.2µm and 0.4″, respectively. Compared with the Renishaw laser interferometer XL-80 laser system, the translational accuracy and the rotational accuracy of the proposed measurement system are less than ±1µm and ±0.2″, respectively, when the linear stage travels 6mm.