The Limits of In-run Calibration of MEMS and the Effect of New Techniques

Inertial sensors can significantly increase the robustness of an integrated navigation system by bridging gaps in the coverage of other positioning technologies, such as GNSS or Wi-Fi positioning [1]. A full set of chip-scale MEMS accelerometers and gyros can now be bought for less than $10, potentially opening up a wide range of new applications. However, these sensors require calibration before they can be used for navigation[2]. Higher quality inertial sensors may be calibrated “in-run” using Kalman filter-based estimation as part of their integration with GNSS or other position-fixing techniques. However, this approach can fail when applied to sensors with larger errors which break the Kalman filter due to the linearity and small-angle approximations within its system model not being valid. Possible solutions include: replacing the Kalman filter with a non-linear estimation algorithm, a pre-calibration procedure and smart array [3]. But these all have costs in terms of user effort, equipment or processing load. This paper makes two key contributions to knowledge. Firstly, it determines the maximum tolerable sensor errors for any in-run calibration technique using a basic Kalman filter by developing clear criteria for filter failure and performing Monte-Carlo simulations for a range of different sensor specifications. Secondly, it assesses the extent to which pre-calibration and smart array techniques enable Kalman filter-based in-run calibration to be applied to lower-quality sensors. Armed with this knowledge of the Kalman filter’s limits, the community can avoid both the unnecessary design complexity and computational power consumption caused by over-engineering the filter and the poor navigation performance that arises from an inadequate filter. By establishing realistic limits, one can determine whether real sensors are suitable for in-run calibration with simple characterization tests, rather than having to perform time-consuming empirical testing

The Limits of In-Run Calibration of MEMS Inertial Sensors and Sensor Arrays

MEMS accelerometers and gyroscope triads now cost less than $10, potentially opening up many new applications. However, these sensors require calibration prior to navigation use. This paper determines the maximum tolerable sensor errors for in-run calibration techniques using a basic Kalman filter by developing criteria for filter failure and performing Monte Carlo simulations for a range of different sensor specifications, and both car and UAV motion-profiles. Gyroscope bias is found to be the most significant with the maximum tolerable value of its SD varying between 0.75 and 2.6 deg/s depending on the value of the specification of the other sensor sources. The paper shows that pre-calibration and smart array techniques could potentially enable in-run calibration to be applied to lower-quality sensors. However, the estimation of scale-factor cross-coupling and gyroscope g-dependent errors could potentially be critical. Armed with this knowledge, designers can avoid both unnecessary design complexity and computational load of over-engineering and the poor navigation performance of inadequate filters

Intelligent GNSS Positioning using 3D Mapping and Context Detection for Better Accuracy in Dense Urban Environments

Conventional GNSS positioning in dense urban areas can exhibit errors of tens of meters due to blockage and reflection of signals by the surrounding buildings. Here, we present a full implementation of the intelligent urban positioning (IUP) 3D-mapping-aided (3DMA) GNSS concept. This combines conventional ranging-based GNSS positioning enhanced by 3D mapping with the GNSS shadow-matching technique. Shadow matching determines position by comparing the measured signal availability with that predicted over a grid of candidate positions using 3D mapping. Thus, IUP uses both pseudo-range and signal-to-noise measurements to determine position. All algorithms incorporate terrain-height aiding and use measurements from a single epoch in time. Two different 3DMA ranging algorithms are presented, one based on least-squares estimation and the other based on computing the likelihoods of a grid of candidate position hypotheses. The likelihood-based ranging algorithm uses the same candidate position hypotheses as shadow matching and makes different assumptions about which signals are direct line-of-sight (LOS) and non-line-of-sight (NLOS) at each candidate position. Two different methods for integrating likelihood-based 3DMA ranging with shadow matching are also compared. In the position-domain approach, separate ranging and shadow-matching position solutions are computed, then averaged using direction-dependent weighting. In the hypothesis-domain approach, the candidate position scores from the ranging and shadow matching algorithms are combined prior to extracting a joint position solution. Test data was recorded using a u-blox EVK M8T consumer-grade GNSS receiver and a HTC Nexus 9 tablet at 28 locations across two districts of London. The City of London is a traditional dense urban environment, while Canary Wharf is a modern environment. The Nexus 9 tablet data was recorded using the Android Nougat GNSS receiver interface and is representative of future smartphones. Best results were obtained using the likelihood-based 3DMA ranging algorithm and hypothesis-based integration with shadow matching. With the u-blox receiver, the single-epoch RMS horizontal (i.e., 2D) error across all sites was 4.0 m, compared to 28.2 m for conventional positioning, a factor of 7.1 improvement. Using the Nexus tablet, the intelligent urban positioning RMS error was 7.0 m, compared to 32.7 m for conventional GNSS positioning, a factor of 4.7 improvement. An analysis of processing and data requirements shows that intelligent urban positioning is practical to implement in real-time on a mobile device or a server. Navigation and positioning is inherently dependent on the context, which comprises both the operating environment and the behaviour of the host vehicle or user. No single technique is capable of providing reliable and accurate positioning in all contexts. In order to operate reliably across different contexts, a multi-sensor navigation system is required to detect its operating context and reconfigure the techniques accordingly. Specifically, 3DMA GNSS should be selected when the user is in a dense urban environment, not indoors or in an open environment. Algorithms for detecting indoor and outdoor context using GNSS measurements and a hidden Markov model are described and demonstrated

Fermionic Zero Modes on Domain Walls

We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass terms could also be the coupling to a scalar field $\Phi$ or a vacuum expectation value of some other field acquired in a phase transition well above the phase transition of the field $\Phi$. We derive the fermionic equations of motion and find the necessary and sufficient conditions for a zero mode to exist. We also find the solutions numerically. In the absence of the Majorana mass terms, the equations are solvable analytically. In the case of massless fermions a zero energy solution exists and we show that although this mode is not discretely normalizable it is Dirac delta function normalizable and should be viewed as part of a continuum spectrum rather than as an isolated zero mode.Comment: 6 pages, 3 figures, matches version published in PR

Pregnancy Medicaid Expansions and Fertility: Differentiating between the Intensive and Extensive Margins

The theoretical and empirical links between public health insurance access and fertility in the United States remain unclear. Utilizing a demographic cell-based estimation approach with panel data (1987-1997), we revisit the large-scale Medicaid expansions to pregnant women during the 1980s to estimate the heterogeneous impacts of public health insurance access on childbirth. While the decision to become a parent (i.e., the extensive margin) appears to be unaffected by increased access to Medicaid, we find that increased access to public health insurance positively influenced the number of high parity births (i.e., the intensive margin) for select groups of women. In particular, we find a robust, positive birth effect for unmarried women with a high school education, a result which is consistent across the two racial groups examined in our analysis: African American and white women. This result suggests that investigating effects along both the intensive and extensive margin is important for scholars who study the natalist effects of social welfare policies, and our evidence provides a more nuanced understanding of the influence of public health insurance on fertility

Informing decisions on the purchase of equipment used by health services in response to incidents involving hazardous materials

Accidents involving release of chemical, biological, radiological or nuclear substances may prompt the need to decontaminate exposed casualties prior to further medical treatment. Health service workers who carry out decontamination procedures wear protective suits to avoid direct contact with contaminants. We developed an analytical framework based on queueing theory to inform UK Department of Health's decisions on the stock of protective suits that ambulance services and hospitals with emergency departments in England should hold. Our aim was to ensure that such allocation gave an accepted degree of resilience to locally identified hazards. Here we give an overview of our work and describe how we incorporated information in the public domain about local hazards with expert opinion about the patterns of demand for decontamination associated with different types of incident. We also give an account of how we worked with decision makers to inform national guidance on this topic

SN1991bg-like supernovae are associated with old stellar populations

SN1991bg-like supernovae are a distinct subclass of thermonuclear supernovae (SNe Ia). Their spectral and photometric peculiarities indicate their progenitors and explosion mechanism differ from `normal' SNe Ia. One method of determining information about supernova progenitors we cannot directly observe is to observe the stellar population adjacent to the apparent supernova explosion site to infer the distribution of stellar population ages and metallicities. We obtain integral field observations and analyse the spectra extracted from regions of projected radius $\sim\,\mathrm{kpc}$ about the apparent SN explosion site for 11 91bg-like SNe in both early- and late-type galaxies. We utilize full-spectrum spectral fitting to determine the ages and metallicities of the stellar population within the aperture. We find that the majority of the stellar populations that hosted 91bg-like supernovae have little recent star formation. The ages of the stellar populations suggest that that 91bg-like SN progenitors explode after delay times of $>6\,\mathrm{Gyr}$, much longer than the typical delay time of normal SNe Ia, which peaks at $\sim 1\,\mathrm{Gyr}$.Comment: 12 pages, 3 figures, 3 tables, submitted to Publications of the Astronomical Society of Australi

Sequential pivotal mechanisms for public project problems

It is well-known that for several natural decision problems no budget balanced Groves mechanisms exist. This has motivated recent research on designing variants of feasible Groves mechanisms (termed as `redistribution of VCG (Vickrey-Clarke-Groves) payments') that generate reduced deficit. With this in mind, we study sequential mechanisms and consider optimal strategies that could reduce the deficit resulting under the simultaneous mechanism. We show that such strategies exist for the sequential pivotal mechanism of the well-known public project problem. We also exhibit an optimal strategy with the property that a maximal social welfare is generated when each player follows it. Finally, we show that these strategies can be achieved by an implementation in Nash equilibrium.Comment: 19 pages. The version without the appendix will appear in the Proc. 2nd International Symposium on Algorithmic Game Theory, 200

Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static non-rotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress-energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.Comment: 5 pages, 4 figures, additional discussio

Activation-triggered subunit exchange between CaMKII holoenzymes facilitates the spread of kinase activity

The activation of the dodecameric Ca2+/calmodulin dependent kinase II (CaMKII) holoenzyme is critical for memory formation. We now report that CaMKII has a remarkable property, which is that activation of the holoenzyme triggers the exchange of subunits between holoenzymes, including unactivated ones, enabling the calcium-independent phosphorylation of new subunits. We show, using a single-molecule TIRF microscopy technique, that the exchange process is triggered by the activation of CaMKII, and that exchange is modulated by phosphorylation of two residues in the calmodulin-binding segment, Thr 305 and Thr 306. Based on these results, and on the analysis of molecular dynamics simulations, we suggest that the phosphorylated regulatory segment of CaMKII interacts with the central hub of the holoenzyme and weakens its integrity, thereby promoting exchange. Our results have implications for an earlier idea that subunit exchange in CaMKII may have relevance for information storage resulting from brief coincident stimuli during neuronal signaling