An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities

An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm

Gain selection method and model for coupled propulsion and airframe systems

A longitudinal model is formulated for an advanced fighter from three subsystem models: the inlet, the engine, and the airframe. Notable interaction is found in the coupled system. A procedure, based on eigenvalue sensitivities, is presented which indicates the importance of the feedback gains to the optimal solution. This allows ineffectual gains to be eliminated; thus, hardware and expense may be saved in the realization of the physical controller

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates

A strategic needs assessment for Nottinghamshire

Peter Murphy, Kirsten Greenhalgh and Craig Parkin from Nottingham Trent University, University of Nottingham and Nottinghamshire Fire and Rescue Service, report on their joint project

Fire and rescue service reconfiguration: a case study in Nottinghamshire

The Fire Cover Review in Nottinghamshire arises out of the Integrated Risk Management Planning process introduced in the UK by the Fire and Rescue 2004 Act,. It is intended to provide the evidence and analysis for the reconfiguration of services and the future deployment of resources in in the short, medium and long terms. Any future reconfigurations of services must be based on contemporary and comprehensive risk assessments of the areas affected.(ODPM 2004). The need to undertake the review pre-dated the current financial crises, the general election and the need for significant reductions in public expenditure in the UK, although these circumstances made the review more challenging and politically sensitive. This paper evaluates the practical implementation of the Integrated Risk Management Planning process and the Fire Cover Review in Nottinghamshire to identify good practice and to generate recommendations for improving the process and its implementation

Determination of airplane model structure from flight data by using modified stepwise regression

The linear and stepwise regressions are briefly introduced, then the problem of determining airplane model structure is addressed. The MSR was constructed to force a linear model for the aerodynamic coefficient first, then add significant nonlinear terms and delete nonsignificant terms from the model. In addition to the statistical criteria in the stepwise regression, the prediction sum of squares (PRESS) criterion and the analysis of residuals were examined for the selection of an adequate model. The procedure is used in examples with simulated and real flight data. It is shown that the MSR performs better than the ordinary stepwise regression and that the technique can also be applied to the large amplitude maneuvers

3-d resistive MHD simulations of magnetic reconnection and the tearing mode instability in current sheets

Magnetic reconnection plays a critical role in many astrophysical processes where high energy emission is observed, e.g. particle acceleration, relativistic accretion powered outflows, pulsar winds and probably in dissipation of Poynting flux in GRBs. The magnetic field acts as a reservoir of energy and can dissipate its energy to thermal and kinetic energy via the tearing mode instability. We have performed 3d nonlinear MHD simulations of the tearing mode instability in a current sheet. Results from a temporal stability analysis in both the linear regime and weakly nonlinear (Rutherford) regime are compared to the numerical simulations. We observe magnetic island formation, island merging and oscillation once the instability has saturated. The growth in the linear regime is exponential in agreement with linear theory. In the second, Rutherford regime the island width grows linearly with time. We find that thermal energy produced in the current sheet strongly dominates the kinetic energy. Finally preliminary analysis indicates a P(k) 4.8 power law for the power spectral density which suggests that the tearing mode vortices play a role in setting up an energy cascade.Comment: 4 pages, 8 figures, accepted for publication in the International Journal of Modern Physics D, proceedings of HEPRO meeting, held in Dublin, in September 200

Galaxies into the Dark Ages

We consider the capabilities of current and future large facilities operating at 2\,mm to 3\,mm wavelength to detect and image the [CII] 158\,$\mu$m line from galaxies into the cosmic "dark ages" ($z \sim 10$ to 20). The [CII] line may prove to be a powerful tool in determining spectroscopic redshifts, and galaxy dynamics, for the first galaxies. We emphasize that the nature, and even existence, of such extreme redshift galaxies, remains at the frontier of open questions in galaxy formation. In 40\,hr, ALMA has the sensitivity to detect the integrated [CII] line emission from a moderate metallicity, active star-forming galaxy [$Z_A = 0.2\,Z_{\odot}$; star formation rate (SFR) = 5\,$M_\odot$\,yr$^{-1}$], at $z = 10$ at a significance of 6$\sigma$. The next-generation Very Large Array (ngVLA) will detect the integrated [CII] line emission from a Milky-Way like star formation rate galaxy ($Z_{A} = 0.2\,Z_{\odot}$, SFR = 1\,$M_\odot$\,yr$^{-1}$), at $z = 15$ at a significance of 6$\sigma$. Imaging simulations show that the ngVLA can determine rotation dynamics for active star-forming galaxies at $z \sim 15$, if they exist. Based on our very limited knowledge of the extreme redshift Universe, we calculate the count rate in blind, volumetric surveys for [CII] emission at $z \sim 10$ to 20. The detection rates in blind surveys will be slow (of order unity per 40\,hr pointing). However, the observations are well suited to commensal searches. We compare [CII] with the [OIII] 88$\mu$m line, and other ancillary information in high $z$ galaxies that would aid these studies.Comment: 11pages, 8 figures, Accepted for the Astrophysical Journa