Unbiased, optimal, and in-betweens: the trade-off in discrete finite impulse response filtering

In this survey, the authors examine the trade-off between the unbiased, optimal, and in-between solutions in finite impulse response (FIR) filtering. Specifically, they refer to linear discrete real-time invariant state-space models with zero mean noise sources having arbitrary covariances (not obligatorily delta shaped) and distributions (not obligatorily Gaussian). They systematically analyse the following batch filtering algorithms: unbiased FIR (UFIR) subject to the unbiasedness condition, optimal FIR (OFIR) which minimises the mean square error (MSE), OFIR with embedded unbiasedness (EU) which minimises the MSE subject to the unbiasedness constraint, and optimal UFIR (OUFIR) which minimises the MSE in the UFIR estimate. Based on extensive investigations of the polynomial and harmonic models, the authors show that the OFIR-EU and OUFIR filters have higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters

Quasinormal modes of Schwarzschild black holes in four and higher dimensions

We make a thorough investigation of the asymptotic quasinormal modes of the four and five-dimensional Schwarzschild black hole for scalar, electromagnetic and gravitational perturbations. Our numerical results give full support to all the analytical predictions by Motl and Neitzke, for the leading term. We also compute the first order corrections analytically, by extending to higher dimensions, previous work of Musiri and Siopsis, and find excellent agreement with the numerical results. For generic spacetime dimension number D the first-order corrections go as $\frac{1}{n^{(D-3)/(D-2)}}$. This means that there is a more rapid convergence to the asymptotic value for the five dimensional case than for the four dimensional case, as we also show numerically.Comment: 12 pages, 5 figures, RevTeX4. v2. Typos corrected, references adde

Alignment of the CMS tracker with LHC and cosmic ray data

The central component of the CMS detector is the largest silicon tracker ever built. The precise alignment of this complex device is a formidable challenge, and only achievable with a significant extension of the technologies routinely used for tracking detectors in the past. This article describes the full-scale alignment procedure as it is used during LHC operations. Among the specific features of the method are the simultaneous determination of up to 200 000 alignment parameters with tracks, the measurement of individual sensor curvature parameters, the control of systematic misalignment effects, and the implementation of the whole procedure in a multi-processor environment for high execution speed. Overall, the achieved statistical accuracy on the module alignment is found to be significantly better than 10μm.© CERN 2014 for the benefit of the CMS collaboration.

Strategies and performance of the CMS silicon tracker alignment during LHC Run 2

The strategies for and the performance of the CMS silicon tracking system alignment during the 2015–2018 data-taking period of the LHC are described. The alignment procedures during and after data taking are explained. Alignment scenarios are also derived for use in the simulation of the detector response. Systematic effects, related to intrinsic symmetries of the alignment task or to external constraints, are discussed and illustrated for different scenarios