General Statistical Design of an Experimental Problem for Harmonics

Four years ago, the Michelin Tire Corporation proposed a problem on experimental design, to improve the manufacturing process for their tires. The idea is basically to determine the effects of placements for various layers built up in the construction of a tire, to allow the design of a smooth tire with a smooth ride. A highly success solution was developed, and it has been reported that this method introduced savings of over half a million dollars in their test processes. This year, Michelin returned to the workshop with an extension to the original problem, to address specific refinements in the testing method. This report summarizes the work completed in course of the five day workshop. It was clear early in the workshop that this problem could be handled quickly by reviewing the analysis which was done in 2000, and extending those ideas to the new problems at hand. We reviewed the required Fourier techniques to describe the harmonic problem, and statistical techniques to deal with the linear model that described how to accurately measure quantities that come from real experimental measurements. The “prime method” and “good lattice points method” were reviewed and re-analysed so we could understand (and prove) why they work so well. We then looked at extending these methods and successfully found solutions to problem 1) and 2) posed by Michelin. Matlab code was written to test and verify the algorithms developed. We have some ideas on problems 3) and 4), which are also described

Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters

The paper deals with issues pertaining the detection of gravitational waves from coalescing binaries. We introduce the application of differential geometry to the problem of optimal detection of the `chirp signal'. We have also carried out extensive Monte Carlo simulations to understand the errors in the estimation of parameters of the binary system. We find that the errors are much more than those predicted by the covariance matrix even at a high SNR of 10-15. We also introduce the idea of using the instant of coalescence rather than the time of arrival to determine the direction to the source.Comment: 28 pages, REVTEX, 12 figures (bundled via uufiles command along with this paper) submitted to Phys. Rev.

Fast Implementation of Transmit Beamforming for Colocated MIMO Radar

Multiple-input Multiple-output (MIMO) radars benefit from spatial and waveform diversities to improve the performance potential. Phased array radars transmit scaled versions of a single waveform thereby limiting the transmit degrees of freedom to one. However MIMO radars transmit diverse waveforms from different transmit array elements thereby increasing the degrees of freedom to form flexible transmit beampatterns. The transmit beampattern of a colocated MIMO radar depends on the zero-lag correlation matrix of different transmit waveforms. Many solutions have been developed for designing the signal correlation matrix to achieve a desired transmit beampattern based on optimization algorithms in the literature. In this paper, a fast algorithm for designing the correlation matrix of the transmit waveforms is developed that allows the next generation radars to form flexible beampatterns in real-time. An efficient method for sidelobe control with negligible increase in mainlobe width is also presented

Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case

In this paper we describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from Gravitational wave signals. All the existing litterature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of a MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias for MLE of physical parameters from the inspiral phase of binary mergers and for noises of gravitational wave interferometers . We also compare the improved error estimate with existing numerical estimates. The value of the second order of the variance expansions allows to get error predictions closer to what is observed in numerical simulations. It also predicts correctly the necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties SNR and estimation errors. For example the timing match filtering becomes optimal only if the SNR is larger than the kurtosis of the gravitational wave spectrum

Constraining Lorentz-violating, Modified Dispersion Relations with Gravitational Waves

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.Comment: 11 pages, 3 figures, 2 tables: title changed slightly, published versio