Order estimation and discrimination between stationary and time-varying (TVAR) autoregressive models

Copyright © 2007 IEEEFor a set of T independent observations of the same N-variate correlated Gaussian process, we derive a method of estimating the order of an autoregressive (AR) model of this process, regardless of its stationary or time-varying nature. We also derive a test to discriminate between stationary AR models of order m,AR(m), and time-varying autoregressive models of order m,TVAR(m). We demonstrate that within this technique the number T of independent identically distributed data samples required for order estimation and discrimination just exceeds the maximum possible order mmax, which in many cases is significantly fewer than the dimension of the problem NYuri I. Abramovich, Nicholas K. Spencer, and Michael D. E. Turle

Time-varying autoregressive (TVAR) models for multiple radar observations

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.We consider the adaptive radar problem where the properties of the (nonstationary) clutter signals can be estimated using multiple observations of radar returns from a number of sufficiently homogeneous range/azimuth resolution cells. We derive a method for approximating an arbitrary Hermitian covariance matrix by a time-varying autoregressive model of order m, TVAR(m), that is based on the Dym-Gohberg band-matrix extension technique which gives the unique TVAR(m) model for any nondegenerate covariance matrix. We demonstrate that the Dym-Gohberg transformation of the sample covariance matrix gives the maximum-likelihood (ML) estimate of the TVAR(m) covariance matrix. We introduce an example of TVAR(m) clutter modeling for high-frequency over-the-horizon radar that demonstrates its practical importanceYuri I. Abramovich, Nicholas K. Spencer, and Michael D. E. Turle

High-Resolution UV Relay Lens for Particle Size Distribution Measurements Using Holography

Shock waves passing through a metal sample can produce ejecta particulates at a metal-vacuum interface. Holography records particle size distributions by using a high-power, short-pulse laser to freeze particle motion. The sizes of the ejecta particles are recorded using an in-line Fraunhofer holography technique. Because the holographic plate would be destroyed in an energetic environment, a high-resolution lens has been designed to relay the interference fringes to a safe environment. Particle sizes within a 12-mm-diameter, 5-mm-thick volume are recorded onto holographic film. To achieve resolution down to 0.5 μm, ultraviolet laser (UV) light is needed. The design and assembly of a nine-element lens that achieves >2000 lp/mm resolution and operates at f/0.89 will be described. To set up this lens system, a doublet lens is temporarily attached that enables operation with 532-nm laser light and 1100 lp/mm resolution. Thus, the setup and alignment are performed with green light, but the dynamic recording is done with UV light. During setup, the 532-nm beam provides enough focus shift to accommodate the placement of a resolution target outside the ejecta volume; this resolution target does not interfere with the calibrated wires and pegs surrounding the ejecta volume. A television microscope archives images of resolution patterns that prove that the calibration wires, interference filter, holographic plate, and relay lenses are in their correct positions. Part of this lens is under vacuum, at the point where the laser illumination passes through a focus. Alignment and tolerancing of this high-resolution lens will be presented, and resolution variation through the 5-mm depth of field will be discussed

Measuring the Neutrino Cross Section Using 8 years of Upgoing Muon Neutrinos Observed with IceCube

The IceCube Neutrino Observatory detects neutrinos at energies orders of magnitude higher than those available to current accelerators. Above 40 TeV, neutrinos traveling through the Earth will be absorbed as they interact via charged current interactions with nuclei, creating a deficit of Earth-crossing neutrinos detected at IceCube. The previous published results showed the cross section to be consistent with Standard Model predictions for 1 year of IceCube data. We present a new analysis that uses 8 years of IceCube data to fit the ν$_{μ}$ absorption in the Earth, with statistics an order of magnitude better than previous analyses, and with an improved treatment of systematic uncertainties. It will measure the cross section in three energy bins that span the range 1 TeV to 100 PeV. We will present Monte Carlo studies that demonstrate its sensitivity