Optimized Blind Gamma-ray Pulsar Searches at Fixed Computing Budget

The sensitivity of blind gamma-ray pulsar searches in multiple years worth of photon data, as from the Fermi LAT, is primarily limited by the finite computational resources available. Addressing this "needle in a haystack" problem, we here present methods for optimizing blind searches to achieve the highest sensitivity at fixed computing cost. For both coherent and semicoherent methods, we consider their statistical properties and study their search sensitivity under computational constraints. The results validate a multistage strategy, where the first stage scans the entire parameter space using an efficient semicoherent method and promising candidates are then refined through a fully coherent analysis. We also find that for the first stage of a blind search incoherent harmonic summing of powers is not worthwhile at fixed computing cost for typical gamma-ray pulsars. Further enhancing sensitivity, we present efficiency-improved interpolation techniques for the semicoherent search stage. Via realistic simulations we demonstrate that overall these optimizations can significantly lower the minimum detectable pulsed fraction by almost 50% at the same computational expense.Comment: 22 pages, 13 figures; includes ApJ proof correction

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system

Pulsar timing analysis in the presence of correlated noise

Pulsar timing observations are usually analysed with least-square-fitting procedures under the assumption that the timing residuals are uncorrelated (statistically "white"). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.Comment: Accepted by MNRA

SuperDARN parameter estimation optimization and implementation of new techniques

Thesis (M.S.) University of Alaska Fairbanks, 2013The Super Dual Auroral Radar Network (SuperDARN) is an international radar network to study the ionosphere and upper atmosphere. The primary target of SuperDARN is field-aligned plasma irregularities in the E- and F-region of the ionosphere. To quantify the characteristics of these irregularities, the radar measures power, Doppler velocity, and spectral width from auto-correlation functions of the received samples. Since the target of interest is overspread, the derived parameters suffer from errors related to cross-range interference. In this thesis, we propose two scenarios to address this problem. First, we implement new approaches to avoid the cross-range interference, and second, we develop new optimization techniques that are more robust and less sensitive in dealing with this interference. New methods include filtering techniques, spectral analysis, and use of inverse techniques. The filtering methods (mismatched and adaptive) offer improvement in both suppressing the side lobes associated with pulse compression techniques and optimal estimation of the main lobe signal-to-noise ratio. Spectral analysis, extracts multiple Doppler velocities in the range while the current time-domain analysis is only capable of measuring one. Instead of dealing with ambiguities, inverse theory applied to SuperDARN received samples can potentially remove the associated cross-range interference, which results in more detailed and accurate information in obtaining the structure and dynamics of the irregularities. More accurate and detailed empirical models resulting from new optimization methods give more information that can be mapped over the current in-progress theoretical models, which finally results in better understanding the physics of the ionosphere

An Extended Virtual Aperture Imaging Model for Through-the-wall Sensing and Its Environmental Parameters Estimation

Through-the-wall imaging (TWI) radar has been given increasing attention in recent years. However, prior knowledge about environmental parameters, such as wall thickness and dielectric constant, and the standoff distance between an array and a wall, is generally unavailable in real applications. Thus, targets behind the wall suffer from defocusing and displacement under the conventional imag¬ing operations. To solve this problem, in this paper, we first set up an extended imaging model of a virtual aperture obtained by a multiple-input-multiple-output array, which considers the array position to the wall and thus is more applicable for real situations. Then, we present a method to estimate the environmental parameters to calibrate the TWI, without multiple measurements or dominant scatter¬ers behind-the-wall to assist. Simulation and field experi¬ments were performed to illustrate the validity of the pro¬posed imaging model and the environmental parameters estimation method