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White noise
About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.
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TL;DR: It is found that contrast sensitivity in spatial noise was independent of eccentricity as long as contrast sensitivity was lower with noise than without, and without M-scaling the effect of increasing eccentricity is similar to that of increasing viewing distance.
77 citations
TL;DR: In this article, a model for double-indexed space invariant linear transformations along with a class of doubleindexed Gaussian sequences built as output of such linear transformations "driven" by white noise is introduced.
Abstract: Publisher Summary Linear recursive processing is a practical solution to the main drawback of digital technology, which is its slowness for many real time signal processing applications. It seems reasonable to try natural generalizations of the various equivalent characterizations of linear recursive time invariant transformations: (1) the algebraic characterization as finite-rank linear operators and (2) the “behavioral” characterization as a transformation described by a finite-order autoregressive form relating the inputs and the outputs. The approach presented in this chapter is to generalize the algebraic characterization that turns to be very fertile and allows building a self-contained theory for statistical recursive processing for a large class of double-indexed sequences. The chapter introduces a model for double-indexed space invariant linear transformations along with a class of double-indexed Gaussian sequences built as “output” of such linear transformations “driven” by white noise. A realization theory is developed leading to an algebraic characterization of those transformations, an approximation property, and a minimal realization algorithm. . After an approximation theorem proving the generality of this class of sequences, the study of their correlation function leads to stochastic identification algorithms and throws some light on spectral factorization properties of double-indexed sequences. The chapter yields a recursive solution to filtering and smoothing problems involving Gaussian sequences.
77 citations
TL;DR: Generally, the positioning performance of PPP in terms of convergence time and positioning accuracy with the final products from CODE, CNES, and WHU is comparable among the three ISB handling schemes, however, estimating ISBs as random walk process or white noise process outperforms that as the random constant when using the GFZ products.
Abstract: The focus of this study is on proper modeling of the dynamics for inter-system biases (ISBs) in multi-constellation Global Navigation Satellite System (GNSS) precise point positioning (PPP) processing. First, the theoretical derivation demonstrates that the ISBs originate from not only the receiver-dependent hardware delay differences among different GNSSs but also the receiver-independent time differences caused by the different clock datum constraints among different GNSS satellite clock products. Afterward, a comprehensive evaluation of the influence of ISB stochastic modeling on undifferenced and uncombined PPP performance is conducted, i.e., random constant, random walk process, and white noise process are considered. We use data based on a 1-month period (September 2017) Multi-GNSS Experiment (MGEX) precise orbit and clock products from four analysis centers (CODE, GFZ, CNES, and WHU) and 160 MGEX tracking stations. The results demonstrate that generally, the positioning performance of PPP in terms of convergence time and positioning accuracy with the final products from CODE, CNES, and WHU is comparable among the three ISB handling schemes. However, estimating ISBs as random walk process or white noise process outperforms that as the random constant when using the GFZ products. These results indicate that the traditional estimation of ISBs as the random constant may not always be reasonable in multi-GNSS PPP processing. To achieve more reliable positioning results, it is highly recommended to consider the ISBs as random walk process or white noise process in multi-GNSS PPP processing.
77 citations
TL;DR: This work presents a novel method, based on a 2-D lattice algorithm, to compute the needed forward prediction matrix polynomials and discusses the difference in the so-obtained2-D spectral estimate as compared with the one obtained by using the prediction matrixPolynomial given by the Whittle-Wiggins-Robinson algorithm.
Abstract: We present a computationally efficient algorithm for computing the 2-D Capon (1969) spectral estimator. The implementation is based on the fact that the 2-D data covariance matrix will have a Toeplitz-block-Toeplitz structure, with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the Gohberg-Heinig (1974) formula that is a function of strictly the forward 2-D prediction matrix polynomials. Furthermore, we present a novel method, based on a 2-D lattice algorithm, to compute the needed forward prediction matrix polynomials and discuss the difference in the so-obtained 2-D spectral estimate as compared with the one obtained by using the prediction matrix polynomials given by the Whittle-Wiggins-Robinson (1963, 1965) algorithm. Numerical simulations illustrate the improved resolution as well as the clear computational gain in comparison to both the well-known classical implementation and the method published by Liu et al.(see IEEE Trans. Aerosp. Electron. Syst., vol.34, p.1314-19, 1998).
77 citations
TL;DR: In this article, the authors derived the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps and proposed a new procedure for testing for the presence of residual bias due to inappropriate noise subtraction in pseudo-Cl estimates.
Abstract: We discuss the derivation of the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps. The method is computationally convenient and it provides unbiased estimates under very broad assumptions. We also propose a new procedure for testing for the presence of residual bias due to inappropriate noise subtraction in pseudo-Cl estimates. We derive the analytic behaviour of this procedure under the null hypothesis, and use Monte Carlo simulations to investigate its efficiency properties, which appear very promising. For instance, for full sky maps with isotropic white noise, the test is able to identify an error of 1% on the noise amplitude estimate.
76 citations