Does eye tremor provide the hyperacuity phenomenon?

This paper is devoted to a study of the role of the fluctuations that the eye is subject to, from the point of view of noise-enhanced processing. To this end, a basic model of the retina is considered, namely a regular sampler subject to space and time fluctuations that model the random sampling and the involuntary eye tremor respectively. The filtering that can be done by the photoreceptor is also taken into account and the study focuses on a stochastic model of a natural scene. To quantify the effect of the noise, a coefficient of correlation between the signal acquired by a given photoreceptor and a given point of the scene that the eye is looking at is considered. It is shown both for academic examples and for a more realistic case that the fluctuations which affect the retina can induce noise-enhanced processing effects. The observed effect is then interpreted as a stochastic control of the retina via the random tremor.

Review of current GPS methodologies for producing accurate time series and their error sources

Jean-Philippe Lucien Montillet

The Global Positioning System (GPS) is an important tool to observe and model geodynamic processes such as plate tectonics and post-glacial rebound. In the last three decades, GPS has seen tremendous advances in the precision of the measurements, which allow researchers to study geophysical signals through a careful analysis of daily time series of GPS receiver coordinates. However, the GPS observations contain errors and the time series can be described as the sum of a real signal and noise. The signal itself can again be divided into station displacements due to geophysical causes and to disturbing factors. Examples of the latter are errors in the realization and stability of the reference frame and corrections due to ionospheric and tropospheric delays and GPS satellite orbit errors. There is an increasing demand on detecting millimeter to sub-millimeter level ground displacement signals in order to further understand regional scale geodetic phenomena hence requiring further improvements in the sensitivity of the GPS solutions. This paper provides a review spanning over 25 years of advances in processing strategies, error mitigation methods and noise modeling for the processing and analysis of GPS daily position time series. The processing of the observations is described step-by-step and mainly with three different strategies in order to explain the weaknesses and strengths of the existing methodologies. In particular, we focus on the choice of the stochastic model in the GPS time series, which directly affects the estimation of the functional model including, for example, tectonic rates, seasonal signals and co-seismic offsets. Moreover, the geodetic community continues to develop computational methods to fully automatize all phases from analysis of GPS time series. This idea is greatly motivated by the large number of GPS receivers installed around the world for diverse applications ranging from surveying small deformations of civil engineering structures (e.g., subsidence of the highway bridge) to the detection of particular geophysical signals. (C) 2017 Elsevier Ltd. All rights reserved.

Elsevier2017

Review of current GPS methodologies for producing accurate time series and their error sources

Jean-Philippe Lucien Montillet

Elsevier2017