Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Statistical Methods for Polarimetric Imagery

Estimation theory is applied to a physical model of incoherent polarized light to address problems in polarimetric image registration, restoration, and analysis for electro-optical imaging systems. In the image registration case, the Cramer-Rao lower bound on unbiased joint estimates of the registration parameters and the underlying scene is derived, simplified using matrix methods, and used to explain the behavior of multi-channel linear polarimetric imagers. In the image restoration case, a polarimetric maximum likelihood blind deconvolution algorithm is derived and tested using laboratory and simulated imagery. Finally, a principal components analysis is derived for polarization imaging systems. This analysis expands upon existing research by including an allowance for partially polarized and unpolarized light

Geostatistical analysis of disease data: accounting for spatial support and population density in the isopleth mapping of cancer mortality risk using area-to-point Poisson kriging

BACKGROUND: Geostatistical techniques that account for spatially varying population sizes and spatial patterns in the filtering of choropleth maps of cancer mortality were recently developed. Their implementation was facilitated by the initial assumption that all geographical units are the same size and shape, which allowed the use of geographic centroids in semivariogram estimation and kriging. Another implicit assumption was that the population at risk is uniformly distributed within each unit. This paper presents a generalization of Poisson kriging whereby the size and shape of administrative units, as well as the population density, is incorporated into the filtering of noisy mortality rates and the creation of isopleth risk maps. An innovative procedure to infer the point-support semivariogram of the risk from aggregated rates (i.e. areal data) is also proposed. RESULTS: The novel methodology is applied to age-adjusted lung and cervix cancer mortality rates recorded for white females in two contrasted county geographies: 1) state of Indiana that consists of 92 counties of fairly similar size and shape, and 2) four states in the Western US (Arizona, California, Nevada and Utah) forming a set of 118 counties that are vastly different geographical units. Area-to-point (ATP) Poisson kriging produces risk surfaces that are less smooth than the maps created by a naïve point kriging of empirical Bayesian smoothed rates. The coherence constraint of ATP kriging also ensures that the population-weighted average of risk estimates within each geographical unit equals the areal data for this unit. Simulation studies showed that the new approach yields more accurate predictions and confidence intervals than point kriging of areal data where all counties are simply collapsed into their respective polygon centroids. Its benefit over point kriging increases as the county geography becomes more heterogeneous. CONCLUSION: A major limitation of choropleth maps is the common biased visual perception that larger rural and sparsely populated areas are of greater importance. The approach presented in this paper allows the continuous mapping of mortality risk, while accounting locally for population density and areal data through the coherence constraint. This form of Poisson kriging will facilitate the analysis of relationships between health data and putative covariates that are typically measured over different spatial supports

Blind Deconvolution of Anisoplanatic Images Collected by a Partially Coherent Imaging System

Coherent imaging systems offer unique benefits to system operators in terms of resolving power, range gating, selective illumination and utility for applications where passively illuminated targets have limited emissivity or reflectivity. This research proposes a novel blind deconvolution algorithm that is based on a maximum a posteriori Bayesian estimator constructed upon a physically based statistical model for the intensity of the partially coherent light at the imaging detector. The estimator is initially constructed using a shift-invariant system model, and is later extended to the case of a shift-variant optical system by the addition of a transfer function term that quantifies optical blur for wide fields-of-view and atmospheric conditions. The estimators are evaluated using both synthetically generated imagery, as well as experimentally collected image data from an outdoor optical range. The research is extended to consider the effects of weighted frame averaging for the individual short-exposure frames collected by the imaging system. It was found that binary weighting of ensemble frames significantly increases spatial resolution

Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation

Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment, has been a subject of growing research in the past decades. Here, we introduce a unified framework that ties together the problems of downscaling, data fusion and data assimilation as ill-posed inverse problems. This framework seeks solutions beyond the classic least squares estimation paradigms by imposing proper regularization, which are constraints consistent with the degree of smoothness and probabilistic structure of the underlying state. We review relevant regularization methods in derivative space and extend classic formulations of the aforementioned problems with particular emphasis on hydrologic and atmospheric applications. Informed by the statistical characteristics of the state variable of interest, the central results of the paper suggest that proper regularization can lead to a more accurate and stable recovery of the true state and hence more skillful forecasts. In particular, using the Tikhonov and Huber regularization in the derivative space, the promise of the proposed framework is demonstrated in static downscaling and fusion of synthetic multi-sensor precipitation data, while a data assimilation numerical experiment is presented using the heat equation in a variational setting

Assessment of Precision and Accuracy of Brain White Matter Microstructure using Combined Diffusion MRI and Relaxometry

Joint modeling of diffusion and relaxation has seen growing interest due to its potential to provide complementary information about tissue microstructure. For brain white matter, we designed an optimal diffusion-relaxometry MRI protocol that samples multiple b-values, B-tensor shapes, and echo times (TE). This variable-TE protocol (27 min) has as subsets a fixed-TE protocol (15 min) and a 2-shell dMRI protocol (7 min), both characterizing diffusion only. We assessed the sensitivity, specificity and reproducibility of these protocols with synthetic experiments and in six healthy volunteers. Compared with the fixed-TE protocol, the variable-TE protocol enables estimation of free water fractions while also capturing compartmental $T_2$ relaxation times. Jointly measuring diffusion and relaxation offers increased sensitivity and specificity to microstructure parameters in brain white matter with voxelwise coefficients of variation below 10%.Comment: 8 figure