We address the problem of modulating a parameter onto a power–limited signal, transmitted over a discrete–time Gaussian channel and estimating this parameter at the receiver. Continuing an earlier work, where the optimal trade–off between the weak–noise estimation performance and the outage probability (threshold–effect breakdown) was studied for a scalar parameter, here we extend the derivation of the weak–noise estimation performance to the case of a multi–dimensional vector parameter. This turns out to be a non–trivial extension, that provides a few insights, and has some interesting implications. Several modifications and extensions of the basic setup are also studied and discussed.
In this paper, we consider the problem of estimating the orientation of an object that has been custom-"painted" by an array of backscatter tags. We pose the problem as a coding matrix design with the objective of minimizing orientation estimation error. We show that it is only necessary to consider a subset of code configurations and provide a tractable linear program to find the optimal coding strategy. We provide simulation results using an icosahedral tag arrangement.
We study the conditions that allow for the alignment of correlated databases with multivariate Gaussian features. We present some analysis tools that allow us to go beyond the achievability result for exact alignment and derive the condition for nearly-exact alignment. Our main theorem gives an expression for the order of magnitude of the error in alignment as a function of mutual information between features.
While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in real-time. One type of such a continuous stream of information is time series data. Due to the richness of information in time series and inadequacy of summary statistics to encapsulate structures and patterns in such data, development of new approaches to learn time series is of interest. In this paper, we propose a novel method, called pattern tree, to learn patterns in the times-series using a binary-structured tree. While a pattern tree can be used for many purposes such as lossless compression, prediction and anomaly detection, in this paper we focus on its application in time series estimation and forecasting. In comparison to other methods, our proposed pattern tree method improves the mean squared error of estimation.
We consider the problem of estimating the unknown location of a spatial signal defined on a circular interval from noisy measurements. Lower bounds are derived for the minimax risk of the localization error defined by the circular distance. The lower bounds reveal the fundamental dependence of the localization error on various problem parameters, including the shape of the signal, the noise level, the length of the interval, the number of sensors, and the number of measurement trials. Le Cam's method and Fano's method are used for the derivation. All lower bounds are non-asymptotic, and different lower bounds are tight in different problem parameters. We also derive a Bayesian Cramer-Rao lower bound for the problem of linear source localization, which helps us understand the tightness of the lower bounds for the circular source in some asymptotic situations as well.