On the Estimation of Randomly Sampled 2D Spatial Fields under Bandwidth Constraints

Abstract

In this paper, we address the problem of the estimation of a spatial field defined over a two-dimensional space with wireless sensor networks. We assume that the field is (spatially) bandlimited and that it is sampled by a set of sensors which are randomly deployed in a given geographical area. Further, we impose a total bandwidth constraint which forces the quantization error in the sensor-to-FC (Fusion Center) channels to depend on the actual number of sensors in the network. With these assumptions, we derive an analytical expression of the mean-square error (MSE) in the reconstructed random field and, on that basis, an approximate closed-form expression of the optimal sensor density which attains the best trade-off in terms of observation, sampling and quantization noises. The analysis is carried out both in Gaussian and Rayleigh-fading scenarios without transmit Channel State Information (CSI). For the latter scenario, we also derive an expression of the common and constant rate at which the observations must be quantized. Computer simulation results illustrate the dependency of the optimal operating point on the variance of the observation noise or the signal-to-noise ratio in the sensor-to-FC channels, as well as the scaling law of the reconstruction MSE (which is also derived analytically) for both scenarios.

Distributed Nonasymptotic Confidence Region Computation Over Sensor Networks

“…On the contrary, with small values of n r , data disseminate only to a limited part of the network due to the depth of the tree which may be larger 6 than 1 + n r /2. Similarly to the flat topology, even in this case FL and TAS are very similar 6 With nr rounds the maximum number of levels of a tree that allows a complete dissemination of data from the leaves up to the root and back is 1 + nr/2. in terms of amount of received data.…”

“…Examples may be the monitoring of an environmental parameter (e.g., temperature or pressure [2]- [4]), the detection of a binary event [5], the estimation of a spatial field [6], the estimation of the coordinates of a signal source [7], etc. Depending on the specific task requirements (fault tolerance, privacy issues, energy constraints), either a centralized or a distributed approach can be adopted.…”

Random sampling via sensor networks: Estimation accuracy vs. energy consumption

“…Remark 1: By using normalized quantities, forρ → +∞, the optimal LSI interpolator in (9) tends to 1 ρ 1 Bz (ν) where 1 Bz (ν) denotes the indicator function equal to 1 for ν ∈ B z and 0 otherwise. It means that the ILP filter considered in [6], [8], [9] is an asymptotic optimal choice when the samples intensity which is much higher than the signal band cardinality in R d .…”

A combined GP-State space method for efficient crowd mapping

“…Note that (3) or other projection based approaches require matrix inversion to estimate f (p) for each different test point. Here m k and P k synthesize the full knowledge acquired until time k independently of the test point.…”

“…Typical applications are oriented to sense specific physical quantities (e.g., temperature) in outdoor environments in well-defined areas [3]. Unfortunately, wireless sensor network technology does not represent a viable solution for automatic mapping because of the prohibitive cost that the deployment of nodes in every place would imply and the consequent scarce flexibility.…”