Quality of Field Reconstruction in Sensor Networks

Abstract

Abstract-We consider the problem of obtaining a high quality estimates of band-limited sensor fields when sensor measurements are noisy and the nodes are irregularly deployed and subject to random motion. We consider the mean square error (MSE) of the estimate and we analytically derive the performance of several reconstruction/estimation techniques based on linear filtering. For each technique, we obtain the mean value of the MSE, as well as its asymptotic expression in the case where the field bandwidth and the number of sensors grow to infinity, while their ratio is kept constant. Our results provide useful guidelines for the design of sensor networks when many system parameters have to be traded off.

The impact of quasi-equally spaced sensor topologies on signal reconstruction

“…(ii) For the computation of the averages in (18), a closed form expression of f λ (z, β, d ) would be required. To the best of our knowledge such expression 3 Given an n×n Hermitian matrix, the empirical cumulative distribution function of its eigenvalues is defined as F is still unknown, although [Nordio et al 2006] provides an algorithm to evaluate the moments of λ in closed form. We compute the averages in (18) numerically.…”

“…This behavior is due to the fact that, with fixed r, the number of rows of G increases with β and, by consequence, the probability of independent rows decreases. It follows that for large β the probability of zero or close to zero eigenvalues increases [Nordio et al 2006]. The histograms have been obtained by computing the eigenvalues of 200 realizations of the matrix T, with M = 6.…”

“…As a first step, let us compute the closed form expression of φ( T 2 ). When x follows the Uniform distribution, from (11) we have φ( T 2 ) = φ(T 2 ) and Nordio et al [2006] …”

“…By defining τ = ( A |Cx(j2πβ [Nordio et al 2006]. We therefore expect that, given β and d , the more equally-spaced the sensor layout is, the higher the value of τ .…”

Estimation of the distribution of randomly deployed wireless sensors

“…There are several cases where this is of practical interest: typically, the change of the distribution of the sensors (from a fixed pattern to a random pattern) can provide an estimate of the speed of the weed in environment monitoring. The estimation of the entire distribution can also improve signal reconstruction as recently proposed in [2]- [3]. In environment monitoring, different algorithms can be used to estimate the sensors location [4]- [5] but these algorithms require a substantial amount of communication between the sensors in large networks.…”