Performance of Linear Field Reconstruction Techniques With Noise and Uncertain Sensor Locations

Abstract

Abstract-We consider a wireless sensor network, sampling a bandlimited field, described by a limited number of harmonics. Sensor nodes are irregularly deployed over the area of interest or subject to random displacement; in addition sensors measurements are affected by noise. Our goal is to obtain a high quality reconstruction of the field, with the mean square error (MSE) of the estimate as performance metric. In particular, we analytically derive the performance of several reconstruction/estimation techniques based on linear filtering. For each technique, we obtain the MSE, as well as its asymptotic expression in the case where the number of field-harmonics and the number of sensors grow to infinity, while their ratio is kept constant. Through numerical simulations, we show the validity of the asymptotic analysis, even for a small number of sensors. We provide some novel guidelines for the design of sensor networks when many parameters, such as field bandwidth, number of sensors, reconstruction quality, and sensor displacement characteristics, to be traded off.

On Bandlimited Signal Reconstruction From the Distribution of Unknown Sampling Locations

“…Recovery of a bandlimited signal from a finite number of ordered nonuniform samples at unknown sampling locations has been studied by Browning [5]. Estimation of periodic bandlimited signals in the presence of random sampling location under two models has been studied by Nordio et al [6]. Their first model studies reconstruction of bandlimited signal affected by noise at random but known locations.…”

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

“…This article and our previous work [Nordio et al 2008] have a common background: both consider the reconstruction of a physical field sampled by a sensor network whose nodes, or sensors, are randomly deployed. In particular, in Nordio et al [2008], we studied the performance of reconstruction techniques, in terms of MSE when various types of linear filters are employed to reconstruct the field from the irregularly spaced noisy samples provided by the network. In Nordio et al [2008], sensors were considered to be randomly deployed with uniform distribution in the 1-dimensional domain [−1/2, 1/2) and subject to unpredictable motion.…”

“…In particular, in Nordio et al [2008], we studied the performance of reconstruction techniques, in terms of MSE when various types of linear filters are employed to reconstruct the field from the irregularly spaced noisy samples provided by the network. In Nordio et al [2008], sensors were considered to be randomly deployed with uniform distribution in the 1-dimensional domain [−1/2, 1/2) and subject to unpredictable motion.…”

“…Here, instead, we evaluate the performance of one reconstruction technique based on linear filtering (i.e., the LMMSE filter providing the best performance, according to Nordio et al [2008]) in the scenario where sensors are stationary and quasi-equally spaced over a d -dimensional domain. We also highlight that making different assumptions on the sensors deployment leads to a new mathematical derivation of the system performance with respect to Nordio et al [2008].…”

“…We also highlight that making different assumptions on the sensors deployment leads to a new mathematical derivation of the system performance with respect to Nordio et al [2008].…”