Sparsity-Aware Sensor Collaboration for Linear Coherent Estimation

Abstract

In the context of distributed estimation, we consider the problem of sensor collaboration, which refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. While incorporating the cost of sensor collaboration, we aim to find optimal sparse collaboration schemes subject to a certain information or energy constraint. Two types of sensor collaboration problems are studied: minimum energy with an information constraint; and maximum information with an energy constraint. To solve the resulting sensor collaboration problems, we present tractable optimization formulations and propose efficient methods which render near-optimal solutions in numerical experiments. We also explore the situation in which there is a cost associated with the involvement of each sensor in the estimation scheme. In such situations, the participating sensors must be chosen judiciously. We introduce a unified framework to jointly design the optimal sensor selection and collaboration schemes. For a given estimation performance, we show empirically that there exists a trade-off between sensor selection and sensor collaboration.Comment: IEEE Transactions on Signal Processin

Sensor Selection for Estimation with Correlated Measurement Noise

“…The prior PDF of x is given by x ∼ N (µ, Σ), where µ = [10,10] T and Σ = I. For simplicity, the row vectors of the measurement matrix H are chosen randomly, and independently, from the distribution N (0, I/ √ n) [13].…”

“…Therefore, the problem of sensor selection/scheduling arises, which aims to strike a balance between estimation accuracy and sensor activations over space and/or time. The importance of sensor selection has been discussed extensively in the context of various applications, such as target tracking [4], bit allocation [5], field monitoring [6], [7], optimal control [8], power allocation [9], [10], optimal experiment design [11], and leader selection in consensus networks [12].…”

Optimal Sensor Collaboration for Parameter Tracking Using Energy Harvesting Sensors

“…A recursive linear minimum mean squared error estimator (R-LMMSE) in the presence of multiplicative noise has been considered in [36], [37]. Motivated by the results in [36], [37] and since we have already assumed that |α| < 1, the following Lemma shows that (13) satisfies the assumption in [37] and hence that the R-LMMSE to be derived is stable. In the following, we denote u k := g T k Wh k .…”

“…In this section, for the purpose of comparison, we assume that the channel state information, i.e., h k and g k , of the statespace model (13) is available at the FC at time k. In this ideal case, R-LMMSE simplifies to the standard Kalman filter shown in Algorithm 2.…”

“…In [12], the optimal collaboration strategy was designed under star, branch and linear network topologies. In [5], [13], [14], the problem of collaboration network topology design was studied by incorporating the cost of sensor collaboration. It was shown that a partially connected network can yield estimation performance close to that of a fully connected network.…”