Joint Sensor and Relay Power Control in Tracking Gaussian Mixture Targets by Wireless Sensor Networks

Abstract

Abstract-This paper considers a wireless sensor network (WSN) for locating a static target or tracking a dynamic target, which is prior characterized by a Gaussian mixture (GM) distribution. An amplify-and-forward relay node is acting as a wireless bridge in relaying the sensor's independent observations of the target to a fusion center (FC). We are concerned with the joint transmitter power allocation for the sensors and relay to optimize the Bayesian filter, which is deployed at the FC for a global estimate of the target. The mean squared error (MSE) of the Bayesian filter is already computationally intractable for fixed sensor and relay transmitter power, so power allocation to minimize its mean squared error is a very challenging problem. In this paper, the problem is addressed by an iterative procedure of very low computational complexity. Simulations are provided to support the efficiency of our proposed power allocation.

PMU Placement Optimization for Efficient State Estimation in Smart Grid

“…can be extended to the case of AC power flows models [38], under which the equation (1) is nonlinear. Like [25] and [26] for nonlinear sensor networks, one can use the unscented transformation and MMSE result of [39] to approximate the RV θ by a Gaussian RV as in (2) or by Gaussian mixture RV and then the conditional RV θ|z(x x x) in (7) for deriving the MMSE estimatorθ in (8) so the resultant MMSE is still an analytical function in x x x as that defined by (9).…”

“…[23], [24]) or for Kalman filtering in sensor networks (see e.g. [25] and [26]). The latter aims to select sensors from the placed ones and as such it is online implemented, while the former is off-line implemented to provide the optimal conditions for the latter online state estimation.…”

“…and rounding the S largest entries of their optimal solution to one and the remaining N − S entries to zero. Note that there is no guarantee that the solution of (26) or (27) is sparse to make such rounding efficient. Moreover, the size of the semidefinite optimization problem (26) is not scalable in N as it invokes the additional slack symmetric matrix variable T of size N × N that involves N (N + 1)/2 additional decision variables.…”

“…Note that there is no guarantee that the solution of (26) or (27) is sparse to make such rounding efficient. Moreover, the size of the semidefinite optimization problem (26) is not scalable in N as it invokes the additional slack symmetric matrix variable T of size N × N that involves N (N + 1)/2 additional decision variables. For a moderate number N such as N = 118, the value of N (N +1)/2 is 7021, which is already a huge number.…”

Security-Reliability Analysis of Multi-hop LEACH Protocol with Fountain Codes and Cooperative Jamming

“…Recently, physical-layer security (PLS) [8]- [9] has been proposed to provide security for wireless communication systems. Due to the simple implementation, PLS is suitable for WSNs [6]- [7]. To enhance secrecy performance, in terms of average secrecy capacity, secrecy outage probability and probability of non-zero secrecy capacity, the authors in [10]- [12] proposed diversity relaying protocols to enhance secrecy capacity via increasing the quality of the data links.…”