Globally Optimized Power Allocation in Multiple Sensor Fusion for Linear and Nonlinear Networks

Abstract

The present paper is concerned with a sensor network, where each sensor is modeled by either a linear or nonlinear sensing system. These sensors team up in observing either static or dynamic random targets and transmit their observations through noisy communication channels to a fusion center (FC) for locating/tracking the targets. Physically, the network is limited by energy resource. According to the available sum power budget, we develop a novel technique for power allocation to the sensor nodes that enables the FC produce the best linear estimate in terms of the mean square error (MSE). Regardless of whether the sensor measurements are linear or nonlinear, the targets are scalar or vectors, static or dynamic, the corresponding optimization problems are shown to be semidefinite programs (SDPs) of tractable optimization and thus are globally and efficiently solved by any existing SDP solver. In other words, new tractably computational algorithms of distributed Bayes filtering are derived with full multisensor diversity achieved. Intensive simulation shows that these algorithms clearly outperform previously known algorithms.Index Terms-Bayes filtering, data fusion, linear and nonlinear sensor network, linear fractional transformation (LFT), power allocation, semidefinite programming (SDP), unscented transformations.

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

“…It is well known (see e.g. [15, Chapter III], [22], [28]) that almost all results for Gaussian target estimation are based on the derivation of the joint Gaussian distribution of the target and its observation. We will see later in the present paper that the joint GM distribution (1) facilitates unified framework for Bayesian and Kalman filters in both linear and nonlinear models.…”

“…Consider a typical third-order nonlinear autoregressive model described mathematically by [22], [28] as…”

“…Unlike (19), the program (82) is convex, which has been solved in [22] by semi-definite programming (SDP). The complexity of SDP is still high for online applications and more importantly, it is not scalable.…”

“…As the sensors are limited by energy resources, sensor transmitter power allocation in linear sensor networks (LSNs) via minimizing estimate distortion at the FC for scalar Gaussian targets has been a subject of considerable interest [16]- [21]. Provided that the target is prior characterized by a Gaussian random variable, our previous work [22] derived a tractable semidefinite program (SDP) for sensor power allocation in both LSNs and nonlinear sensor networks (NSNs). The SDP allows the FC to determine the best linear estimate in terms of the mean squared error (MSE) irrespective of targets that are scalar or vector, static or dynamic.…”

Power allocation for Gaussian Mixture model prior knowledge in wirless sensor networks

“…Recently [3] considered power allocation in sensor network assuming that information source follows Gaussian distribution. However, Gaussian Mixture distribution is a more judicious choice for prior knowledge because any nonGaussian distribution can be represented by sum of Gaussian distributions [4].…”