Ranging Energy Optimization for Robust Sensor Positioning Based on Semidefinite Programming

Abstract

Abstract-Sensor positioning is an important task of location-aware wireless sensor networks. In most sensor positioning systems, sensors and beacons need to emit ranging signals to each other. Sensor ranging energy should be low to prolong system lifetime, but sufficiently high to fulfill prescribed accuracy requirements. This motivates us to investigate ranging energy optimization problems. We address ranging energy optimization for an unsynchronized positioning system, which features robust sensor positioning (RSP) in the sense that a specific accuracy requirement is fulfilled within a prescribed service area. We assume a line-of-sight (LOS) channel exists between the sensor and each beacon. The positioning is implemented by time-of-arrival (TOA) based two-way ranging between a sensor and beacons, followed by a location estimation at a central processing unit. To establish a dependency between positioning accuracy and ranging energy, we assume the adopted TOA and location estimators are unbiased and attain the associated Cramér-Rao bound. The accuracy requirement has the same form as the one defined by the Federal Communication Commission (FCC), and we present two constraints with linear-matrix-inequality form for the RSP. Ranging energy optimization problems, as well as a practical algorithm based on semidefinite programming are proposed. The effectiveness of the algorithm is illustrated by numerical experiments.Index Terms-Cramér-Rao bound, localization, semidefinite programming, wireless sensor networks.

Robust Power Allocation for Integrated Visible Light Positioning and Communication Networks

“…• Gaussian distribution: If only the mean and variance are known, the Gaussian distribution can maximize the entropy of the uncertain parameter without additive constraints. This model has been adopted in [35]- [37] because the CRLB is asymptotically achieved by the maximum-likelihood (ML) estimator even for finite data size [38], [39]. • Arbitrary distribution: The location estimators based on approximate ML [40], [41], and multidimensional scaling (MDS) [42] can also achieve the CRLB.…”

“…• Arbitrary distribution: The location estimators based on approximate ML [40], [41], and multidimensional scaling (MDS) [42] can also achieve the CRLB. However, the estimation errors do not necessarily follow a Gaussian distribution [35], [43]. In this case, although the distribution of the position error e p is unavailable, its mean and variance also can be assumed to be known [35], [42], [44].…”

“…However, the estimation errors do not necessarily follow a Gaussian distribution [35], [43]. In this case, although the distribution of the position error e p is unavailable, its mean and variance also can be assumed to be known [35], [42], [44].…”

Power adaptation for vector parameter estimation according to Fisher information based optimality criteria

“…In [11] , optimal power allocation schemes for LMMSE estimation are derived by taking channel estimation errors into account. In [12][13][14][15][16][17][18][19][20][21] , the optimal power allocation problem is considered for position estimation in wireless localization and radar systems. In [14] , the transmit power allocation problem is formulated as a semidefinite program by using the squared position error bound as the objective function.…”

“…It is noted that theoretical lower bounds for estimation error are commonly used in the literature to define optimality criteria for developing power adaptation strategies in estimation problems [10,[12][13][14][15][16][17][18][19][20][21][22][23][24][25] . In the absence of prior information, lower bounds generated from the Fisher information matrix (FIM) are usually adopted due to their practicality.…”