Localisation of Sensor Nodes with Hybrid Measurements in Wireless Sensor Networks

Abstract

Localisation in wireless networks faces challenges such as high levels of signal attenuation and unknown path-loss exponents, especially in urban environments. In response to these challenges, this paper proposes solutions to localisation problems in noisy environments. A new observation model for localisation of static nodes is developed based on hybrid measurements, namely angle of arrival and received signal strength data. An approach for localisation of sensor nodes is proposed as a weighted linear least squares algorithm. The unknown path-loss exponent associated with the received signal strength is estimated jointly with the coordinates of the sensor nodes via the generalised pattern search method. The algorithm’s performance validation is conducted both theoretically and by simulation. A theoretical mean square error expression is derived, followed by the derivation of the linear Cramer-Rao bound which serves as a benchmark for the proposed location estimators. Accurate results are demonstrated with 25%–30% improvement in estimation accuracy with a weighted linear least squares algorithm as compared to linear least squares solution.

Hybrid RSS/AOA Localization using Approximated Weighted Least Square in Wireless Sensor Networks

“…is the run number andx i is the estimate of the true target location, x oi , during the i th run. We compare the performance of our algorithm to that of the LS method in [17], WLLS algorithm in [23], and LS_WLS and WLS method in [22]. We also evaluate the performance of the real ECWLS algorithm, which replaces the estimated noise with the true noise variances in the ECWLS algorithm.…”

“…The error covariance matrix for LS is simple to compute (see Appendix A, which corrects the missing terms in the correlation matrix presented in [24]). The weighted LS algorithm using the covariance matrix is termed the WLLS algorithm [23]. Although the LS method is intuitive and simple, the performance comparisons in [24] and in Section 6 in this paper showed that the WLS method outperforms the LS method, while the WLS method is, in turn, outperformed by the WLLS algorithm due to the introduction of error covariance weights.…”

“…The range-based localization assumes that each anchor node is able to have the positions of the node and RSS as well as the AOA of the received signals and, hence, theoretically, the exact location of the target is attainable. However, the errors in RSS/AOA measurements are severe, and sophisticated integration of the RSS and AOA measurements has been investigated [17][18][19][20][21][22][23]. The challenge of the range-based localization algorithms is to overcome the limitation of the noisy RSS/AOA measurements with a practical computational complexity.…”

“…In [22], using a spherical representation of the target, a closed-form LS equation was derived with selected weights based on the distance from the target (the WLS algorithm). In [23], a generalized least squares (GLS) approach using an error covariance matrix (the WLLS algorithm) was used, but it requires precise noise variance data that may not be available in practice. The performance comparison study in [24] reported that the WLS algorithm exhibits state-of-art performance, with a complexity comparable to that of the LS method but without the requirement for noise variance data.…”

A Linear Estimator for Network Localization Using Integrated RSS and AOA Measurements

“…Note that this is in sharp contrast to the existing approaches for joint RSS and AOA localization (both non-cooperative [10]- [14] and cooperative [17]- [19]), where the measurement errors of angle observations were considered as Gaussian random variables. The von Mises distribution is a circular analogue of the Gaussian one, and since we are dealing here with directional data, it comes more natural to consider this distribution rather than the Gaussian one [20], [21].…”