Accurate Analysis of Weighted Centroid Localization

Abstract

Source localization of primary users (PUs) is a spectrum awareness feature that can be very useful in enhancing the functionality of cognitive radios (CRs). When the cooperating CRs have limited information about the PU, weighted centroid localization (WCL) based on received signal strength (RSS) measurements represents an attractive low-complexity solution. This paper proposes a new analytical framework to accurately calculate the performance of WCL based on the statistical distribution of the ratio of two quadratic forms in normal variables. In particular, we derive an analytical expression for the root mean square error (RMSE) and an exact expression for the cumulative distribution function (CDF) of the two-dimensional location estimate. The proposed framework accounts for the presence of independent and identically distributed (i.i.d.) shadowing as well as correlated shadowing with distance-dependent intensity. The methodology is general enough to include the analysis of the one-dimensional error, which leads also to the evaluation of the bias of the position estimate. Numerical results confirm that the analytical framework is able to predict the performance of WCL capturing all the essential aspects of propagation as well as CR network spatial topology.

Connectivity-Based Localization in Ultra-Dense Networks: CRLB, Theoretical Variance, and MLE

“…10 that both the proposed method and 'fsolve' perform better than 'fminsearch'. This improve performance is because the nonlinear Equation (48) provides a clearer description for the MLE than the cost function (47). Although the proposed method and 'fsolve' have the optimal performance, the average running time of the proposed method is only one third of that of 'fsolve', as shown in Fig.…”

“…Other numerical iterative methods, such as the MATLAB functions 'fminsearch' and 'fsolve', can also be used to solve (47) and (48).…”

“…(1) The cost functions (47) and (48) are first proposed here based on the MLE. Using the proposed cost functions (47) and (48), other numerical iterative methods can be developed to obtain the optimal performance.…”

Energy-Efficient Fuzzy-Logic-Based Clustering Technique for Hierarchical Routing Protocols in Wireless Sensor Networks

“…Furthermore, they have the same battery, radio, sensing, and storage capabilities.There are no recharging capabilities.The BS is able to estimate the locations of the sensor nodes by using any localization technique. This may be based on utilizing GPS [57,58] or by adopting GPS-free localization such as weighted centroid localization [59,60,61], which is based on the received signal strength. Generally, a small error in localization will not be significant for the overall clustering result since the values are calculated as relative variances between the lowest and highest values.…”

Optimisation method with node selection and centroid algorithm in underwater received signal strength localisation

“…CL algorithm involves relatively simple calculations and hence results in lower localisation accuracy. In order to improve the localisation accuracy, a weighted CL (WCL) method has been proposed [10, 11] that combines both CL and RSS. WCL improves the accuracy to an extent but we have identified that there exists two major deficiencies: (a) the accuracy deteriorates at the corners and sides of the geometric figure due to the centroid property [12] and (b) the localisation accuracy decreases significantly if an inappropriate node is selected.…”