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In this paper, we propose a new approach for localization in wireless sensor networks based on semi-supervised Laplacian regularized least squares algorithm. We consider two kinds of localization data: signal strength and pair-wise distance between nodes. When nodes are close within their physical location space, their localization data vectors should be similar. We first propose a solution using the alignment criterion to learn an appropriate kernel function in terms of the similarities between anchors, and the kernel function is used to measure the similarity between pair-wise sensor nodes in the networks. We then propose a semi-supervised learning algorithm based upon manifold regularization to obtain the locations of the non-anchors. We evaluate our algorithm under various network topology, transmission range and signal noise, and analyze its performance. We also compare our approach with several existing approaches, and demonstrate the high efficiency of our proposed algorithm in terms of location estimation error.

Wireless sensor location estimation is an important area and attracts considerable research interests. In this paper, we present a novel graph embedding method for the localization problem by using signal strengths. We view the wireless sensor nodes as a group of distributed devices, and employ an appropriate kernel function to measure the similarity between sensors. The kernel function can be naturally defined according to the signal strength matrix. Then we formulate the localization problem as a graph embedding problem. Finally, we use the kernel locality preserving projection (KLPP) technique to estimate the relative locations of all sensor nodes. Given sufficient number of anchors, the relative locations can be transformed into physical locations. The main advantage of formulating the localization problem as graph embedding problem is that it allows us to construct a graph to preserve the topological structure of the sensor networks. We evaluate our method based on various network topologies, and analyze its performance. We also compare our method with several existing methods, and demonstrate the high efficiency of our proposed method.

This paper studies the problem of determining the sensors' locations in wireless sensor networks. To alleviate the influence of the noise and the inaccurate measurement in the complicated environment, rather than estimating the pairwise Euclidean distance between sensors, we use the geodesic distance to measure the dissimilarity between sensors, and employ the isomap algorithm to determine the relative locations of sensors. Given sufficient anchors, the relative locations can be aligned to absolute locations by using coordinate transformation. The coordinate transformation matrix can be obtained by minimizing the sum of squares of the errors between the true locations of the anchors and their transformed locations. Since isomap is parameter-sensitive, we also present an adaptive parameter selection procedure based on the locations of anchors. Simulation results show that the isomap algorithm achieves smaller average location error with little quantity of anchors.

Our solution builds on a kernel-based method called the support vector machine (SVM) for determining the locations of the nodes. The basic SVM algorithm contains two steps: (1) one-region classification using the SVM; and (2) multi-region localization which is a repeated application of one-region classification for a number of different regions. In this paper, we first analyze the error effects of the choice of regions in the multi-region localization, which influences the accuracy of the localization results significantly. The realization of a choice of regions is posed as a beacon node coverage problem, i.e., the spatial distribution of the beacon nodes is determined from the coverage point of view. Second, we develop a method to arrange the regions, which we call expanded coverage region distribution, in order to avoid the problem of border effects in existing solutions. We show that expanded cover region distribution can reduce the localization errors. Our results show that, by optimally choosing and arranging the regions based on our analysis, we can significantly enhance the performance of SVM based localization. Furthermore, the optimal choice of regions to avoid the border effects can be similarly applied in other kernel-based learning methods for localization.