# Intersection and Complement Set (IACS) Method to Reduce Redundant Node in Mobile WSN Localization
## 2 Literature Review
### Monte Carlo Based Localization Method  
Monte Carlo-based localization algorithm normally starts with a uniform random distribution of particles over a configuration space. If the node moves, the particles shift to predict its new state. When new data is sensed, the particles are resample based on Recursive Bayesian estimation. The algorithm's goal is to converge the particles toward the actual position of the node. From the convergence, location information can be extracted.  
The preliminary algorithm of the Monte Carlo-based localization is MCL [15]. It estimates the blind node location based on the data from seed nodes. A seed node is a node that is equipped with positioning hardware such as Global Positioning System (GPS). However, the MCL is able to achieve a good estimation of the location information; the high dependency on the positioning hardware increases the costs of the localization process. Therefore, Mobile and Static sensor network Localization (MSL) and MSL* are proposed to reduce the dependency on the seed nodes. The MSL and MSL*improve the MCL by taking the location information not only from the seed nodes but also from neighboring normal nodes [16]. Normal nodes are the nodes that contains location information estimated from the seed nodes. The inclusion of normal nodes in this cooperative method reduces the seed nodes cost and improves the localization accuracy within the range of its radio signal. The accuracy is improved due to additional information received from the normal nodes instead of solely depending on the seed nodes.  
Looking at the advantage of MCL, MSL and MSL\({}^{\star}\), other Monte Carlo-based localization methods are proposed by prior researchers. Among them are Monte-Carlo Box (MCB), VMSL, VMSL\({}^{\star}\), WMCL, and LCC. The focus of these methods is to improve the sampling efficiency while retaining the accuracy of the prior Monte Carlo methods. The sampling efficiency looks into sampling nodes with significant information instead of taking all information from the adjacent nodes. The purpose of selective sampling is to reduce execution time, computation cost, and communication cost of a localization process. Each of the proposed methods have their own unique properties to improve sampling efficiency. For example, MCB [17] uses square bounding box to optimize the number of valid samples from the seed nodes. Samples are selected from the intersection area of the bounding box between the current and the previous location of the seed nodes. On the other hand, VMSL, VMSL\({}^{\star}\) and WMCL [18] introduce a technique that reduce the MCB bounding box size. The research of sampling efficiency continues with the introduction of the LCC [4] scheme. The LCC utilizes an adjacency matrix and set theory instead of a bounding box method as in prior MCB-based methods. From the result, it can be seen that LCC outperformed MCB. This is because LCC reduces additional data broadcast cost that is needed by the MCB-based method to create the bounding box.  
Considering the advantage of the LCC scheme over other sampling methods, LCC is selected as the benchmark in this paper. To make this paper self-contained, an extensive simulation on both MSL\({}^{\star}\) and LCC is done to investigate the research gap. The investigation is explained in the next section.