利用最大散度差于室内无线网络定位分析
Localization Analysis Based on Maximum Scatter Difference in Indoor WLAN Environments

在本研究中将最大散度差应用在无线网络室内定位上，最大散度差主要是可以解决线性鉴别分析在计算类内散度矩阵时所遭遇的奇异性矩阵问题，它是利用类间散度矩阵与类内散度矩阵之差作为目标函数，由于不需要构造类内散度矩阵的反矩阵，故可以避免掉奇异性矩阵的问题。本研究中其定位的方式是透过指纹特征比对法的概念来进行定位，共分为两个阶段：在离线阶段，利用最大散度差将原始讯号数据库作前置处理；在在线阶段，将接收到的实时讯号数据利用最大似然法计算出目前接收讯号的所在位置。将最大散度差应用于室内无线网络进行定位，不仅可以避免奇异性矩阵的问题并且还可以降低定位时的计算量，从实验结果得知此应用是可以实行的。
In this paper, we utilize Maximum Scatter Difference (MSD) for indoor localization over Wireless Local Area Network (WLAN) received signal data. Maximum Scatter Difference can solve the singular matrix problems by linear discriminant analysis calculates the inverse matrix of within-class scatter matrix. The objective functions of Maximum Scatter Difference are to maximize the inter-class scatter matrix and minimize the within-class scatter matrix. Therefore, Maximum Scatter Difference cannot need to construct the inverse matrix of within-class scatter matrix. It can avoid the singular matrix problems. We utilize location fingerprinting approaches for indoor localization. The approaches are divided into two parts including off-line and on-line stages. In the off-line stage, we collected received signal data are projected onto the feature space of Maximum Scatter Difference. In the on-line stage, we receive real-time signal data compared with the off-line stage that was collected data using Maximum Likelihood (ML) to estimate current location. Maximum Scatter Difference applied to indoor WLAN localization that not only avoids the singular matrix but also reduces the localization computation. From Simulation results show that this algorithm can be implemented.