Multidimensional Vector Regression for Accurate and Low-Cost Location Estimation in Pervasive Computing

Abstract

Abstract-In this paper, we present an algorithm for multidimensional vector regression on data that are highly uncertain and nonlinear, and then apply it to the problem of indoor location estimation in a wireless local area network (WLAN). Our aim is to obtain an accurate mapping between the signal space and the physical space without requiring too much human calibration effort. This location estimation problem has traditionally been tackled through probabilistic models trained on manually labeled data, which are expensive to obtain. In contrast, our algorithm adopts Kernel Canonical Correlation Analysis (KCCA) to build a nonlinear mapping between the signal-vector space and the physical location space by transforming data in both spaces into their canonical features. This allows the pairwise similarity of samples in both spaces to be maximally correlated using kernels. We use a Gaussian kernel to adapt to the noisy characteristics of signal strengths and a Maté rn kernel to sense the changes in physical locations. By using real data collected in an 802.11 wireless LAN environment, we achieve accurate location estimation for pervasive computing while requiring a much smaller set of labeled training data than previous methods.

Machine Learning Based Localization

“…Thus, one could be able to exploit directly the high correlation statistics between the similarity of signal strengths and that of sensor locations. This insight was observed by [Pan et al (2006)], who proposed to use Kernel Canonical Correlation Analysis (KCCA) [Akaho (2001), Hardoon et al (2004)] for the regression that maps a vector in the signal-strength space to a location in the physical space. We briefly present KCCA below and then how it is used for the localization problem.…”

“…Recently, a number of techniques that employ the concepts from machine learning have been proposed [Brunato & Battiti (2005), Nguyen et al (2005), Pan et al (2006), Tran & Nguyen (2006), , Tran & Nguyen (2008b)]. The main insight of these methods is that the topology implicit in sets of sensor readings and locations can be exploited in the construction of possibly non-Euclidean function spaces that are useful for the estimation of unknown sensor locations, as well as other extrinsic quantities of interest.…”

“…We can also solve the localization problem as a regression problem [Pan et al (2006), Tran & Nguyen (2008b)]. We can use a regression tool to infer the Euclidean distances between S and the beacon nodes based on the signal strengths that S receives from these nodes, or when S cannot hear directly from them, based on the hop-count distances between S and these nodes.…”

“…After these distances are learned, trilateration can be used to estimate the location of S. Alternatively, we can apply a regression tool that maps the signal strengths S receives from the beacon nodes directly to a location. One such a tool was proposed by [Pan et al (2006)], which is based on Kernel Canonical Correlation Analysis [Hardoon et al (2004)]. …”

“…The only assumption is the existence of a set of beacon nodes at known locations. The information serving as input to the learning can be signal strengths [Nguyen et al (2005), Pan et al (2006)] or hop-count information [Tran & Nguyen (2006), ], which can be obtained easily at little cost.…”