Indoor Localization Using Semi-Supervised Manifold Alignment with Dimension Expansion

Abstract

Location estimation plays a crucial role in Location-Based Services (LBSs) with satisfactory user experience. The Wireless Local Area Network (WLAN) localization approach is preferred as a cost-efficient solution to indoor localization on account of the widely-deployed WLAN infrastructures. In this paper, we propose a new WLAN Received Signal Strength (RSS)-based indoor localization approach using the semi-supervised manifold alignment with dimension expansion. In concrete terms, we first construct an innovative objective function based on the augmented physical coordinates and the corresponding WLAN RSS measurements. Second, the closed-form solution to the objective function is derived out according to the Lagrange multiplier equation, which results in the manifold in physical coordinate space. Third, the target location is estimated by matching the transformed newly-collected RSS against the manifold. The localization performance with noise perturbation is analyzed upon the constructed objective function, and meanwhile, the closed-form solution to the objective function with respect to multiple types of measurements is also derived out for the sake of leveraging all of the potential measurements for indoor localization. The extensive testing results show that the proposed approach performs well in localization accuracy even at low calibration load, and its performance can be further improved by using multiple types of measurements for localization.

Pedestrian Motion Learning Based Indoor WLAN Localization via Spatial Clustering

“…Figure 13 shows the probabilities of locating the new RSS data into its actually belonging subarea which is defined as correct localization, as well as probabilities into its adjacent subareas which is defined as adjacently correct localization. In addition, combining with Table 1, we can find that compared with [12][13][14], the proposed approach can generally achieve higher localization accuracy with lower time complexity and without the demand for fingerprints calibration. [12] Probability of correct localization by [13] Probability of correct localization by [14] Probability of adjacently-correct localization by the proposed Probability of adjacently-correct localization by [12] Probability of adjacently-correct localization by [14] Probability of adjacently-correct localization by [13] 71 Based on the area-level localization result, the users' motion behavior can be preliminarily analyzed by calculating the activity frequency in each subarea and the transfer probability between different physical subareas as shown in Figure 14.…”

“…Finally, according to the transfer relations of motion paths between different physical subareas, the physical logic ← ; // Current pixel (7) while is not equal to do (8) for (each adjacent pixel around , ) // Pixel traversal (9) if is an inaccessible pixel then (10) Continue; (11) else if belongs to EPL set then (12) Continue; (13) else if is neither in EPL set nor in PPL set then (14) Add into PPL set; (15) Set as the father pixel of ; (16) Calculate the Euclidean distance from to , ; (17) Calculate the Manhattan distance from to , ; (18) Set = + ; (19) else if belongs to PPL set then (20) Calculate the distance from to , ; Figure 6: Definition of the vertical, parallel, and angular distances.…”

“…Input: RSS segments Output: Signal clusters (1) = 1; // Initialize the number of RSS clusters (2) for (each RSS segment seg rss ) do // Data traversal (3) Calculate the AP -dimensional linear distance between seg rss and each of the rest RSS segments; (4) Save the RSS segments with the AP -dimensional linear distance smaller than a given threshold, , into set C ; (5) if (the number of elements in C is not smaller than a given threshold, Min) then (6) continue; (7) else (8) for (each RSS segment in C , seg rss ) do // Data traversal (9) if (the number of RSS segments in C is not smaller than the threshold Min) then (10) Merge C into C ; (11) else (12) continue; (13) end if (14) end for (15) Set C as the -th signal cluster; As a special case, when a user is located in at the moment , he/she may enter an anonymous physical subarea at the next moment. In this case, we assume that the user is equally likely to appear in every physical subarea at the moment + 1, such that…”

A Comprehensive Survey of Machine Learning Based Localization with Wireless Signals

“…-Utilize generative models to capture the possible mapping between the features and possible variations or different dimensions (in case of different features sets, e.g., from a set of possible CSI values from limited observations). A few papers have considered that, e.g., [90], [138], [139], [177]. However, more research is still needed.…”