An indoor tracking and navigation system based on measurements of received signal strength (RSS) in wireless local area network (WLAN) is proposed. In the system, the location determination problem is solved by first applying a proximity constraint to limit the distance between a coarse estimate of the current position and a previous estimate. Then, a Compressive Sensing-based (CS--based) positioning scheme, proposed in our previous work , , is applied to obtain a refined position estimate. The refined estimate is used with a map-adaptive Kalman filter, which assumes a linear motion between intersections on a map that describes the user's path, to obtain a more robust position estimate. Experimental results with the system that is implemented on a PDA with limited resources (HP iPAQ hx2750 PDA) show that the proposed tracking system outperforms the widely used traditional positioning and tracking systems. Meanwhile, the tracking system leads to 12.6 percent reduction in the mean position error compared to the CS-based stationary positioning system when three APs are used. A navigation module that is integrated with the tracking system provides users with instructions to guide them to predefined destinations. Thirty visually impaired subjects from the Canadian National Institute for the Blind (CNIB) were invited to further evaluate the performance of the navigation system. Testing results suggest that the proposed system can be used to guide visually impaired subjects to their desired destinations.

The recent growing interest for indoor Location-Based Services (LBSs) has created a need for more accurate and real-time indoor positioning solutions. The sparse nature of location finding makes the theory of Compressive Sensing (CS) desirable for accurate indoor positioning using Received Signal Strength (RSS) from Wireless Local Area Network (WLAN) Access Points (APs). We propose an accurate RSS-based indoor positioning system using the theory of compressive sensing, which is a method to recover sparse signals from a small number of noisy measurements by solving an `1-minimization problem. Our location estimator consists of a coarse localizer, where the RSS is compared to a number of clusters to detect in which cluster the node is located, followed by a fine localization step, using the theory of compressive sensing, to further refine the location estimation. We have investigated different coarse localization schemes and AP selection approaches to increase the accuracy. We also show that the CS theory can be used to reconstruct the RSS radio map from measurements at only a small number of fingerprints, reducing the number of measurements significantly. We have implemented the proposed system on a WiFi-integrated mobile device and have evaluated the performance. Experimental results indicate that the proposed system leads to substantial improvement on localization accuracy and complexity over the widely used traditional fingerprinting methods.

The low rank feature of location estimation in Wireless Sensor Networks (WSNs) makes it feasible to use nuclear norm minimization as an accurate and fast solution for low-dimensional embedding problems. In this paper, a novel localization algorithm for WSNs is proposed by using nuclear norm for rank minimization. We formulate the location finding problem from only a small fraction of random entries of Euclidean Distance Matrix (EDM) as a low-rank matrix recovery problem, subject to a set of linear equality constraints. We show that a measurement matrix using orthogonal projection obeys the RIP and thus, supports a sufficient condition for the recovery of the low-rank matrix with overwhelming probability. For simplicity, Singular Value Thresholding (SVT) algorithm, a standard convex optimization approach, is used for the nuclear norm minimization. Simulation results demonstrate that in a 100 m × 100 m area, for a small scale network with 100 nodes, only 20% of measurements is needed to achieve a 0.5 m localization error, while 3% needed to achieve a 0.05 m error for a comparatively large scale network with 1000 nodes.

The sparse nature of location finding problem makes the theory of compressive sensing desirable for indoor positioning in Wireless Local Area Networks (WLANs). In this paper, we address the received signal strength (RSS)-based localization problem in WLANs using the theory of compressive sensing (CS), which offers accurate recovery of sparse signals from a small number of measurements by solving an ¿1-minimization problem. A pre-processing procedure of orthogonalization is used to induce incoherence needed in the CS theory. In order to mitigate the effects of RSS variations due to channel impediments, the proposed positioning system consists of two steps: coarse localization by exploiting affinity propagation, and fine localization by the CS theory. In the fine localization stage, access point selection problem is studied to further increase the accuracy. We implement the positioning system on a WiFi-integrated mobile device (HP iPAQ hx4700 with Windows Mobile 2003 Pocket PC) to evaluate the performance. Experimental results indicate that the proposed system leads to substantial improvements on localization accuracy and complexity over the widely used traditional fingerprinting methods.