A Mixed Approach to Similarity Metric Selection in Affinity Propagation-Based WiFi Fingerprinting Indoor Positioning

Abstract

The weighted k-nearest neighbors (WkNN) algorithm is by far the most popular choice in the design of fingerprinting indoor positioning systems based on WiFi received signal strength (RSS). WkNN estimates the position of a target device by selecting k reference points (RPs) based on the similarity of their fingerprints with the measured RSS values. The position of the target device is then obtained as a weighted sum of the positions of the k RPs. Two-step WkNN positioning algorithms were recently proposed, in which RPs are divided into clusters using the affinity propagation clustering algorithm, and one representative for each cluster is selected. Only cluster representatives are then considered during the position estimation, leading to a significant computational complexity reduction compared to traditional, flat WkNN. Flat and two-step WkNN share the issue of properly selecting the similarity metric so as to guarantee good positioning accuracy: in two-step WkNN, in particular, the metric impacts three different steps in the position estimation, that is cluster formation, cluster selection and RP selection and weighting. So far, however, the only similarity metric considered in the literature was the one proposed in the original formulation of the affinity propagation algorithm. This paper fills this gap by comparing different metrics and, based on this comparison, proposes a novel mixed approach in which different metrics are adopted in the different steps of the position estimation procedure. The analysis is supported by an extensive experimental campaign carried out in a multi-floor 3D indoor positioning testbed. The impact of similarity metrics and their combinations on the structure and size of the resulting clusters, 3D positioning accuracy and computational complexity are investigated. Results show that the adoption of metrics different from the one proposed in the original affinity propagation algorithm and, in particular, the combination of different metrics can significantly improve the positioning accuracy while preserving the efficiency in computational complexity typical of two-step algorithms.

ViFi: Virtual Fingerprinting WiFi-Based Indoor Positioning via Multi-Wall Multi-Floor Propagation Model

“…(7) Typical orders are o = 1 (inverse Manhattan distance) and o = 2 (inverse Euclidean distance, used in ViFi). Similarity metrics using modified versions of the inner product between RSS vectors have also been proposed [38], [39].…”

“…Previous work addressed the impact of k on positioning accuracy of deterministic WkNN algorithms in real fingerprinting systems, and two approaches emerged: a) a dynamic k selection i.e. that, however, increases complexity without guaranteeing the optimal performance in all cases [39], [40], and b) a static k selection, that minimizes the average positioning error over a set of Test Points. The parameter k that minimizes the average error is referred to as k opt .…”

Performance Comparison of WiFi and UWB Fingerprinting Indoor Positioning Systems

“…Dynamic k schemes typically rely on the introduction of a variable threshold in order to determine the value of k depending on the specific positioning request [19,23,24]. • Similarity metric: Different similarity metrics have been proposed [20]. A popular choice is the use of the inverse Minkowski distance with order o ≥ 1 (orders typically used are o = 1, i.e., the Manhattan distance, and o = 2, i.e., the Euclidean distance).…”

“…Several choices are possible for the data to be collected: in the case of UWB, channel impulse response (CIR) location-dependent features have been proposed as fingerprints, because of the possibility of the accurate temporal resolution of multipath components typically forming the CIR [15]. In parallel, in the view of the cost-effective reuse of pre-existing communication infrastructure, fingerprinting emerges as one of the most appealing solutions in the case of WiFi-based IPSs [5]; in this case, the use of WiFi access points (APs) as ANs and the collection of RSS values in the RN positions have been widely proposed and analyzed [16][17][18][19][20][21].…”

WIPP: Wi-Fi Compass for Indoor Passive Positioning with Decimeter Accuracy

“…To achieve the affinity propagation clustering [40,41], we first define ϕ i = aoa i toa i T as the vector of the i -th joint AOA and TOA measurement, where the notation "T" denotes the transpose operation. The matrix of the joint AOA and TOA measurements is shown below.…”