G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, $ 70 $ 115 $ 185 $ Optimal RSS Threshold in Connectivity-Based Localization Schemes Gianni Giorgetti Sandeep K.S. Gupta Gianfranco Manes ACM MSWiM - Vancouver October 28, 2008 IMPACT LAB Arizona State University

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 What is this about? Localization: the problem of locating devices and/or people Localization based on proximity We can reduce the error by optimal selection of one of the parameters Optimal RSS Threshold in Connectivity-Based Localization Schemes

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Remote Monitoring Applications Gateway Server Mesh sensor network (x, y) = ?

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Why not to use GPS? GPS Board $ x N GPS Receiver - 70 $ x N Wireless Node $ x N Sensor Board $ x N Shopping List: NOT RELIABLE INDOORS Sometimes “good enough” is good enough

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Collaborative Localization Inputs: A set of anchor nodes In-network measurements Output: Node Coordinates RF-Based Approaches: Scene analysis (Fingerprinting) Range-Based (RSS, Interferometric) Connectivity d1d1 d2d2 d3d3 d4d4 d5d5

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Radio-Based, Range-Free Localization What we like about connectivity: 1.Easy to acquire 2.Easy to communicate (binary value) 3.Easy to process 4.Reasonable accuracy 1 HOP 2 HOPS 3 HOPS

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Example – 49 node network Comm. Range = ~ 33 m Connectivity = 9 Avg. Error = 6 – 10 m (0.2 – 0.3 R) Comm. Range = ~ 33 m Connectivity = 9 Avg. Error = 6 – 10 m (0.2 – 0.3 R)

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Does it work indoors?

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Why it doesn’t work… Every node is in the radio range of every node Nodes at different locations have the same neighbor sets Impossible to distinguish between nodes at different locations IDEA: TO REDUCE CONNECTIVITY BY SETTING A TRESHOLD. WHAT IS THE OPTIMAL VALUE?

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, D Localization RSS 1 RSS 2 RSS 3 RSS 4 … Connectivity-Based Localization = -72 dBm

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Log-Normal Shadowing Model Path-Loss Exponent

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Measurement Model Connectivity is a random variable Probability of detecting the nodes as “connected” Parameter Estimation Problem: We want to estimate d using observations C={0,1}. Is there a value P th that will reduce the estimation error?

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Fisher Information Large value of F  Small Error Small value of F  Large Error Fisher Information: measures the amount of information that a random variable carries about an unknown parameter Cramér-Rao bound: minimum theoretical estimation error

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 What does F tell us? The available Fisher information: 1.Decreases with the distance 2.Decreases with the noise in the RSS data 3.Depends on how we set the threshold

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 A toy problem RSS [dBM] pdf There are two nodes (Node 1 and Node 2). You have to decide which one is closer using connectivity information. How do you set the threshold?

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Optimal Connectivity Threshold RSS [dBM] pdf 1 1 For a single device the optimal threshold is equal to the expected received power. (p = 0.5)

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Network Localization Fisher Information Matrix Cramér-Rao Bound: Anchors Blind Nodes

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 CRB for 2D Network

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 CRB for 3D Network Using the CRB we can determine the optimal threshold We cannot compute the CRB at runtime (it requires knowledge of the node positions)

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Optimal Connectivity Setting the optimal threshold is equivalent to finding an optimal connectivity value. Easier to deal with (it doesn’t depend on the hardware) We investigated how this optimal connectivity value changes with different network parameters.

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Invariance of the optimal conn. GOOD NEWS: The optimal connectivity doesn’t change with network scaling and with the propagation model parameters

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Approximation and Simulations The Optimal Connectivity value increases with the network size. We find a formula to approximate the optimal connectivity value 2D

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008 Using the approximate formula we find: Opt. Conn = 9.27 (Pth = dBm) Opt. Conn = 11.1 (Pth = dBm) Case Studies

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, THANKS!