Indoor Localization Without the Pain Krishna Kant Chintalapudi, - PowerPoint PPT Presentation

Foreword Algorithm Details Measuring Quality and Performance Indoor Localization Without the Pain Krishna Kant Chintalapudi, Anand Padmanabha Iyer, Venkata N. Padmanabhan Presentation by Adam Przedniczek 2011-10-19 This presentation was based on the publication Indoor Localization Without the Pain by Krishna Kant Chintalapudi, Anand Padmanabha Iyer and Venkat Padmanabhan, MobiCon ’10 . Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance 1 Foreword Indoor Positioning Systems EZ Localization Algorithm Related Solutions 2 Algorithm Details Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges 3 Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions Indoor Localization Without the Pain

Foreword Indoor Positioning Systems Algorithm Details EZ Localization Algorithm Measuring Quality and Performance Related Solutions What’s an IPS An Indoor Positioning System (IPS) or Indor Location System is a term used for distributed system of portable devices used to wirelessly localize people and objects inside an indoor space. Due to the signal attenuation caused by construction materials, inside the buldings we cannot rely on the sattelite signal. Instead of using GPS, one can make use of such indoor features as e.g. ambient sound, light/color or WiFi signal. IPS applications Augmented reality Targeted advertising Store navigation and airport maps Guided tours of museums Indoor Localization Without the Pain

Foreword Indoor Positioning Systems Algorithm Details EZ Localization Algorithm Measuring Quality and Performance Related Solutions Key concept of EZ approach WiFi-based indoor localization with no pre-deployment calibrations. We assume WiFi coverage but we do not assume knowledge of the network physical layout (e.g. APs position). We construct RF signal model based on Received Signal Strength (RSS) measurements recorded by the mobile devices and corresponding to APs in their view. This measurements are taken at various unknown locations and reported to a localization server. Ocassionally, we obtain a location fix e.g. GPS lock at the entrance or near a window. There’s no need even for the floorplans. Indoor Localization Without the Pain

Foreword Indoor Positioning Systems Algorithm Details EZ Localization Algorithm Measuring Quality and Performance Related Solutions Indor localization schemes Localization in indoor robotics SLAM (Simultaneous Localization and Mapping) method building a map of the enviroment using sensors e.g. odometers or LADAR. Systems relied on specialized infrastructure LANDMARC system (based on RFID). Schemes building RF signal maps Calibration-intensive: RADAR, Horus, SurroundSense. Assuming a very dense WiFi deployment: DAIR. Model-Based Techniques TIX, ARIADNE. Ad-Hoc localization DV-Hop, DV-Dist, SPA, N-Hop. Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges Figure: System overview Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges Figure: Relative position Localizablity ”Given enough distance constraints between APs and mobile devices, it is possible to estabilish all their locations in a relative sense. Knowing the absolute locations of any three non-colinear mobile devices then allows determination of the absolute locations of the rest.” Z. Yang, Y. Liu, and X.-Y. Li. Beyond Trilateration: On the Localizability of Wireless Ad-Hoc Networks. Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges Measuring distance from Received Signal Strength (RSS) p i , j = P i − 10 γ i log d i , j + R � d i , j = ( � x j − � c i ) T ( � x j − � c i ) d i , j [ m ] - distance between i th AP and j th mobile user. p i , j [ dBm ] - i th AP’s signal strength measured at j th mobile user. x j ∈ R 2 - locations of the i th AP and j th mobile user. � c i , � P i - i th AP transmit power (RSS measured at a distance of 1m). γ i - path loss exponent. R - a random variable that hopes to capture models imperfections. Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges How d i , j can be computed in Log-Distance Path Loss model? If the P i and γ i are given, d i , j can be computed as follows: Pi − pi , j d i , j = 10 ( ) 10 γ i A novel approach of EZ algorithm We DO NOT assume the a priori knowledge of P i and γ i !!! We threat them as unknowns in addition to the unknown locations of APs and mobile users. Let m and n are numbers of APs and mobile users respectively. Each RSS observation adds single equation to LDPL model, thus we have set of mn simultaneous equations. The number of unknowns is equal to 4 m + 2 n . If we have enough locations, then mn > 4 m + 2 n and it makes the LDPL system uniquely solvable. Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges Choosing the right set of RSS measuremts Three (or more) collinear locations cannot be used in trilateration to determine an unknown location. RSS observations cannot be co-circular with respect to the AP. Even avoiding co-circular observations and having enough equations, the LDPL model don’t have to be Figure: Non-localizability uniquely solvable. ր Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges How to ensure that LDPL system has an unique solution? Open problem: What are the necessary and sufficient conditions under which LDPL has an unique solution? In practice we ensure following three conditions to make sure that the LDPL can be uniquely solved: 1 Each unknown location must see at least 3 APs. 2 Each AP must be seen from at least 5 locations. 3 The Jacobian of the system of LDPL equations must have a full rank. Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges How to tackle this set of over-determined equations? We’re searching for a solution that minimizes the least mean absolute error (N is the number of equations): J EZ = 1 � | P ij − P 0 i + 10 γ i log d ij | N i , j Optimization iterative schemes such as the Newton-Raphson or Gradient Descent have failed due to immense number of J EZ local minima. Simulated annealing and genetic algorithms (GA) also failed, because they can miss some local minima. Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges Hybrid algorithm: Genetic Algorithm + Gradient Descent 1 Pick initial generation of solution randomly and refine then using Gradient Descent. 2 Let U be the number of all unknowns. Solutions S ∈ R U 1 fitness is estimated by computing J EZ . The successive generations evolves as follows: We retain 10% of solutions with the highest fitness. We add 10% randomly generated solutions (refined using GD). 20% of solutions are perturbated based mutations . 60% are derived by picking 2 solutions S old 1 , S old from prevoius 2 generation and mixing them S new = � + ( � a • S old a ) • S old 1 − � 1 2 a ∈ Uniform ( (0 , 1) U ) where � 3 The algorithm terminates when solutions do not improve for ten consecutive generations. Indoor Localization Without the Pain

Main Concept Foreword Solving the System of LDPL Equations Algorithm Details Reducing the Search Space Measuring Quality and Performance Differences in Receiver Gain Real World Challenges How can we speed up solving LDPL system If we know the floorplan we can narrow the search of the location to within the floor perimeter. We can limit AP transmission powers to (-50, 0) dBm and loss exponent γ i to (1.5, 6.0). We can cut down the total number of variables from 4 m + 2 n to 4 m . The GA has to pick only 4 m unknowns related to AP parameters and the remaining 2 n can be computed using trilateration. We can use already determined locations. Indoor Localization Without the Pain