Indoor Localization Without the Pain

Transcription

1 Krishna Kant Chintalapudi, Anand Padmanabha Iyer, Venkata N. Padmanabhan Presentation by Adam Przedniczek This presentation was based on the publication by Krishna Kant Chintalapudi, Anand Padmanabha Iyer and Venkat Padmanabhan, MobiCon 10.

2 1 Foreword Indoor Positioning Systems EZ Localization Algorithm Related Solutions 2 3 Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

3 Indoor Positioning Systems EZ Localization Algorithm 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

4 Indoor Positioning Systems EZ Localization Algorithm 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.

5 Indoor Positioning Systems EZ Localization Algorithm 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.

6 Figure: System overview

7 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.

8 Measuring distance from Received Signal Strength (RSS) p i,j = P i 10γ 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. c i, x j R 2 - locations of the i th AP and j th mobile user. 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.

9 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: d i,j = 10 ( P i p i,j 10γi ) 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 4m + 2n. If we have enough locations, then mn > 4m + 2n and it makes the LDPL system uniquely solvable.

10 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 uniquely solvable. Figure: Non-localizability

11 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.

12 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 Pi 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.

13 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 fitness is estimated by computing 1 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 S1 old, S old 2 from prevoius generation and mixing them S new = a S1 old + ( 1 a) S2 old where a Uniform( (0, 1) U ) 3 The algorithm terminates when solutions do not improve for ten consecutive generations.

14 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 4m + 2n to 4m. The GA has to pick only 4m unknowns related to AP parameters and the remaining 2n can be computed using trilateration. We can use already determined locations.

15 How significant are receiver gain differences There are differences in RSS measured by different mobile devices at the same location, even among devices of the same make and model. Mobile device RSS [dbm] Laptop Xenovo X61-41 HP IPAQ #1-43 HP IPAQ #2-31 Samsung SGHi780 #1-51 Samsung SGHi780 #2-49 HTC ADV HTC ADV Table: Gain differences across tested devices

16 The very first solution to gain differences problem For each user we can simply introduce an unknown parameter G that corresponds to the receiver gain. p k ij = P i G k + 10γ i log d k ij + R The G k value is estimated using genetic algorithm with narrowing the search space to a generous span (-20, 20) db. But there s a better way...

17 Relative Gain Estimation Algorithm (1) We re trying to estimate the difference in gain between i th and j th mobile device G ij = G i G j and the uncertainty σ( G ij ). The difference in RSS obtained using two different mobile devices is equal to their gain difference, but only when this mesuremts were taken in the same location. But how we knew that this receivers are close to each other? Let k 1 and k 2 are 2 mobile devices at 2 unknown locations j 1 and j 2. We have their RSS measurents from m APs: Q k 1 j 1 = p k 1 1 j 1, p k 1 2 j 1,..., p k 1 m j 1 Q k 2 j 2 = p k 2 1 j 2, p k 2 2 j 2,..., p k 2 m j 2

18 Relative Gain Estimation Algorithm (2) We transform both vectors by subtracting from all its elements their very first item: V k 1 j 1 = 0, p k 1 2 j 1 p k 1 1 j 1,..., p k 1 m j 1 p k 1 1 j 1 V k 2 j 2 = 0, p k 2 2 j 2 p k 2 1 j 2,..., p k 2 m j 2 p k 2 1 j 2 For both vectors this differences are independent of its receiver gain. Thus, if vectors V k 1 j 1 and V k 2 j 2 are close to each other, then we can assume that j 1 and j 2 are proximate. Then we can create a set M k 1k 2 of RSS measurements pairs k (p 1 k x j 1, p 2 x j 2 ) at proximate locations. Now, we can state: G k 1k 2 1 = M k (p 1k 2 1 p 2 ) σ( G k 1k 2 ) = 1 M k 1k 2 (p 1,p 2 ) M k 1 k 2 (p 1,p 2 ) M k 1 k 2 (p 1 p 2 G k 1k 2) 2

19 Relative Gain Estimation Algorithm (3) We compute G ij and σ( G ij ) for every pair of mobile devices whenever it s possible. Some mobile devices might not have even a single pair of measurements in proximate location. In such cases we can use the transitivity property: G ij = G ik + G kj. Finally, we build graph with mobile devices in nodes. The 2 nodes are connected if and only if they have at least a single measurement at proximate location. In each connected component we randomly choose root node and assign its gain by sampling uniformly randomly in the interval (-20, 20) db. Gains for the rest of nodes from this component are computed by solving set of equations of the form G j G i = G ij in a weighted least mean square sence with weights set to σ( G ij ).

20 How to finally localize a new device with unknown gain Beacuse we don t know the gain of the new mobile device, we must rebuild our set of equation to the gain-independent form: p k i 2 j p k i 1 j = P i2 P i1 + γ i1 log(d i1 j) γ i2 log(d i2 j) The location of the new device is derived by solving set of such simultaneous equations in a least mean square sense.

21 Picking the right subsets of APs and of unknown locations We cannot select all APs that could be seen on a given floor because they might belong to neightbour building. Selecting all APs from our own network is still problematic because of the computational hardship. Some of the APs are seen as multiple SSIDs. During training phase we must choose the RSS mesurements taken at difreent locations.

22 APSelect algorithm APSelect The main concept of APSelect is to choose the set of RSS measurements that minimize the information overlap in the sence of a some similarity metric. 1 We normalize all RSS measurements p ij to lie within the range pˆ ij (0, 1). 2 Then we introduce the similarity metric λ ij = 1 1 n k pˆ ik pˆ jk and cluster the most similar clusters. 3 We iterate the clustering process till all pairs of clusters have similarity lower than 90%. Finally we choose the clusters representatives.

23 LocSelect algorithm LocSelect We can reuse APSelect algorithm and flip the problem by treating AP as locations and vice versa.

24 Algorithms taken into consideration Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions EZ EZ + Loc (EZ with known AP locations and measurements) RADAR Horus

25 Small building floorplan Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions Figure: Small building floorplan

26 Small building performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions Figure: Localization error CDF in small building

27 Large building floorplan Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions Figure: Large building floorplan

28 Large building performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions Figure: Localization error CDF in large building

29 Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions How accuracy depend on amount of training data Figure: Dependence on amount of training data

30 Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions How long it takes EZ to estimate its model # APs # mobile devs. known Lenovo T61 HP PRoline Table: Time of building the RF model (given in minutes)

31 Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions Thank you