An RSSI Gradient-based AP Localization Algorithm

Transcription

1 An RSSI Gradient-based AP Localization Algorithm Presenter: Cheng-Xuan, Wu Year: 2014, Volume: 11, Issue: 2 Pages: , DOI: /CC Cited by: Papers (2) IEEE Journals & Magazines

2 Outline 1. Introduce 2. Related Work 3. Localization Algorithm 3.1 RSSI gradient 3.2 Direction clustering 4. Evaluation 4.1 Experiment setup 4.2 Influence of clustering number 4.3 Performance comparison of different algorithms 4.4 Computation and energy cost 5.Conclusion

3 1. Introduce Indoor position: from GPS to existing Aps. Require knowledge of the location of Aps. But there impossible to get Aps location to estimate AP location by Wi-Fi signals. War-driving: use GPS and collect Wi-Fi fingerprint. There exist several methods to process the fingerprints data to infer the locations of Aps: Cell-ID centroid weighted centroid algorithm. algorithms exhibit high error and high variation.

4 Triangulation with directional phased array antennas (other AP location method) Requires specialized hardware components (limited). Present a novel gradient-based AP localization approach. Only using off-the-shelf smartphones. Estimate direction (minus gradient) of AP just from the local RSSI. Direction clustering method : identify and filter gross measurement errors. Choosing directions with low measurement errors to triangulate AP location. Proposed algorithm can obtain accurate AP location with low cost.

5 2. Related Work localize the Wi-Fi clients nearest-neighbor [1] neural networks [11] fuzzy logic [12] kernel methods [13] compressive sensing [14] projection approach [15] principal component [16] and probabilistic approaches [17,18] localize the Wi-Fi AP various position-bearing information (GPS, RSSI, AoA) to obtain AP position estimate. GPS-based AP localization : outdoor (Power hungry, localization error 10m up) AoA-based Ap localization: limited (directional antennas, not commodity) RSSI-based localization : low cost centroid algorithm (cannot handle outside)

6 Analyzing the statistical characteristics of RSSI difference from heterogeneous devices. Youngsu [24]: proposed normal distributed model to correct the RSSI difference to enhance AP position estimation accuracy. Koo [25]: adopted multidimensional scaling technique to construct the relative map of all APs with RSSI values. Koo [26]: proposed a range-based AP localization which adopted the RSSI-based ranging schemes to estimate the distance between AP and measurement point. Recently, signal strength gradient is leveraged to locate Aps.

7 3. Localization Algorithm AP localization algorithm: RSSI gradient clustering Leveraged to cope with the gradient directions with gross errors (i.e. gradient outliers) arising out of presence of radio reflections. 3.1 RSSI gradient 3.2 Direction clustering 3.3 Selection of AP location

8 3.1 RSSI Gradient The minus gradient direction RSSI increases most rapidly approximately corresponds to the transmitting direction of an AP.

9 G(x,y) and G(x,y): horizontal and vertical direction gradients gradient norms and gradient angles corresponding to all sampling locations. only use the gradient angles to locate the AP.

10 interesting observation : arrows are all pointing to different directions, there seems to be a clustering effect. gradients are not pointing to random directions but towards roughly one of a handful of possible location. Most arrows are pointing towards the real AP location and other arrows (gradient outliers) are pointing to the AP images arising out of presence of reflections.

11 3.2 Direction clustering k-means algorithm : group all the gradients into several clusters. Each group of measurement points has the minor angular residuals approximately pointing towards the same location. Effectively identify and eliminate gradients outliers. Only select the accurate gradients to infer AP position.

12 3.2.1 Algorithm Steps 1. Randomly select K points as cluster heads. 2. Calculate all points angular residuals with each cluster heads. residuals with each heads. 3. Assign the point (x i, y i ) to the cluster. (min residuals) 4. Identify direction outliers and remove.(π/2) 5. Until all points have been clustered into k groups. 6. Update cluster heads by minimizing weighted sum square. Iterative until all cluster head lower than threshold. angular residuals

13 3.2.2 Location Update of Cluster heads Steepest descent method Newton method Quasi Newton method Conjugate gradient method Variable metric method (Davidon-Fletcher-Powell method) DFP

14 3.2.2 DFP The method to updating the position of cluster head i. n: points in group. (xi,yi): cluster head. (xj,yj): points in cluster. Rssi j : point s rssi. aj: aradient direction.

15 1. Algorithm initialization. a) cluster head is initialized to x (1). b) permissible error : ε. 2. For m=1, set H m = I m (I m is a unit matrix). Calculate the gradient gm = Si(X (m) ) of S i in the location x(m). 3. Let d(m) = Hmgm check whether the gradient of S i has converged. a. If Si(X (m) ) ε, stop iteration and we get the final result x(m). b. if not, then go to step 4).

16 4. Start from x(m), search along the direction d(m) with the search step length λm min until Si x m + λmd m = λ 0Si(x m + λdm) then update coordinate of cluster head x m + 1 = x m + λm m 5. If m=2, set x(1)=x(m+1) and return to step 2; if not, go to step For g m + 1 = Si(X (m) ), P (m) = x (m+1) x m, q (m) = x (m+1) x m use the DFP method to obtain the correctional matrix. let H m + 1 = Hm + H, m = m + 1, then return to step 3.

17 3.2.3 Cluster Number optimization Statistical means (Anderson-Darling normality test) to learn the value of k. Would like the angular residual within one cluster should be single modal. Use the idea from the G-means algorithm and learn the number of clusters k, checking the angular residual values in each cluster follows a Gaussian distribution. start with the k=1 and successively increment k. Check residual values in each cluster satisfy a statistical test for normality. If they do, we stop the procedure; otherwise, we increment k and repeat.

18 4. Evaluation 4.1 Experiment setup 4.2 Influence of clustering number 4.3 Performance comparison of different algorithms 4.4 Computation and energy cost

19 4.1 Experiment setup 7th floor of Institute of Computing Technology of Chinese Academy of Science A. Cluster & gradient algorithm (proposed) B. No-cluster & gradient algorithm ( leverages all gradient directions) C. weighted centroid algorithm experimental area : 28 grids (4m*3m) Sampling period : 300ms and 100 samples (each grid). Average all RSSI to obtain a steady RSSI value. Keep smartphone direction as same.

20 4.2 Influence of clustering number Anderson-Darling normality test method To learn the optimal number of clusters optimal number of clusters: 4 As the cluster number increased: more fake AP mirrors formed by radio reflection are identified. AP localization error decreases sharply from 6.3 meters to 1.5 meters.

21 4.3 Performance comparison of different algorithms AP Cluster & gradient algorithm weighted centroid algorithm No-cluster & gradient

22 4.4 Computation and energy cost Computation complexity Energy cost

23 4.4.1 Computation complexity (1) Y: K-mean G: DFP n: number of grids k: number of clusters. t1: iteration times of the k-means-based direction clustering algorithm. t2 : average iteration times of the OFP method in an iteration of the k- means-based direction clustering algorithm.

24 4.4.1 Computation complexity (2) Using hardware: Matlab 2007b PC with 2.9GHz AMD Athlon II X GB Ram K-mean cluster to 4

25 4.4.2 Energy cost Calculation is completed on a server or PC. Consider the energy cost of RSS fingerprint collection. E = mp ts/s (6) m: number of RSS fingerprints collected in a grid. p: radio power when the smartphone is scanning the environmental Aps. M: sampling period of a fingerprint. S: Square of the whole RSS fingerprint collection area. s : Square of a grid.

26 5.Conclusion By introducing direction clustering method to identify and eliminate the inaccurate gradients. The proposed algorithm can obtain an accurate AP position estimate. Outperforms the weighted centroid algorithm and algorithm using all gradients. Its localization error is robust whether the AP is located inside or outside of sampling collection area. In our future work, we plan to perform more experiments in a wide variety of scenarios and integrate it in our practical localization system.