Sensor Positioning in Wireless Ad-hoc Sensor Networks Using Multidimensional Scaling Xiang Ji and Hongyuan Zha Dept. of Computer Science and Engineering, The Pennsylvania State University INFOCOM 2004 Presenter: Sheng-Shih Wang March 15, 2004

Outline Introduction Previous Works Challenges Calculating Relative Positions With Multidimensional Scaling Aligning Relative Positions Distributed Sensor Positioning Methods Experimental Results Conclusion

Introduction Why the physical positions of sensors is important For object detection or tracking For communication protocol establishment

Previous Works Global Positioning System (GPS) High cost Other Methods Class 1 Improve the accuracy of distance estimation with different signal techniques RSSI, ToA, TDoA, AoA

Previous Works (cont.) Class 2 Relies on a large amount of sensor nodes with positions known (i.e., beacon or anchor node) densely distributed in a sensor network Class 3 Employ distance vector exchange to find the distances from the non-anchor nodes to the anchor nodes Class 4 Locally calculate maps of adjacent nodes with trilateration or multilateration

Challenges Estimated distances of AC and BC are increased

Challenges (cont.) Estimated distances of AC and BC are increased

Challenges (cont.) In real world (irregular radio pattern) In real world (irregular radio pattern) The radio range of a sensor is different at different directions

Challenges (cont.) The complexity of the terrain leads to different signal attenuation factors and radio ranges

Calculating Relative Positions With Multidimensional Scaling The Multidimensional Scaling (MDS) The analysis of dissimilarity of data on a set of objects Discover the spatial structures in the data Advantages for position estimation MDS always generates relatively high accurate position estimation even based on limited and error-prone distance information

The Classical MDS The classical MDS [3] (If all pairwise distances of sensors are collected)

The Classical MDS (cont.)

The Iterative MDS The iterative MDS

The Iterative MDS (cont.) Known position: A,B,C,D Unknown position: E,F

Aligning Relative Positions To compute the physical positions of sensors Align the relative positions to physical positions with the aid of sensors with positions known Includes shift, rotation, and reflection of coordinates

Distributed Sensor Positioning Methods Employ distance measurement model of RSSI The power of the radio signal attenuates exponentially with distance Receiver can estimate the distance to the sender by measuring the attenuation of radio signal strength

Distributed Position Estimation with Anchor Sensors Adjacent area Adjacent area: the sensor position are estimated with MDS The average radio range is estimated with the hop count and physical distance

Distributed Position Estimation with Anchor Sensors (cont.) A: Starting Anchor D, H: Ending Anchors

Distributed Position Estimation with Anchor Sensors (cont.) Local map

On Demand Distributed Position Estimation Study case: one sensor ’ s position is needed to be estimated

Experimental Results --- Simulation Model Simulator: Matlab 400 nodes Randomly placed 100-by-100 square region

Experimental Results --- Two Strategies The 1st strategy The average radio range is 10 The 2nd strategy The region is equally divided into four non-overlapped square regions Sensors have different radio ranges The average radio ranges in different small square regions are 7, 8.5, 10, and 11.5

Experimental Results --- Evaluation Criteria n: the total number of sensors m: the number of anchors A low error means good performance of the evaluated method

Physical positions of sensors in an adjacent area Recovered relative positions (classical MDS) After alignment (classical MDS)

Experimental Results --- Classical MDS The increase of error rates different conditions is always slower than the increase of distance measurement error  The classical MDS is robust in tolerating measurement errors of sensor distance

Experimental Results --- Iterative MDS Error rates of sensor positioning increase when the percentage of sensor pairwise distances collected and the number of iteration increase

Experimental Results --- Iterative MDS (cont.) When the collected pairwise distance and the number of iteration are fixed, the error rates of sensor positioning increase with the increase of distance measurement error

Experimental Results --- Results (cont.) Errors when applying the distributed positioning method with anchor sensors to all sensors in a square region with an uniform radio range and different distance measurement errors The distance measurement error rate

Experimental Results --- Results (cont.) Errors when applying the distributed positioning method with anchor sensors to all sensors in a square region with different signal attenuation factors (radio ranges)

Experimental Results --- Results (cont.) Errors when applying the distributed on demand positioning method to one sensor in two square region with uniform and different signal attenuation factors, respectively 8 anchors (5% of total number of sensors)

Conclusion The MDS-based positioning technique Compute relative positions of sensors The distributed sensor positioning method Get the accurate position estimation Reduce error cumulation The on demand position estimation method For one or several adjacent sensors positioning Can work in networks with anisotropic topology and complex terrain Advantage Effective, Efficient

Experimental Results --- Results The physical positions of sensors in an adjacent area

Experimental Results --- Results (cont.) The recovered relative positions of sensors in an adjacent area based on classical MDS

Experimental Results --- Results (cont.) These sensors’ physical positions after alignment

Calculating Relative Positions With MDS

Distributed Sensor Positioning Methods