Adaptive Radio Interferometric Positioning System Modeling and Optimizing Positional Accuracy based on Hyperbolic Geometry

2 Motivation Location is an important information in many sensor network application Example –Environment monitor

3 Radio Interferometric Positioning (RIP) System Proposed by Vanderbilt University High accuracy –Error < 1m Long sensing range –Few nodes can cover wide area Low cost –Using standard sensor network devices (Mica2), no additional specialized hardware

4 Original RIP system Anchor nodes are placed in known locations The positional error of RIP system is highly affected by target locations and the selection of beacon nodes Original RIP system is “static” –The selection of beacon nodes is fixed, doesn’t change depend on target locations T Beacon

5 Our Contribution Design, implement and evaluate an adaptive RIP system –Dynamically select beacon nodes based on target locations

6 Flow of RIP system Two ranging rounds In each ranging round, we need select beacon nodes –Two nodes are selected as senders (sender-pair) –Other nodes become receivers RangingPositioning Anchor node (known location)

7 RIP ranging Ranging_result = distance(T,sender1) – distance(T,sender2) = d 1 – d 2 Each ranging result in a hyperbolic curve Two ranging needed for positioning Sender-pairs selected in two ranging round are called Sender Pair Combination (SPC) T sender1 sender2 sender1 sender2 d1d1 d2d2 d1d1 d2d2

8 Flow of RIP system 1.Target location 2.Selection of SPC RangingPositioning Error range Error positional Uncontrollable Can approximate from historical location Controllable

9 How SPC selection affect positional error Ranging with error => Hyperbolic curve with error => Positioning with error sender1 sender2 sender1 sender2 sender1 sender2 sender1 sender2 Error range T T’T’ T T’T’

10 How SPC selection affect positional error (cont.) Displacement of a hyperbolic curve –Shortest distance from hyperbolic curve with error to target sender1 sender2 sender1 sender2 Error range T T

11 How SPC selection affect positional error (cont.) Intersectional angle of hyperbolic curves T’T’ TT T’T’ T T’T’ θ θ θ θ= 90° θ= 60° θ= 30°

12 How SPC selection affect positional error (cont.) Intersectional angle of hyperbolic curves sender1 sender2 sender1 sender2 sender1 sender2 sender1 sender2 Error range T T’T’ T T’T’ θ θ

13 Adaptive RIP system Given changing target locations ( from historical data ), select optimal SPC with minimal Error positional Estimation Error Model –Predict Error positional using specific SPC –We run Estimation Error Model for all SPC, and find the SPC with minimum error

14 Estimation Error Model Known Variables –Target location –SPC –Error range Unknown –Error positional

PT is the estimation Error positional N is the projection point of T on H 12 –TN is the displacement of hyperbolic curves H 12 θ is the intersectional angle of hyperbolic curves H 12 and H 34 Find TM (TN) and θ geometrically –Find PT geometrically 15 Geometrical Derivation of Estimation Error Model Error range

16 Validation of Estimation Error Model

17 Adaptive RIP system Given changing target locations ( from historical data ), select optimal SPC with minimal Error positional For multi-target positioning, select optimal SPC with minimal average Error positional for all targets

18 Estimation Error of SPC 3 System architecture SPC selector RIP engine Estimation Error Model SPC, Target positions Estimation Error positional Target positions Adaptive SPC Estimation Error of T 5 Estimation Error of T 4 Estimation Error of T 3 Estimation Error of T 2 Estimation Error of T 1 SPC2 Estimation Error of SPC 2 Estimation Error of SPC 1 Optimal SPC Target position SPC1

19 Evaluation of adaptive RIP system Single-target positioning experiment Multi-target positioning experiment A~F are anchor nodes Each grid is 1m 2

20 Single-target positioning experiment Static RIP Adaptive RIP Blue line : target path Blue point : ground truth Red point : estimation position

21 Average error (meter)90-th percentile (meter) Static RIP Adaptive RIP Improvement47%55% Single-target positioning experiment walking repeatedly 5 times, around 50 samples

22 Multi-target positioning experiment 6 targets –1 moving (blue point) –5 static (1~5 green points)

23 Average error (meter) 90-th percentile (meter) Static RIP Adaptive RIP Improvement60%61% Multi-target positioning experiment Static

24 Conclusion Since the Error positional of RIP system is impacted by target location and SPC selection, an adaptive RIP system is needed Build upon Estimation Error Model, our adaptive RIP system can dynamically find optimal SPC with minimal Error positional based on target location Our adaptive RIP system outperforms static RIP system in both single-target and multi-target positioning

25 Q & A

26 Thank you

27 Flow of RIP system 1.Start RIP system 2.Select 2 anchor nodes as senders 3.Other anchor nodes become receiver 4.Ranging 5.If 1 st ranging => goto 2 and do 2 nd ranging else => goto 6 do positioning 6.Positioning 7.End T Sender1 Sender2 Receiver2 Receiver1 Sender1 Sender2Receiver2 Receiver1 RangingPositioning Anchor node (known location) 1 st ranging 2 nd ranging

28 Geometrical Derivation of Estimation Error Model Steps: 1.Find TN (TM) 2.Find θ 3.Find PT geometrically If we know TN, TM, θ, we can derivative PT geometrically Known Variables: Target location SPC Error range mNmN mMmM