Scalable Location Performance Analysis in IEEE 802.11-17 Document
Explore a detailed analysis of scalable location performance in the IEEE 802.11-17 document, focusing on simulation procedures, measurements, and location estimation techniques using DToA and CToA methods. The document discusses clock offsets, multipath errors, client tracking, and clock knowledge for accurate positioning in wireless networks.
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Nov 2017 doc.: IEEE 802.11-17/1758r0 Further Scalable Location Performance Analysis Date: 2017-11-08 Authors: Name Erik Lindskog Affiliations Address Qualcomm Phone email elindsko@qca.qualcomm.com alirezar@qca.qualcomm.com Ali Raissinia Qualcomm nkakani@qca.qualcomm.com Naveen Kakani Qualcomm Submission Slide 1 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 General Simulation Procedure Setup: 6 ASs in circle with 50 m radius 1 client AS2 (x2,y2) 2 Unknowns: AS clock offsets , , (w.r.t. client clock, i.e. =0) Client coordinates x0,y0 AS3 AS1 3 1 Client (x0,y0) Modeling of imperfections: For simplicity Clock offsets i=0 but unknown No clock drifts modeled 1 ns stdev Gaussian clock gitter Abs of (1 m stdev Gaussian) multipath error 0.33 ns residual error when clock knowledge assumed AS4 AS6 0= 0 6 4 AS5 5 Submission Slide 2 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 DToA Simulation Procedure Not all transmissions depicted! Measurements: One transmission in each direction between each pair of ASs Client listens to transmissions AS2 (x2,y2) AS1 AS3 Location estimation: E.g. iteration with Newton s method to solve for least squares solution to non-linear system of equations for measured DToAs. When specified, showing average of 10 realizations of each client drop Client (x0,y0) AS4 AS6 AS5 AS to AS multipath error same in both directions. Submission Slide 3 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 CToA Simulation Procedure Not all transmissions depicted! Measurements: One transmission in each direction between each pair of ASs Client listens to transmissions AS2 (x2,y2) AS1 AS3 Location estimation: E.g. iteration with Newton s method to solve for least squares solution to non-linear system of TOD/TOA equations position. When specified, showing average of 10 realizations of each client drop For method using tracked clock knowledge, a first estimation of the clock offsets are computed from 10 realizations. Client (x0,y0) AS4 AS6 AS5 Submission Slide 4 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 DToA and CToA w/o client tracking Client outside circle Multipath error Proxy - Abs of Gaussian MU-ranging protocol uses symmetric AS to AS multipath errors Tracked clocks are initialized using average of 10 other measurements CToA here outperforms DToA when NOT considering client position tracking. Call in comment:: Submission Slide 5 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 DToA and CToA w/o client tracking CToA with tracked clocks Submission Slide 6 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 DToA and CToA with client tracking Client outside circle Multipath Proxy - Abs of Gaussian MU-ranging protocol uses symmetric AS to AS multipath errors Client location tracking modeled by averaging 10 measurements Tracked clocks are initialized using average of 10 other measurements DToA here outperforms (or equals) CToA when considering client position tracking. Call in comment:: Submission Slide 7 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 DToA and CToA with client tracking Note elongated shape of location error also for CToA with tracked clocks. Submission Slide 8 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Thank You Submission Slide 9 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Appendix Submission Slide 10 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Newton s method for solving non-linear equation (x ) f Solve equation: F = *x ( ) f F (x ) f x x1 x3x2 etc. = x x* Submission Slide 11 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Solving of non-linear system of equations F = *x ( ) f - solve for x* Non linear system of equations: Use Newton s method for multiple variables: f = + = * ( ) i f x ( ) ( ) ( ) F f x f x f x x where Linearization: k k x j Over-determined non-linear system of equation to solve for x: + ( ) ( ) F f x f x x k k Least squares solution for iterative step: ( ) ) k 1 = = T T ( ) ( ) ( ) ( x x x f x f x f x F f x + 1 k k k k k Iterate according to: ( ) ) k 1 = + T T ( ) ( ) ( ) ( x x f x f x f x F f x + 1 k k k k k Submission 12 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 DToA Differential Time-of-Arrival Location See [1,2 and 3] Submission Slide 13 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Propagation paths and time stamps Illustrating timing diagram showing double sided feedback of time-stamps: Client AP2 AP1 t1 UL MU NDP t5 t2 DL NDP t3 t4 t2, t3 AP to STA feedback t6 t1, t4 STA to AP feedback Submission Slide 14 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Double-Sided Differential Distance Calculation The client STA listens to the exchanges between the AP1 and AP2 and records the time t5 when it receives the UL MU NDP from AP2 and the time t6 when it receives the DL NDP from AP1. The client also listens to the relayed t2 and t3 from AP1 and the relayed t1 and t4 in the feedback from AP2. The differential distance between the client STA and AP1 vs. AP2 can now be calculated as follows: D_01 = [t6 t5 (t3 t2 + T_12)] * c Using T_01 = [(t4 t1) (t3 t2)]/2 We get D_01 = [t6 t5 (t3 t2 + 0.5*t4 0.5*t1 0.5*t3 + 0.5*t2)]*c Or finally: D_12 = [t6 t5 0.5*t3 + 0.5*t2 0.5*t4 + 0.5*t1]*c Note that the above expression for the differential distance D_12 does not depend on the ToF, T_12, between AP1 and AP2. Thus this method of calculating D_12 is insensitive to LOS obstructions between AP1 and AP2. Submission Slide 15 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 DToA Location Estimation Calculations Rij In two dimensions with 3 APs: AP1 AP2 Unknowns: Client coordinates x0,y0 2 unknowns t1 DTOF12 = t6 t5 0.5*t3 + 0.5*t2 0.5*t4 + 0.5*t1 t2 t4 t3 Client (x0,y0) t5 t6 R02(x0,y0) Equations: Differential ToF equations DToA12 = (R01-R02)/c DToA13 = (R01-R03)/c DToA23 = (R02-R03)/c 3 equations Solve for location, e.g. with Newton iterations described in following slides. (x3,y3) AP3 Submission Slide 16 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Solving of non-linear system of equations F = *x ( ) f - solve for x* Non linear system of equations: Use Newton s method for multiple variables: f = + = * ( ) i f x ( ) ( ) ( ) F f x f x f x x where Linearization: k k x j Over-determined non-linear system of equation to solve for x: + ( ) ( ) F f x f x x k k Least squares solution for iterative step: ( ) ) k 1 = = T T ( ) ( ) ( ) ( x x x f x f x f x F f x + 1 k k k k k Iterate according to: ( ) ) k 1 = + T T ( ) ( ) ( ) ( x x f x f x f x F f x + 1 k k k k k Submission 17 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Our derivatives To simplify the equations, measure time in light seconds - the distance light travels in one second. = = ( , ) DToA f x y R R 0 0 ij ij i j ( ) ( )2 ( ) ( )2 2 2 = + = + R x x y y R x x y y 0 0 j j j 0 0 i i i ( ) ( ) x y ( , ) ( , ) ( , ) ( , ) R x y R x y R x y R x y 0 0 0 0 0 0 0 0 i j i j = ( , ) f x y , 0 0 x y ij 0 0 x x x x y y x x y y 0 0 j j = 0 0 ( , ) i i f x y , 0 0 x y ij ( , ) ( , ) ( , ) ( , ) R x y R y R x y R y 0 0 0 0 0 0 0 0 i j i j Submission Slide 18 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Iterative solution for client position (x0,y0) Step calculation. LS solution to: x x x x x x x x y y y y 0 ( 1 y 0 ( 2 y 0 ( 1 y 0 ( 2 y ( ( ( ) ) ) , ) , x ) , ) , y ) R R R R DTOA R R 01 x 0 0 02 x 0 0 01 y 0 0 02 y 0 0 12 01 02 x x x x x x y 0 = 0 ( 1 y 0 ( 3 y 0 ( 1 y 0 ( 3 y DTOA R R 13 01 03 y , x ) , x ) , y ) , ) R R R R 0 01 x 0 0 03 x 0 0 01 y 0 0 03 y 0 0 DTOA R R x x x x x 23 02 03 0 ( 2 y 0 ( 3 y 0 ( 2 y 0 ( 3 y , ) , ) , ) , ) R R R R 02 0 0 03 0 0 02 0 0 03 0 0 Note: Time in units of light seconds Iterations: + ( ) 1 ( ) x k x k x 0 0 0 = + + ( ) 1 ( ) y k y k y 0 0 0 Submission 19 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Joint Clock Offsets and Client Location Estimation See [4,5 and 6] Submission Slide 20 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Joint Clock Offsets and Client Location and Estimation Calculations We are here using the CToA method [4,5 and 6] only to do joint AP clock offset and client position estimation. We are not modeling nor tracking any drift in the clocks. We are not using the Kalman filter approach for the calculations described in [4,5 and 6] here. Submission Slide 21 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Joint Clock Offsets and Client Location Estimation In two dimensions with 3 APs: Rij Unknowns: AP clock offsets and (w.r.t. client clock, i.e. =0) Client coordinates x,y 5 unknowns AP1 TOD1 AP2 TOA2 1 2 Client (x0,y0) R02(x0,y0) Equations: AP to AP propagations: TOAi i = TODj - j + Rij/c AP to client propagations: TOA0 = TODj - j + R0j(x,y)/c 9 equations TOA0 0= 0 Solve for location, e.g. with Newton iterations described in following slides. 3 (x3,y3) AP3 Submission Slide 22 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Solving of non-linear system of equations F = *x ( ) f - solve for x* Non linear system of equations: Use Newton s method for multiple variables: f = + = * ( ) i f x ( ) ( ) ( ) F f x f x f x x where Linearization: k k x j Over-determined non-linear system of equation to solve for x: + ( ) ( ) F f x f x x k k Least squares solution for iterative step: ( ) ) k 1 = = T T ( ) ( ) ( ) ( x x x f x f x f x F f x + 1 k k k k k Iterate according to: ( ) ) k 1 = + T T ( ) ( ) ( ) ( x x f x f x f x F f x + 1 k k k k k Submission 23 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Our derivatives To simplify the equations, measure time in light seconds - the distance light travels in one second. = , , , = + ( , ) TOA TOD f x y R 0 0 1 2 3 i j ij ij i j ( ) ( )2 2 = + R x x y y ij j i j i ( , ) ( , ) R x y R x y x x y y 1 0 0 1 0 0 0 1 0 1 ( , ) ( , ) x y R x y R x y ( , , , , ) 10 f x y v v v 0 0 1 x 0 0 1 y 0 0 0 0 1 2 3 x x ( , ) ( , ) R x y R x y x y = = 2 0 0 2 0 0 0 2 0 2 ( , , , , ) f x y v v v , 20 0 0 1 2 3 x y ( , ) ( , ) x y R y R y 0 0 0 0 2 x 0 0 2 y 0 0 ( , , , , ) f x y v v v ( , ) ( , ) R x y R x y x y 20 0 0 1 2 3 3 0 0 3 0 0 0 3 0 3 ( , ) ( , ) x y R x y R x y 0 0 3 0 0 3 0 0 = depending 1 ( , , , , ) on entry f x y v v v , , 0 0 1 2 3 v v v 1 2 3 Submission Slide 24 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 Iterative solution for client position (x0,y0) Step calculation. LS solution to: x x x x y y 0 ( 1 y 0 ( 1 y 1 0 0 ( ( ( ) ) ) , x ) , y ) R R TOA TOD R 01 x 0 0 01 y 0 0 0 1 01 1 x x TOA TOD R 0 ( 2 y 0 ( 2 y 0 1 0 0 2 02 2 , x ) , y ) R R R 02 x 0 0 02 y 0 0 TOA TOD R x x x 0 3 03 3 0 ( ( ( ( ( ( ) ) ) ) ) ) 0 ( 3 y 0 ( 3 y 0 0 1 + TOA TOD y , ) , ) R R 1 2 12 1 2 0 03 0 0 03 0 0 = + TOA TOD R 0 0 0 1 1 0 1 3 13 1 3 1 + TOA TOD R 0 0 0 1 1 2 1 21 2 1 2 + TOA TOD R 0 0 0 1 1 2 3 23 2 3 3 + TOA TOD R 1 0 0 1 1 3 1 31 3 1 + TOA TOD R 0 0 0 1 0 3 2 23 3 2 0 0 1 1 Note: Time in units of light seconds Iterations: + ( ) 1 ( ) v k v k v 1 1 1 + ( ) 1 ( ) x k x k x + = + 0 0 0 = + ( ) 1 ( ) v k v k v 2 2 2 + ( ) 1 ( ) y k y k y + 0 0 0 ( ) 1 ( ) v k v k v 3 3 3 Submission 25 Erik Lindskog (Qualcomm)
Nov 2017 doc.: IEEE 802.11-17/1758r0 References Submission Slide 26 Erik Lindskog (Qualcomm)
Erik Lindskog (Qualcomm) Slide 27 Nov 2017 doc.: IEEE 802.11-17/1758r0 References [1] Client Positioning using Timing Measurements between Access Points , Erik Lindskog, Naveen Kakani, Raja Banerjea, Jim Lansford and Jon Rosdahl, IEEE 802.11-13/0072r1. [2] A Low Overhead Receive Only Wi-Fi Based Location Mechanism , Erik Lindskog, Hong Wan, Raja Banerjea, Naveen Kakani and Dave Huntingford, Proceedings of the 27th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, Florida, September 2014, pp. 1661-1668. [3] Passive Location , Erik Lindskog, Naveen Kakani and Ali Raissinia, IEEE 802.11-17/0417r0. [4] Scalable Location Protocol , Erik Lindskog, Naveen Kakani and Ali Raissinia, IEEE 802.11- 17/0417r0. [5] High-Accuracy Indoor Geolocation using Collaborative Time of Arrival (CToA) - Whitepaper , Leor Banin, Ofer Bar Shalom, Nir Dvorecki, Yuval Amizur, IEEE 802.11-17/1387r0. [6] Collaborative Time of Arrival (CToA) , Ofer Bar Shalom, Yuval Amizur, Leor Bani, IEEE 802.11- 17/1308r0. [7] Scalable Location Performance , Erik Lindskog, Naveen Kakani and Ali Raissinia, IEEE 802.11- 17/1372r1. [8] CToA Protocol Analysis , Ofer-Bar Shalom, Yuval Amizur, Leor Banin and Nir Dvorecki, IEEE 802.11-17/1309r0. Submission
