september, 2005 doc: ieee 15-05-0524-00-004a qi, li, umeda, hara and kohno (nict) slidetg4a1...

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September, 2005 Doc: IEEE 15-05-0524-00-004a

Qi, Li, Umeda, Hara and Kohno (NICT) Slide 1

Project: IEEE P802.15 Working Group for Wireless Personal Area Networks Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs)(WPANs)

Submission Title: [Three ranging-related schemes]Date Submitted: [September, 2005]Source: [Yihong Qi, Huan-Bang Li, Masataka Umeda, Shinsuke Hara and Ryuji Kohno,

Company: National Institute of Information and Communications Technology ]Contact: Yihong Qi Voice:+81 46 847 5092, E-Mail: [email protected]]Abstract: [Three ranging-related schemes are presented: 1. for the problem that the first

arriving signals are often weak and NLOS, positioning using mulitpath delays will improve the accuracy. 2. a reduced dimensional approach is proposed for the bad GDOP problem. 3. a coherent delay estimation scheme is devised which works well with low sampling rate and feasible ADC implementation.]

Purpose: [to discuss three ranging-related schemes ]Notice: This document has been prepared to assist the IEEE P802.15. It is offered

as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein.

Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15.

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Outline Positioning using multipath delays (cf. first arrival

detection) Positioning in an ill-conditioned geometry (bad

GDOP (geometric dilution of precision)) A coherent delay estimation scheme with low

sampling rate Conclusions

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Two Positioning Schemes

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Current/conventional schemes

Ranging: first arrival detection

Positioning: based on multiple range estimates triangulation weighted least square (LS) methods

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What are problems with the current schemes?

Positioning accuracy will be degraded due to

Weak first arriving signals, e.g., 6dB lower than the strongest path.

NLOS first arriving signals Bad GDOP (geometric dilution of precision)

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Positioning using multipath delays

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Motivation

The second and later arriving signals also carry information on the position of interest. cf. weak and/or NLOS first arriving signals

Positioning using both Multipath delays Their statistic information (e.g., mean,

variance)

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Two numerical examples based on analytical results

For illustration purpose, some simplifying assumptions on multipath delays:

Exponential or equal gain models The minimum delay resolution being the inverse

of chip duration Gaussian NLOS delay variables

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Numerical example 1

Positioning accuracy vs. num of multipath

Equal gain

Exponential gain with -6dB

Exponential gain with -3dB

Observation: use of more strong multipaths can improve the positioning accuracy

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Numerical example 2

For a fair comparison:

Using• fixed total energy;• relative accuracy

improvement, compared with the conventional method using only the first arrivals

Three types of system channels

1

2

3

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Numerical example 2 (cont’d)

relative accuracy improvement vs. standard deviation of NLOS delays

Observation: using more multipaths is especially effective for accuracy improvement in wideband systems

1MHz

100MHz

5MHz

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A reduced-dimensional method for bad GDOP (geometric dilution

of precision) cases

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What is the bad GDOP?

Good GDOP case: nodes are distributed evenly

a2

a3

a1

p

Mobile node

a2a3a1

p

Mobile node

Bad GDOP case: all nodes are lined up

The error is small.

The error is large.

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What is the problem?

a2

a3

a1

p

m

Bad dim: x Good dim: y

Two dimensional positioning

estimation (x,y) vs.

an essentially one-dimensional

problem (y axis only)

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A reduced dimension approach

1. Find the good dim(s)

2. Perform a regular positioning in the good dimension

3. Estimate the coordinate in the bad dim(s) separately

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A simulation result for 2-D bad GDOP

Conventional method

Reduced dimensional method

Theoretical limit

Positioning accuracy vs. standard deviation of ranging errors

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Flashback

Positioning using multipath delays For the problem of weak and/or NLOS first

arriving signals Con: increased computation complexity

A reduced-dimensional approach for positioning For bad GDOP geometry

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Coherent delay estimation with low sampling rate and feasible ADC

implementation

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Correlator A/D

Delay estimation/First-arrival detection

A delay estimate

)(tr

)(tsA transmit signal

A basic system model

)(tc

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Two ways of implementing ADC

LO

LPF

LPF

code-correlator

code-correlator

BPF

π/2

ADC

ADC

outputMatched toGaussian pulse

Spreadingcode

Difficult to implement

easy to implement

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What is the problem?

tm+1tn

h(tn)

h(tm)

h(tm+1)

h(tm+Z-1)

tm+2 tm+Z

Given samples of a correlation function, how to estimate the time instant corresponding to the peak?

?̂correlation function

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What is information we know?

tm+1tn

tm+2 tm+Z

correlation

autocorrelation

correlation = autocorrelation of s(t) +noise

The expression is known. Statistics is known.

correlation function

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A natural way to use all information

Formulate maximum likelihood estimation (ML).

However, it is complicated: One dimension iterative searching Nonlinear autocorrelation function involved Lots of samples (N) involved

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Our approach: simplified MLE

tm+1 tn

h(tn)

h(tm)

h(tm+1)

h(tm+Z-1)

tm+2 tm+Z

Intuition: samples near the peak are more important.

• Use less samples

• Taylor expansion of autocorrelation function around the peak

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A simple solution

,)(1

)(ˆ

333

333

thW

thWt

T

T

.function ation autocorrel theis )( ,

)0()()2(

)()0()(

)2()()0(

samples ,))()()(()(

instants; time,)(

1

3

213

213

g

gTgTg

TggTg

TgTgg

tctctc

tttT

mmm

Tmmm

W

tc

t

where

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A simple solution

• An algebraic solution, no iterative search• Less than 4 samples in general• No nonlinear function any more• Independent of noise level • Optimal in the sense that the estimate is approaching to the theoretical lower limit as over-sampling is sufficiently large.

,)(1

)(ˆ

333

333

thW

thWt

T

T

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Simulation parameters

• PRF=30.875MHz• Sampling rate fs (ADC)=494MHz (=16xPRF)• Ternary sequence with length of 31• Gaussian Pulse with bandwidth 500MHz• AWGN Channel

Conventional method: Pick up the largest sampleInterpolation method: Not include the autocorrelation info. .

)(1

)(ˆ

33

33

th

tht

T

T

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Simulation result 1R

MS

Est

imat

ion

Err

or [

nsec

]

Eb/N0 [dB]

ADC after Code Correlator

ADC before Code Correlator Conventional method

Simplified ML

Interpolation

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Simulation result 2

Eb/N0=-3dB

Conventional method

Interpolation

Simplified ML

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Advantages Working well at low sampling rate (less than signal

bandwidth) Feasible ADC implementation Low computation complexity

Same level of complexity compared with conventional schemes Independent of noise level

Ongoing work: incorporating decay patterns for multipath scenarios

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Conclusions

Positioning using multipath delays A reduced dimensional approach for

positioning in bad GDOP A coherent delay estimation scheme with

low sampling rate and feasible ADC implemetation

september, 2005 doc: ieee 15-05-0524-00-004a qi, li, umeda, hara and kohno (nict) slidetg4a1...

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