1. Submission Title: [Three ranging-related schemes]
Project: IEEE P Working Group for Wireless Personal Area Networks (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: ,
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 P 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.
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2. Three Ranging-related Schemes
Yihong Qi, Huan-bang Li, Masataka Umeda, Shinsuke Hara and Ryuji Kohno
NICT, JAPAN
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3. Outline
Positioning using multipath delays (cf. the current first arrival detection)
Positioning in an ill-conditioned geometry (the bad GDOP problem)
A coherent delay estimation scheme with low sampling rate
Conclusions
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4. Two Positioning Schemes
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5. Current/conventional schemes
Ranging: first arrival detection with LOS (line-of-sight) assumption
Positioning: based on multiple ranging estimates
triangulation
weighted least square (LS) methods
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6. 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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7. Positioning using multipath delays
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8. Motivation An NLOS delay estimate:
dtotal = d0 (real distance) + lnlos (NLOS induced path length error) + n (estimation error)
The second and later arriving signals also carry information on the distance of interest.
An NLOS delay estimate
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9. Analytical results Positioning accuracy is improved by using
Multipath delay estimates
It is sufficient to adopt those strong multipaths.
Statistic information of lnlos (e.g., mean, variance)
No accuracy improvement without incorporating the statistic information.
E.g., the maximum a priori (MAP) estimator
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10. 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 the chip duration
The NLOS induced path length error being independent Gaussian variables
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11. Numerical example 1 Positioning error 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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12. Numerical example 2 1 2 3 Three types of system channels
For a fair comparison:
Using
fixed total energy;
relative accuracy improvement, compared with the conventional method using only the first arrivals 2 3
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13. Numerical example 2 (cont’d)
relative accuracy improvement vs.
standard deviation of NLOS induced error
100MHz
Observation:
using more multipaths is especially effective for accuracy improvement in wideband systems
5MHz
1MHz
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14. Flashback Positioning using multipath delays
Sufficient to use the strong multipath
Good for wideband systems
Tradeoff:
accuracy improvement
computation complexity
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15. A reduced-dimensional method for the bad GDOP problem
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16. What is the bad GDOP? Good GDOP case: nodes are distributed evenly
The error is small.
The error is large.
Mobile node
Mobile node a2 a1 a3 a1 a2 a3
Good GDOP case: nodes are distributed evenly
Bad GDOP case: all nodes are lined up
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17. What is the core problem?
Two dimensional positioning estimation (x,y) vs.
an essentially one-dimensional problem
(y axis only) m a3 a1 a2
Bad dim: x
Good dim: y
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18. A reduced dimension approach
Find the good dim(s)
Perform a regular positioning in the good dimension
Estimate the coordinate(s) in the bad dim(s) separately
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19. A simulation result for 2-D bad GDOP
Positioning error vs. standard deviation of ranging errors
Conventional method
Reduced dimensional method
Theoretical limit
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20. Flashback Positioning using multipath delays
For the problem of weak and/or NLOS first arriving signals
Con: increased computation complexity
A reduced-dimensional approach to the bad GDOP positioning
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21. Coherent delay estimation with low sampling rate and feasible ADC implementation
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22. A Review of 406r0
Two issues
Main part: Delay estimation with mitigation of sampling induced errors
Extension: a first arrival detection scheme based on the sequential cancellation principle
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23. First-arrival detection
A basic system model
Delay estimation/
First-arrival detection
Correlator
A/D
A delay estimate
A transmit signal
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24. Two ways of implementing ADC
easy to implement
Difficult to implement
code- correlator
LPF
ADC
Matched to
Gaussian pulse
BPF
Spreading
code
output
code- correlator
LPF
ADC LO
π/2
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25. What is the problem?
h(tn)
correlation function
h(tm+1)
h(tm+Z-1)
h(tm)
tm+1
tm+2
tm+Z tn
Given samples of a correlation function, how to estimate the time instant corresponding to the peak?
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26. What is information we know?
correlation function
tm+1 tn
tm+2
tm+Z
correlation
autocorrelation
correlation = autocorrelation of s(t) +noise
The expression is known.
Statistics is known.
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27. A natural way to organize 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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28. Our approach: simplified MLE
Intuition:
samples near the peak are more important.
h(tn)
h(tm+1)
h(tm+Z-1)
h(tm) 
Use less samples
Taylor expansion of autocorrelation function around the peak
tm+1
tm+2
tm+Z tn
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29. A simple solution
where
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30. 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.
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31. 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 sample
Interpolation method:
Not include the autocorrelation info.
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32. Simulation result 1 ADC before Code Correlator Conventional method
RMS Estimation Error [nsec]
Interpolation
Simplified ML
ADC after Code Correlator
Eb/N0 [dB]
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33. Simulation result 2 Eb/N0=-3dB Conventional method Interpolation
Simplified ML
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34. Advantages
Working well at low sampling rate (less than twice of the signal bandwidth)
Feasible ADC implementation
Low computation complexity
Same level of complexity compared with conventional schemes
Independent of noise level
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35. Some questions from 406r0
Performance in a multipath environment (ongoing work)
Relate to the decay pattern of the multipaths in a cluster, specifically, its bandwidth vs. the bandwidth of the UWB signal
Accommodate the multipath information by modifying
Signal autocorrelation function
Noise statistics
Fix point calculation of ADC
The quantization error being approximated by a random variable of uniform distribution
Noise statistics is modified to incorporate such errors
Similar performance is observed
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36. 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 implementation
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