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Broadband Systems Laboratory

Advisor : Prof. Chin-Liang  Wang

Presented by Yih-Shyh Chiou

September 4, 2006

後 卓 越 計 畫 進 度 報 告

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Why Tracking and Prediction Are Needed in an Indoor Location Estimator (1/2)

• Assume that at time t=t1 two people are detected at ranges R1 and R2; on the next sample at time t=t1+T, again two people are detected– The question arises as to whether these two people detected

on the second sample are the same two people or two new people

RR2

R1

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Why Tracking and Prediction Are Needed in an Indoor Location Estimator (2/2)

1 0; # 1t t n

#1 #21The first sample, t t

• On the nth sample, the people predicted and measured position, and , respectively nynx

1 ( / sec)nx a m

R=R1 R=R2

1The second sample, t t T

#1 #2

ny

; #t T n

1n nx x aT

The prediction window

The distance further away

sampling time = T

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g-h Filter

1, , 1 , 1

1, , 1 1, , 1

* * *

* * * *

( )

( )

n n n n n n

n n n n n n n n

nn

n n

hx x y x

T

x x Tx g y x

• The present velocity and position g-h track update (filtering) equations:

• The g-h transition equations or prediction equations:

• The prediction update equations of the g-h filter

1, , 1, , 1,

* * * * *, n n n n n n n n n nx x x x Tx

, 1

, , 1 , , 1 , 1

*

* * * * *( ), ( ) n n

n n n n n n n n n n

n

n n n

y xx x h x x g y x

T

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,

ˆ ˆ,

predicted position, velocity

updated position, velocity

measured positionn

x v

x v

y

1 ˆ ˆ

ˆn n n

n n

T

x x v

v v

1

ˆ

( )ˆ ˆ

n n n

n nn n T

x x y x

y xv v

Prediction step

Updating stepˆ ˆ,x v

,x v

ˆ ˆ,new x v

ny

and are tuning constantsbetween 0 and 1

: Measurement has no effect: History has no effect

Filter-

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Properties

• Properties of the g-h tracking filter– Steady-state performance for constant-velocity target– Steady-state response for target with constant acceleration– Tracking errors due to random range measurement error

• To obtain the filter, we can take g-h filter and replace g with and h with

• The tracker is a low-pass filter used to smooth out the effects of measurement noise

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