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National Taiwan UniversityGraduate Institute of Electronics Engineering
National Taiwan UniversityGraduate Institute of Electronics Engineering
ACCESS IC LABORTORY
Under-Graduate ProjectUnder-Graduate ProjectParticle Filter for Indoor Location TrackingParticle Filter for Indoor Location Tracking
Presenter: Chihhao Chao (趙之昊 )
Advisor: Prof. An-Yeu Wu
2007.03.07 Wednesday
Graduate Institute of Electronics Engineering, NTU
P2Chihhao Chao (趙之昊 )
What is Indoor Location / Tracking?What is Indoor Location / Tracking?
Graduate Institute of Electronics Engineering, NTU
P3Chihhao Chao (趙之昊 )
Hidden Markov Model (HMM)Hidden Markov Model (HMM)
x(t) — the hidden state at time t
y(t) — the observation at time t
— dependency
motion model
sensor model
The dynamic system is simply modeled by HMM.
Note:
Motion and Sensor models are effected by noise.
Our goal :
Accurately estimate the hidden states from the observations.
Tracking Target
Sensor (Photographer)
Graduate Institute of Electronics Engineering, NTU
P4Chihhao Chao (趙之昊 )
Linear / Nonlinear ModelsLinear / Nonlinear Models
Linear Nonlinear
Motion model Xt = At-1t Xt-1 + Bt-1tUt-1 Xt = ft-1t (Xt-1,Ut-1)
Sensor model Zt = CtXt + DtVt Zt = gt(Xt,Vt)
motion model
sensor model
ZtZt-1
XtXt-1X: Random variable for hidden states
Z: Random variable for observed states
U, V: Noise
t: time
Graduate Institute of Electronics Engineering, NTU
P5Chihhao Chao (趙之昊 )
Real Location / Tracking CaseReal Location / Tracking Case
sensor t
Obs
erve
d si
gnal
1
t
Obs
erve
d si
gnal
2 Particle Filter
t
Estimation
Tracking the target in a noisy environment Measurement is not reliable Poor accuracy, w/o Bayesian filters
Particle filter
Exact Value
Probability Density Function
Exact Value
Graduate Institute of Electronics Engineering, NTU
P6Chihhao Chao (趙之昊 )
What is Particle Filters?What is Particle Filters? A powerful, state-of-the-art mathematic tool
used in localization, tracking, computer vision, machine learning... fields.
A kind of Bayesian filter
)(xp
tx
)|()( ...1 tttt zxpXxp (equal when )n
set of n particles Xt
True Signal
Linear Filter
Particle Filter
Graduate Institute of Electronics Engineering, NTU
P7Chihhao Chao (趙之昊 )
Particle Filter Basic ConceptParticle Filter Basic Concept
Day 1Day 2Day 3Day 4
Guess Observe
Day1 NA 2
Day2 2 1
Day3 Not sure...
2
Day4 2 1
Day5 1The guess is based on previous observations.
Graduate Institute of Electronics Engineering, NTU
P8Chihhao Chao (趙之昊 )
Particle Filter: Bayesian FilteringParticle Filter: Bayesian Filtering
Two phases:1. Prediction Phase
(calculate Prior Density)
2. Measurement Phase (measure and normalize calculate Posterior Density)
Iteration tIteration t+1
Posterior Density at t-1
Prior Density at t
Posterior Density at t+1
Posterior Confidence RegionPrior
Confidence Region
Posterior Density at t
Graduate Institute of Electronics Engineering, NTU
P9Chihhao Chao (趙之昊 )
Suggested BackgroundSuggested Background Programming language (required)
C / C++ / Matlab
Signal & System (suggested) Probability & Statistics (suggested)
What You Will Learn?What You Will Learn? Reinforce what you learned in programming, signal & systems,
and probability & statistics
Basic algorithms for location / tracking application
The ability to repeat experiments in papers/books.
Graduate Institute of Electronics Engineering, NTU
P10Chihhao Chao (趙之昊 )
ScheduleSchedule