national taiwan university graduate institute of electronics engineering national taiwan university...

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?



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)



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



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



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



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.



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



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.



ScheduleSchedule

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