1. National Taiwan University Graduate Institute of Electronics Engineering National Taiwan University Graduate Institute of Electronics Engineering A CCESS IC L ABORTORY Under-Graduate Project Particle Filter for Indoor Location Tracking Presenter: Chihhao Chao ( 趙之昊 ) Advisor: Prof. An-Yeu Wu 2007.03.07 Wednesday

2. Graduate Institute of Electronics Engineering, NTU P2 Chihhao Chao ( 趙之昊 ) What is Indoor Location / Tracking?

3. Graduate Institute of Electronics Engineering, NTU P3 Chihhao Chao ( 趙之昊 ) 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)

4. Graduate Institute of Electronics Engineering, NTU P4 Chihhao Chao ( 趙之昊 ) Linear / Nonlinear Models LinearNonlinear Motion model X t = A t-1  t X t-1 + B t-1  t U t-1 X t = f t-1  t (X t-1,U t-1 ) Sensor model Z t = C t X t + D t V t Z t = g t (X t,V t ) motion model sensor model ZtZt Z t-1 XtXt X t-1 X: Random variable for hidden states Z: Random variable for observed states U, V: Noise t: time

5. Graduate Institute of Electronics Engineering, NTU P5 Chihhao Chao ( 趙之昊 ) Real Location / Tracking Case sensor t Observed signal 1 t Observed signal 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

6. Graduate Institute of Electronics Engineering, NTU P6 Chihhao Chao ( 趙之昊 ) 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 (equal when ) set of n particles X t True Signal Linear Filter Particle Filter

7. Graduate Institute of Electronics Engineering, NTU P7 Chihhao Chao ( 趙之昊 ) Particle Filter Basic Concept Day 1Day 2Day 3Day 4 GuessObserve Day1NA2 Day221 Day3Not sure... 2 Day421 Day51 The guess is based on previous observations.

8. Graduate Institute of Electronics Engineering, NTU P8 Chihhao Chao ( 趙之昊 ) Particle Filter: Bayesian Filtering Two phases: 1. Prediction Phase (calculate Prior Density) 2. Measurement Phase (measure and normalize  calculate Posterior Density) Iteration t Iteration t+1 Posterior Density at t-1 Prior Density at t Posterior Density at t+1 Posterior Confidence Region Prior Confidence Region Posterior Density at t

9. Graduate Institute of Electronics Engineering, NTU P9 Chihhao Chao ( 趙之昊 ) Suggested Background Programming language (required) C / C++ / Matlab Signal & System (suggested) Probability & Statistics (suggested) 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.

10. Graduate Institute of Electronics Engineering, NTU P10 Chihhao Chao ( 趙之昊 ) Schedule