HUMAN AND SYSTEMS ENGINEERING:

1. HUMAN AND SYSTEMS ENGINEERING: Introduction to Particle Filtering Sanjay Patil and Ryan Irwin Intelligent Electronics Systems, Human and Systems Engineering Center for Advanced Vehicular Systems URL: www.cavs.msstate.edu/hse/ies/publications/seminars/msstate/2005/particle_filtering/

2. Abstract • The conventional techniques in speech recognition applications • models speech as Gaussian mixtures • performs below average under noisy condition ( performance VALUES) • are linear modeling techniques • Nonlinear techniques • can model speech as a time-varying and non-stationary signal • can help model the noisy conditions • can compensate for mismatched channel conditions • Particle filtering (topic of today’s seminar) • is one such nonlinear method • is based on sequential Monte Carlo technique • works by approximating the probability distribution • Research world-over desires to have a comprehensive modelfor speech so as to make turn application of speech more viable for real-life scenario. Particle filter may give us this chance.

3. Analogy – concept of hidden state and observations • You are talking with a person and you are aim to understand what is his/her mind. • Observations : facial expression • What are we looking for : intentions • What do we have : • initial notion of how the person is going to be • idea of how what intentions follow the previous one • idea of how observations (conversion) is related to the previous observed intentions After getting first observation and the previous intention, the next intention is estimated, Then on second observation, the next intention is estimated, In this way, the cycle continues, till the last observation.

4. 200 samples 5000 samples 500 samples • Drawing samples to represent a probability distribution function • Concept of particles and their weights • Consider a some pdf p(x) • Generate some random samples • Conclusion • More the number of samples better is the distribution function represented. • The number of samples drawn at a particular probability represent the weight (contribution) by those samples towards the distribution function • The contribution is called as the weight of the sample. • Each sample is called as ‘Particle’ weight

5. Particle filtering algorithm • Condensation Algorithm • Survival of the fittest • Different Names • Sequential Monte Carlo filters • Bootstrap filters Problem Statement • Tracking the state (parameters or hidden variables) as it evolves over time • Sequentially arriving (noisy and non-Gaussian) observations • Idea is to have best possible estimate of hidden variables

6. Particle filtering algorithm continued General two-stage framework (Prediction-Update stages) • Assume that pdf p(xk-1 | y1:k-1) is available at time k -1. • Prediction stage: • This is a priori of the state at time k ( without the information on measurement). Thus, it is the probability of the state given only the previous measurements • Update stage: • This is posterior pdf from predicted prior pdf and newly available measurement.

7. Particle filtering algorithm step-by-step (1) Initial set-up: No observations available Known parameters – x0, p(x0), p(xk|xk-1), p(yk|xk), noise statistics Draw samples to represent x0 by its distribution p(x0) time Measurements / Observations States (unknown / hidden) cannot be measured

8. Particle filtering algorithm step-by-step (2) Known parameters – x0, p(x0), p(xk|xk-1), p(yk|xk), noise statistics Still no observations or measurements are available. Predict x1 using equation time Measurements / Observations States (unknown / hidden) cannot be measured

9. Particle filtering algorithm step-by-step (3) Known parameters – x0, p(x0), p(xk|xk-1), p(yk|xk), noise statistics First observation / measurement is available. Update x1 using equation time Measurements / Observations States (unknown / hidden) cannot be measured

10. Particle filtering algorithm step-by-step (4) Known parameters – x0, p(x0), p(xk|xk-1), p(yk|xk), noise statistics Second observation / measurement is NOT available. Predict x2 using equation time Measurements / Observations States (unknown / hidden) cannot be measured

11. Particle filtering algorithm step-by-step (5) Known parameters – x0, p(x0), p(xk|xk-1), p(yk|xk), noise statistics Second observation / measurement is available. update x2 using equation time Measurements / Observations States (unknown / hidden) cannot be measured

12. time Measurements / Observations States (unknown / hidden) cannot be measured • Particle filtering algorithm step-by-step (6) Known parameters – x0, p(x0), p(xk|xk-1), p(yk|xk), noise statistics kth observation / measurement is available. Predict and Update xk using equation

13. Particle filtering - visualization • Drawing samples • Predicting next state • Updating this state • What is THIS STEP??? • Resampling….

14. Applications • Most of the applications involve tracking • Visual Tracking – e.g. human motion (body parts) • Prediction of (financial) time series – e.g. mapping gold price, stocks • Quality control in semiconductor industry • Military applications • Target recognition from single or multiple images • Guidance of missiles • For IES NSF funded project, particle filtering has been used for: • Time series estimation for speech signal (Java demo) • Speaker Verification (details on next slide)

15. Speaker Verification • Time series estimation of speech signal • Speaker Verification: • Hypothesis: particle filters approximate the probability distribution of a signal. If large number of particles are used, it approximates the pdf better. Only needed is the initial guess of the distribution. • ! How are we going to achieve this..

16. Pattern Recognition Applet • Java applet that gives a visual of algorithms implemented at IES • Classification of Signals • PCA - Principle Component Analysis • LDA - Linear Discrimination Analysis • SVM - Support Vector Machines • RVM - Relevance Vector Machines • Tracking of Signals • LP - Linear Prediction • KF - Kalman Filtering • PF – Particle Filtering URL: http://www.cavs.msstate.edu/hse/ies/projects/speech/software/demonstrations/applets/util/pattern_recognition/current/index.html

17. Classification – Best Case • Data sets need to be differentiated • Classifying distinguishes between sets of data without the samples • Algorithms separate data sets with a line of discrimination • To have zero error the line of discrimination should completely separate the classes • These patterns are easy to classify

18. Classification – Worst Case • Toroidals are not classified easily with a straight line • Error should be around 50% because half of each class is separated • A proper line of discrimination of a toroidal would be a circle enclosing only the inside set • The toroidal is not common in speech patterns

19. Classification – Realistic Case • A more realistic case of two mixed distributions using RVM • This algorithm gives a more complex line of discrimination • More involved computation for RVM yields better results than LDA and PCA • Again, LDA, PCA, SVM, and RVM are pattern classification algorithms • More information given online in tutorials about algorithms

20. Signal Tracking – Kalman Filter • The input signals are now time based with the x-axis representing time • Signal tracking algorithms interpolate data • Interpolation ensures that the input samples are at regular intervals • Sampling is always done on regular intervals • Kalman filter is shown here

21. Signal Tracking – Particle Filter • Algorithm has realistic noise • Gaussian noise is actually generated at each step • Noise variances and number of particles can be customized • Algorithm runs as previously described • State prediction stage • State update stage • Average of the black particles is where the overall state is predicted

22. Summary • Particle filtering promises to be one of the nonlinear techniques. • More points to follow

23. References • S. Haykin and E. Moulines, "From Kalman to Particle Filters," IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, Pennsylvania, USA, March 2005. • M.W. Andrews, "Learning And Inference In Nonlinear State-Space Models," Gatsby Unit for Computational Neuroscience, University College, London, U.K., December 2004. • P.M. Djuric, J.H. Kotecha, J. Zhang, Y. Huang, T. Ghirmai, M. Bugallo, and J. Miguez, "Particle Filtering," IEEE Magazine on Signal Processing, vol 20, no 5, pp. 19-38, September 2003. • N. Arulampalam, S. Maskell, N. Gordan, and T. Clapp, "Tutorial On Particle Filters For Online Nonlinear/ Non-Gaussian Bayesian Tracking," IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174-188, February 2002. • R. van der Merve, N. de Freitas, A. Doucet, and E. Wan, "The Unscented Particle Filter," Technical Report CUED/F-INFENG/TR 380, Cambridge University Engineering Department, Cambridge University, U.K., August 2000. • S. Gannot, and M. Moonen, "On The Application Of The Unscented Kalman Filter To Speech Processing," International Workshop on Acoustic Echo and Noise, Kyoto, Japan, pp 27-30, September 2003. • J.P. Norton, and G.V. Veres, "Improvement Of The Particle Filter By Better Choice Of The Predicted Sample Set," 15th IFAC Triennial World Congress, Barcelona, Spain, July 2002. • J. Vermaak, C. Andrieu, A. Doucet, and S.J. Godsill, "Particle Methods For Bayesian Modeling And Enhancement Of Speech Signals," IEEE Transaction on Speech and Audio Processing, vol 10, no. 3, pp 173-185, March 2002.