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HUMAN AND SYSTEMS ENGINEERING:. Gentle Introduction to Particle Filtering. Sanjay Patil 1 and Ryan Irwin 2 Graduate research assistant 1 , REU undergrad 2 Human and Systems Engineering URL: /. Abstract. Particle Filtering:

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Human and systems engineering

Gentle Introduction to Particle Filtering

Sanjay Patil1 and Ryan Irwin2

Graduate research assistant1,

REU undergrad2

Human and Systems Engineering


  • Particle Filtering:

  • Most conventional techniques for speech analysis are based on modeling signals as Gaussian Mixture Models in Hidden Markov Model based systems.

  • To overcome the mismatched channel conditions, and/or significantly reduce the complexity of the models, Nonlinear approaches are expected to perform better than the conventional techniques.

  • Particle filters, based on sequential Monte Carlo methods, is one such nonlinear methods.

  • Particle filtering allows complete presentation of the posterior distribution of the states. Statistical estimates can be computed easily even in the presence of nonlinearities.

  • Nonlinear Methods – necessity

  • Drawing Samples from a Probability distribution. (introduce ‘Particle’)

  • Sequential Monte Carlo Methods – necessity, different names – bootstrap, condensation algorithm, survival of the fittest.

  • Steps in particle filtering (explaining the algorithm – block schematic)

  • Actual example – (along with all the steps)

  • Brief review and applications for tracking

  • As can be applied to Speaker Verification

  • Demo

  • Concept of samples and its weights

200 samples

  • Take p(x)=Gamma(4,1)

  • Generate some random samples

  • Plot basic approximation to pdf

  • Each sample is called as ‘Particle’

500 samples

5000 samples

  • Condensation Algorithm

  • Survival of the fittest

  • Different Names –

    • Sequential Monte Carlo filters

    • Bootstrap filters

General Problem Statement – Filtering – estimation of the states

  • 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

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 the prior of the state at time k ( without the information on measurement). Thus, it is the probability of the the state given only the previous measurements

  • Update stage:

    • This is posterior pdf from predicted prior pdf and newly available measurement.

  • Drawing samples

  • Predicting next state

  • Updating this state

  • What is THIS STEP???

  • Resampling….

  • All the applications are mostly tracking applications in different forms….

  • 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

  • What is the application for IES NSF funded project –

  • Time series estimation for speech signal (Java demo)

  • Speaker Verification (details on next slide)

  • 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

  • Different data sets need to be differentiated without looking at all the data samples

  • Classifications 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

  • Toroidals are not classified very successfully 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 input signals are now time based with the x-axis representing time

  • All the signal tracking algorithms are implemented with interpolated data

  • The interpolation ensures that the input samples are at regular intervals

  • Sampling is always done on regular intervals

  • The linear prediction algorithm is a linear way to predict signals with no noise

  • The Kalman filter and particle filter are based on prediction of the states of the signal

  • States are related to the observations through the state equation

  • The particle filtering algorithm introduces process and measurement noise

  • At each iteration possible states are given by the black points

  • The average of the black points is where the overall state is predicted to be

  • 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.