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Lab 4: Particle filter

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Universit´e Grenoble Alpes and ENSIMAG Master SIAM

Stochastic modelling for neurosciences

Lab 4: Particle filter

Objectives: Implementing a particle filter.

Let us consider a discretized auto-regressive model forj= 0, . . . , n, Xj+1=φXj+Uj

withUj ∼ N(0, τ2) and where the observation is

Vj =Xj+ηj

withηj ∼ N(0, σ2).

1. Simulaten= 100 observations withφ= 0.9,τ2= 0.1,σ2= 1 starting withX0=−10.

We want to filter X1:n from the observations V1:n.

2. Implement the particle filter using the transition density as proposal distribution, with K = 100,500,1000,2000 particles. Sample one filter trajectory and compare to the true simulatedX. 3. Implement the particle filter with the optimal proposal equal, at timej

N

τ2σ2 τ2+σ2

φXj−1

τ2 +Vj

σ2

, τ2σ2 τ2+σ2

Références

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