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1 importance sampling and particle filtering.
| Content Provider | CiteSeerX |
|---|---|
| Author | Vaswani, Namrata Problem, I. |
| Abstract | Given a nonlinear state space model, satisfying the Hidden Markov Model (HMM) assumptions: 1) State sequence, Xt, t = 0, 1, 2,.. is a Markov process, i.e. p(xt xt−1, past) = p(xt xt−1). 2) Observations, Yt, t = 1, 2,.. “conditionally independent given state at t”, i.e. p(yt xt, past, future) = p(yt xt) where past � {Y1:t−1, X1:t−1}, future � {Yt+1:T,Xt+1:T}. 3) p(x0), p(xt xt−1), p(yt xt) are known: often expressed using a system and observation model format. B. Goal 1) Denote x0:t = {x0, x1,..xt} and y1:t = {y1, y2,..yt} 2) Find a good approximation to p(x0:t y1:t) or at least to p(xt y1:t) referred to as the posterior. Goal is to estimate I(ft) = ft(xt)p(xt y1:t)dxt (1) for any function of the state ft C. Some Other Techniques 1) If the state space model were linear and Gaussian, then p(xt y1:t) is also Gaussian and its mean and variance are calculated using the Kalman filter. 2) Nonlinear and Gaussian: Extended Kalman Filter (EKF), Gaussian sum filter. Problem: use first or second order Taylor series approximation to original nonlinear system, error in Jacobian estimates propagates over time, may be unstable in certain cases (error keeps increasing): loss of track. If one bad observation: loss of track, cannot come back Cannot track heavily non-Gaussian or multimodal posteriors2 |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Xt Y1 Xt Xt Importance Sampling Particle Filtering Yt Xt Second Order Taylor Series Approximation Gaussian Sum Filter State Ft Multimodal Posteriors2 Jacobian Estimate Observation Model Format Original Nonlinear System State Sequence State Space Model Nonlinear State Space Model Bad Observation Cannot Track Markov Process Good Approximation Hidden Markov Model Kalman Filter Extended Kalman Filter Denote X0 Past Y1 Certain Case |
| Content Type | Text |
