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The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in the particle filter algorithm as the number of particles gets large. After a decomposition of the error into two terms, we show that the difference between the estimator and the conditional mean is asymptotically normal when the resampling is done at every step in the filtering process. Two nonlinear/non-Gaussian examples are tested to verify this conclusion.
This paper is concerned with the convergence and long-term stability analysis of the feedback particle filter (FPF) algorithm. The FPF is an interacting system of $N$ particles where the interaction is designed such that the empirical distribution of
We consider situations where the applicability of sequential Monte Carlo particle filters is compromised due to the expensive evaluation of the particle weights. To alleviate this problem, we propose a new particle filter algorithm based on the multi
This article considers the problem of storing the paths generated by a particle filter and more generally by a sequential Monte Carlo algorithm. It provides a theoretical result bounding the expected memory cost by $T + C N log N$ where $T$ is the ti
Particle filters are a powerful and flexible tool for performing inference on state-space models. They involve a collection of samples evolving over time through a combination of sampling and re-sampling steps. The re-sampling step is necessary to en
Parameter estimation in multidimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, the membrane potential evolution in single neurons