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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 time horizon, $N$ is the number of particles and $C$ is a constant, as well as an efficient algorithm to realise this. The theoretical result and the algorithm are illustrated with numerical experiments.
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
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
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
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this algorithm c
Recurrent neural networks (RNNs) have been extraordinarily successful for prediction with sequential data. To tackle highly variable and noisy real-world data, we introduce Particle Filter Recurrent Neural Networks (PF-RNNs), a new RNN family that ex