# Path Storage in the Particle Filter

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 $T+CN\log N$ 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.

### Citation

P.E. Jacob, L.M. Murray and S. Rubenthaler (2015). Path Storage in the Particle Filter. *Statistics and Computing*. **25**(2):487--496. [doi] [online]

```
@Article{Jacob2015,
title = {Path storage in the particle filter},
author = {Pierre E. Jacob and Lawrence M. Murray and Sylvain Rubenthaler},
journal = {Statistics and Computing},
year = {2015},
volume = {25},
number = {2},
pages = {487--496},
doi = {10.1007/s11222-013-9445-x}, url = {http://arxiv.org/abs/1307.3180}
}
```