by **N. Chopin, J. Ridgway, M. Gerber & O. Papaspiliopoulos**

SMC^{2} is an efficient algorithm for sequential estimation and state inference of state-space models. It generates N_{θ} parameter particles θ^{m}, and, for each θ^{m}, it runs a particle filter of size N_{x} (i.e. at each time step, N_{x} particles are generated in the state space **). We discuss how to automatically calibrate N_{x} in the course of the algorithm. Our approach relies on conditional Sequential Monte Carlo updates, monitoring the state of the pseudo random number generator and on an estimator of the variance of the unbiased estimate of the likelihood that is produced by the particle filters, which is obtained using nonparametric regression techniques. We observe that our approach is both less CPU intensive and with smaller Monte Carlo errors than the initial version of SMC^{2}.