This paper analyzes the particle filter approach to filtering time series, highlighting its limitations and proposing improvements. The authors argue that the particle filter is not robust to outliers due to its reliance on discrete support for representing the prior distribution and the design of the simulators. They introduce an auxiliary particle filter method that addresses these issues, offering greater efficiency and flexibility. The auxiliary particle filter uses an additional variable to improve the simulation process, allowing for more accurate estimation of the filtering density. The paper also discusses the use of stratification in particle filters to perform Bayesian inference on model parameters and maximum likelihood estimation. The methods are illustrated using a stochastic volatility model and a time series model of angles. The authors conclude that the auxiliary particle filter provides a more robust and efficient approach to filtering, particularly in the presence of outliers.This paper analyzes the particle filter approach to filtering time series, highlighting its limitations and proposing improvements. The authors argue that the particle filter is not robust to outliers due to its reliance on discrete support for representing the prior distribution and the design of the simulators. They introduce an auxiliary particle filter method that addresses these issues, offering greater efficiency and flexibility. The auxiliary particle filter uses an additional variable to improve the simulation process, allowing for more accurate estimation of the filtering density. The paper also discusses the use of stratification in particle filters to perform Bayesian inference on model parameters and maximum likelihood estimation. The methods are illustrated using a stochastic volatility model and a time series model of angles. The authors conclude that the auxiliary particle filter provides a more robust and efficient approach to filtering, particularly in the presence of outliers.