This paper analyzes the particle filter approach to time series filtering, highlighting its robustness issues with outliers and the discrete support representation of the prior distribution. The authors propose an auxiliary particle filter that addresses these problems by introducing stratification, which allows for online Bayesian calculations and maximum likelihood estimation. The method is illustrated using a stochastic volatility model and a time series model of angles. The paper discusses the statistical basis of particle filters, their weaknesses, and the improvements made by the auxiliary particle filter. It also explores the adaptability of the method to various models, including non-linear Gaussian models, log-concave measurement densities, and limited dependent processes. The authors compare their method with existing literature, emphasizing its simplicity, efficiency, and broader applicability.This paper analyzes the particle filter approach to time series filtering, highlighting its robustness issues with outliers and the discrete support representation of the prior distribution. The authors propose an auxiliary particle filter that addresses these problems by introducing stratification, which allows for online Bayesian calculations and maximum likelihood estimation. The method is illustrated using a stochastic volatility model and a time series model of angles. The paper discusses the statistical basis of particle filters, their weaknesses, and the improvements made by the auxiliary particle filter. It also explores the adaptability of the method to various models, including non-linear Gaussian models, log-concave measurement densities, and limited dependent processes. The authors compare their method with existing literature, emphasizing its simplicity, efficiency, and broader applicability.