Many problems in engineering require estimation of the state of a system which changes over the time using a set of noisy measurements made on the system. In this project we focus on the state-space approach to modelling dynamic systems. First of all we study the Kalman filter algorithm which achieves the optimal solution in linear and Gaussian models. The Kalman filter minimises the variance of the estimation error. In nonlinear and/or Non-Gaussian models, approximations to the distribution of interest must be performed. We study some suboptimal algorithms such as the Monte Carlo methods and in particular, we focus on the Particle filter which is a Sequential Monte Carlo method. Over the project, several experiments in MATLAB are done with the goal of discussing and comparing the algorithms performances in several situations to demonstrate their theoretical features.