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Many physical systems are nonlinear and non-Gaussian in their state-space models. Particle Filter (PF) is a sequential Monte Carlo method that uses sets of sample scenarios, i.e. “particles” to represent probability densities, and it can be applied for state estimation in nonlinear/non-Gaussian state-spaces models. Conventional variants of PF do not assume any noise for the system input, while the corresponding measurement models disregard the system input as an argument. In reality, physical systems receive inputs contaminated with the measurement noise. In this work, a generalized particle filter algorithm is developed that handles the noisy input of the state-space model in a probabilistic framework. Three advanced variants of PF are then developed to improve the filtering accuracy. Performance of the developed filters are then verified with simulation of univariate and bivariate non-stationary growth models as benchmarks.

State Estimation for General Class of Dynamical Systems: An Extension to Particle Filters