Constrained estimation with truncated Gaussians

The state estimation problem consists of estimating the hidden state of a dynamic system, governed by a stochastic linear or nonlinear process model, from a set of noisy observations, which depend on the hidden state by a stochastic linear or nonlinear observation model. This problem is often solved recursively using Bayesian filtering. In the recursive Bayesian filtering approach, a new state estimate is determined at every time-step, given the latest measurement and some knowledge of the state at the previous time-step. However, incorporating a priori knowledge in the form of equality or inequality constraints on the states proves to be difficult and is still a topic of ongoing research [1, 2].