A new algorithm for latent state estimation in non-linear time series models

We consider the problem of optimal state estimation for a wide class of non-linear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering, where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.