Non-Gaussian filtering using probability histogram

The problem of determining minimum variance estimates for non-Gaussian situations is treated using probability histogram. To obtain a posteriori probability density function in the presence of non-Gaussian noise it is necessary generally to determine the Bayesian recursion results which describe the behavior of a posteriori probability density function of the state, but these relations are generally very difficult to solve. In this paper, the state estimation problem has been recast as the state noise estimation problem using the approximation to the system equations. It is not necessary to determine the recursion relations which describe the behavior of a posteriori probability density function of the state since the state noise is white. Hence, the estimation problem is made to be simplified and it is convenient to use probability histogram. Experiments show that the proposed filter performs better than the Kalman filter for non-Gaussian situations and very closes to the Kalman filter for Gaussian situations. In addition, this filter is significantly less computationally intensive than the Kalman filter (in the scalar case). Experiments show also that the proposed filter (PFIF) performs stably.