A prediction algorithm with a limited number of particles for state estimation of high-dimensional systems

The ensemble transform Kalman filter (ETKF) is a state estimation algorithm that is widely applied to estimating the state of nonlinear high-dimensional systems, such as data assimilation that combines observations and a numerical simulation model. The ETKF is an efficient algorithm that uses a relatively small number of particles to represent a probability density function for the state of a system. However, the existing methods for obtaining a predictive distribution for the ETKF are not necessarily applicable to general situations. One of the common methods, the Monte Carlo method, can be influenced by random errors if the use of a large number of particles is not allowed due to the computational cost of the simulation model. Another common method, the multiplicative inflation method, does not allow us to make arbitrary choices of the stochasticity of the system. The purpose of this work is to overcome these problems. In this study, we propose a new algorithm for obtaining particles that represent the predictive distribution. The proposed algorithm allows us make a prediction under an arbitrary system noise covariance matrix. Since it does not use random numbers, it well works even when the number of particles is limited.