Sequential Estimation of States and Parameters of Nonlinear State Space Models Using Particle Filter and Natural Evolution Strategy

This paper proposes a new sequential estimation method for simultaneously estimating states and parameters of a state space model. Particle filter (PF) is known as a method that can estimate states in difficult sequential state estimation problems with nonlinearity and non-Gaussianity. PF updates an ensemble consisting of multiple particles representing states of a state space model in order to estimate the true state, based on observation, at each time step. However, when PF estimates not only states but also parameters of the state space model at the same time, it is observed that the estimation accuracy deteriorates. When estimating both states and parameters, PF utilizes particles representing states and particles. In order to overcome the problem of PF, we propose a new method that sequentially estimates states by PF and parameters by the separable natural evolution strategy (SNES). SNES is one of the most powerful black-box function optimization methods. In order to confirm the effectiveness of the proposed method, we compare the performance of the proposed method and that of PF using two nonlinear state space models, the Van der Pol model and the Lorenz model. In the Van der Pol model, the median MSE values of the state and the parameter of the proposed method were 0.003610 and 0.01468 and those of PF were 4.228 and 6.520, respectively. In the Lorenz model, the median MSE values of the state and the parameter of the proposed method were 0.002639 and 0.003479 and those of PF were 309.5 and 1.470, respectively. The smaller MSE is, the better the performance is.