Ensemble Kalman filtering of out-of-sequence measurements for continuous-time model

In sensor fusion scheme, measurements from multiple sensors usually arrive at different rate, and out-of-sequence which are called out-of-sequence measurements (OOSMs). To observe the state of a system using the information from OOSMs, the covariance of the process noise accumulated from time to time is necessary. However, by assuming that all noises are Gaussian in Kalman filter, it is difficult to determine the covariance of the accumulated process noise from a system that is described by a continuous-time nonlinear model. This paper introduces an integration method to estimate the state, the state covariance and the covariance of the accumulated process noise from a continuous-time nonlinear model. Together with an OOSM update algorithm using Ensemble Kalman filter (EnKF), we can realize an OOSM filter for most nonlinear systems efficiently. The algorithm requires low number of particles, derivative-free, without a necessity of finding backward transition function for the system.