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

Abstract

In sensor fusion scheme, measurements from multiple sensors usually arrive at different rate, and outof-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.

Using Ensemble Kalman Filter for Distributed Sensor Fusion

“…Therefore, a group distribution of particles is freely transformed. This property of EnKF is similar to other particle-based filters which make it is applicable to most system including continuous-time system, see [15]. One disadvantage of using EnKF is that heavy calculation and large bandwidth is necessary for both calculation and communication between nodes.…”

“…where 1 q ∈ R q is a column vector with all elements equal one, and 0 r ∈ R r is a column vector with all elements equal zero, and C = C ⊗ I n ∈ R nr×nq . Then, the optimal solution (4) and (5) leads to the same solution as (15). (Proof) see Section 3 in [11].…”