Sequential LMMSE Filtering with Out-of-Sequence Observations Under Nonlinear System

In this work, the state estimation problem is taken into consideration in the simultaneous presence of sensor faults, out-of-sequence measurements (OOSM) and nonlinear dynamics. We derive the analytic formulae of linear minimum mean squared error (LMMSE) estimation with the arbitrary delay OOSMs and the observation faults, then outline a sequential LMMSE filtering under nonlinear dynamics. The sequential filtering lies first in fulfilling a nonlinear estimation using in-sequence observations, secondly perform a LMMSE correction to the nonlinear estimates with OOSMs. The proposed approach's feasibility is demonstrated by numerical comparisons.