Generalized LMMSE Filtering with Out-of-Sequence Observations in Arbitrary Constant Delay

Focusing on the problem of state estimation in the presence of sensor faults and Out-of-sequence measurement (OOSM) observations synchronously, we derive a formulation of Linear minimum mean squared error (LMMSE) filter with the arbitrary time delay of OOSM, the generalization of the present work lies in simultaneous treatment of correlated faults together with OOSMs that arrive at an arbitrary delay in a linear-optimal manner. The approach is demonstrated in a numerical comparison.