Optimal Sequential Estimation for Asynchronous Sampling Discrete-Time Systems

The asynchronous optimal estimation problem is studied for linear discrete-time stochastic systems subject to a uniform state updating rate and random nonuniform measurement sampling rates. For the case where there are samples within a state updating period, a modified measurement equation from the original system is established for synchronization. Based on the established state-space model, an optimal sequential filter (SF) is developed in terms of the linear minimum variance (LMV) within a state updating period (SUP). It is noted that the SF is more suitable for dealing with the estimation problem of asynchronous sampling systems than other algorithms. Moreover, the proposed SF possesses the same estimation accuracy as that of the augmented batch filter (ABF), as well as a reduced computational cost. The equivalence of their estimation accuracy is strictly proven. Finally, the multisensor case is discussed. The effectiveness of the proposed algorithms is verified with simulation research.