Optimal sequential fusion estimation for sampled-data systems with random delays and multiplicative noise

This article is concerned with the optimal sequential fusion filter design issue for a class of sampled-data systems subject to random transmission delays and multiplicative noise. The considered delay is modeled as a multistate Markov chain, while the multiplicative noise corrupting the observation measurements is assumed be a white noise sequence with known statistical properties. First, by reorganizing the original measurements, the solvability of the addressed problem is cast into the feasibility of an optimal estimation issue for the hybrid Markovian jump system without delays. Then, an optimal sequential fusion filter is constructed by utilizing a dynamic model with finite jumps on basis of the arrival order of measurements from different sensors, guaranteeing estimation performances both at sampling instants and within the sampling intervals. Moreover, the desired estimator gains can be computed via solving a series of coupled differential Riccati equations with jumps and coupled differential Lyapunov equations. Further, a stationary sequential fusion filter is achieved with the guarantee of the exponentially mean-square stability. Finally, two simulation examples are provided to verify the validity of the proposed algorithms.