State estimation for asynchronous sensor systems with Markov jumps and multiplicative noises

This paper is concerned with the asynchronous state estimation problem for sensor systems subject to Markov jump parameters and multiplicative noises. The asynchronous sensors considered can have arbitrary sampling rates and arbitrary initial sampling instants. By transforming the asynchronous measurements within each fusion interval into an augmented measurement, the equivalent measurement equation and state equation at the fusion time instant are constructed. Based on the two equations, a linear minimum mean-squared error (LMMSE) estimator is developed using the orthogonality projection principle. Due to the existence of the common process noise in the equivalent process and measurement noises, the equivalent process and measurement noises are cross-correlated and the equivalent measurement noises are autocorrelated. These correlations are taken into account in the estimator design. The stationary case is also studied and the sufficient condition is established for the stability of the proposed estimator. A target tracking example is provided to illustrate the effectiveness of the proposed estimator.