Distributed Asynchronous Fusion Estimator for Stochastic Uncertain Systems With Multiple Sensors of Different Fading Measurement Rates

Abstract

This paper is concerned with the distributed fusion estimation problem for time-varying stochastic uncertain systems with multiple asynchronous sampling sensors of different fading measurement rates. Stochastic uncertainties of multiplicative noises exist in the state and measurement equations. The phenomena of fading measurements of different sensors are depicted by a group of stochastic variables with known statistics. Different sensors have different sampling rates. Sampling period of each sensor is uniform and an integer multiple of the state update period. By transforming the multiplicative noises into the additive noises, local estimators (LEs) and estimation error cross-covariance matrices between any two LEs are derived at the state update points. A real-time distributed fusion estimator (DFE) is obtained by using the matrix-weighted fusion estimation algorithm in the linear unbiased minimum variance sense. The asymptotic stability and steady-state property are analyzed. A new conception of $\boldsymbol{{period}}$ steady state is presented and the $\boldsymbol{{period}}$ steady-state properties of the LEs, cross-covariance matrices, and DFE are proven. Though DFE has lower accuracy than the centralized fusion estimator, it has better robustness and flexibility since it has a parallel structure. To avoid the calculation of cross-covariance matrices, a sequential covariance intersection fusion estimator is given by using two-sensor covariance intersection fusion algorithm. It has lower accuracy but smaller computational cost than DFE, and better accuracy than LEs. Two examples are given to show the effectiveness of the proposed algorithms.