Gaussian estimation for non‐linear stochastic uncertain systems with time‐correlated additive noises and packet dropout compensations

Abstract

This paper discusses the problem of state estimation for non-linear stochastic uncertain systems with time-correlated additive noise and packet dropout compensations. Both process noise and measurement noise are additive forms of noise that can be described as Gaussian first-order Markov processes. The stochastic uncertainty of the system is described by synchronous correlated white multiplicative noise. When the measurement information from the current epoch is lost, a compensation strategy based on measurement information prediction is used. First, the state information, process noise, and measurement noise are augmented to enable the construction of a new vector to be estimated, and the filter, predictor, and smoother of the system are designed using a Gaussian iterative estimation algorithm based on innovation analysis. The multiplicative noise in the process equation is estimated in real time. Second, a numerical implementation of the proposed algorithm is derived based on the third-degree spherical-radial Cubature Kalman filter(CKF). Finally, the proposed algorithm is compared with an extended Kalman filter (EKF) based on Taylor series expansion. The effectiveness of the proposed algorithm is verified by comparing the simulation results.