Recursive Filtering for Two‐Dimensional Markov Jump Linear System With Time Correlated Multiplicative Noises and Energy Harvesting Constrains

ABSTRACT This article investigates the linear minimum mean square error estimation for the two‐dimensional Markovian jump linear system with time‐correlated multiplicative noises and energy harvesting sensor. The time‐correlated multiplicative noise is described by a linear dynamic model driven by white noise. The sensor harvests energy from the natural environment, and the energy levels at the energy harvester are characterized by some random variables that follow a certain probability distribution. The transmission of measurements is closely related to the energy level of the sensor, and only when the current energy storage exceeds the transmission energy consumption, the measurements are transmitted to the remote estimator. The main goal of this study is to formulate an iterative coupled new‐type estimator with jumping parameters and design the estimated gain reasonably to guarantee the minimum error covariance at each step. Firstly, two new‐type coupling estimators are derived by introducing several new recursive terms. By employing the induction method, the unbiasedness of the proposed two estimators is first ensured and the parameters of the estimator are supplied. Subsequently, an upper bound on the estimation error covariance with the jumping property is given based on the spectral norm. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed estimation scheme.