Optimal estimation in wireless sensor networks with double measurements and multiplicative noise

The optimal estimation for wireless sensor network systems is studied, where the measurements are observed from two different wireless channels, and the system is corrupted by multiplicative noises. In the system model, the probability of each packet-drop of measurements is different. The optimal estimator is derived by probability method and Kalman filtering formulae based on projection theorem, the proposed optimal estimator is different from previous works, and some properties of the estimation error covariance are proposed, which will be useful to analyze the statistical convergence properties and the upper and lower bounds on the expected state error covariance in future.