Optimal linear estimators for multi-sensor stochastic uncertain systems with packet losses of both sides

Optimal linear estimators (OLEs) are designed for networked control systems (NCSs) with stochastic uncertainties, multiple sensors and multiple packet loss rates. Packet losses of both sides from sensors to an estimator (S–E) and from a controller to an actuator (C–A) are taken into account. A group of mutually uncorrelated stochastic variables obeying Bernoulli distributions are employed to depict the phenomenon of multiple packet losses from different S–E channels. The stochastic uncertainties in state and output matrices are depicted by white multiplicative noises. The OLEs dependent on the packet loss rates are presented in the least mean square (LMS) sense via the orthogonal projection approach (OPA) which is a universal and useful tool to obtain the optimal linear estimators in LMS sense. They are solved by three recursive equations including one Riccati equation, one Lyapunov equation and one simple difference equation. The stability of the OLEs is studied. A sufficient condition is provided to guarantee the steady-state property for time-invariant systems. Finally, a mass–spring–damper system is applied to confirm the performance of the derived algorithms.