Recursive state estimation for stochastic nonlinear non-Gaussian systems using energy-harvesting sensors: A quadratic estimation approach

In this paper, the recursive quadratic state estimation problem is investigated for a class of stochastic nonlinear systems (SNSs) subject to non-Gaussian noises through energy-harvesting sensors. Stochastic nonlinearities are taken into account in both state and measurement equations. The energy-harvesting technique is employed to mitigate the phenomenon of energy depletion and supply energy for data transmissions between the sensors and the remote estimator. By augmenting the state/measurements and their respective second-order Kronecker powers, the original SNS is converted into a new nonlinear system that exploits more information about the non-Gaussian noises, and the resultant quadratic estimator can then be designed by developing an efficient recursive variance-minimization algorithm. Subsequently, an upper bound is proven to exist on the estimation error covariance matrix via solving certain matrix difference equations, and such an upper bound is minimized by resorting to the design of appropriate gain parameters of the quadratic estimator. Moreover, we analyze the monotonicity of the trace of the minimal upper bound with respect to the probability of measurement transmission. Finally, a simulation example is given to demonstrate the effectiveness of the proposed quadratic estimation algorithm.