A Kalman Filtering Approach for Validation of Sensor Networks Monitoring Distributed Parameter Systems

A Kalman Filtering approach is proposed for validation of sensor nodes in sensor networks designed to monitor distributed parameter systems. It is shown that the numerical solution of the associated partial differential equation results into a set of nonlinear ordinary differential equations. With the application of diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system is obtained in the linear canonical form. This transformation enables to obtain local estimates about the state vector of the system through the application of the standard Kalman Filter recursion. The method enables to estimate the dynamics of the distributed parameter system by processing the measurements from a small number of sensors without knowing the associated boundary and initial conditions. Moreover, by comparing the estimates provided by the Kalman Filter against the real measurements of the sensors, it becomes possible to diagnose sensors' failures.