Abstract
When we are to estimate the state of distributed parameter systems by measurement data from a finite number of measuring devices, it is desirable to choose the optimum location for the measuring devices so as to minimize the cost due to the estimation error. The optimum sensor location depends on statistical characteristics of disturbances which are unknown a priori.
This paper proposes an adaptive algorithm for the measurement optimization available in a class of discrete-time distributed parameter systems subjected to unknown disturbance characteristics. We derive a recrrence form to compute both the time correlation and the space correlation of the innovation terms of the measurement data from a finite number of sensor locations. The adaptive algorithm utilizes the correlation from the moving average of the measurment data to estimate the disturbance characteristics.
In particular, for a distributed parameter system disturbed at a finite number of unknown points as seen in atmospheric dispersion of stack effluents, we investigate analytically the optimum sensor location which minimizes the estimation error cost. Then we apply the adaptive algorithm to estimate unknown parameters such as disturbance point sources and variances. It is shown that the convergence of the adaptation may be improved by optimizing the sensor location.
