Kalman filter applied to estimation of neutron flux distribution and optimum allocation of in-core detectors

Estimation of the spatial distributions of prompt neutrons and delayed neutron precursors has been studied by analyzing the output signals of in-core neutron detectors. In this paper, application of distributed Kalman filter is attempted for a one-dimensional core model having statistical fluctuations. Assuming that their statistics are determined by Schottky formula, the error covariance matrix of estimation is computed in order to evaluate the filter performance. In the computation of this matrix, the algebraic Riccati equation is solved by generalized Neuton-Raphson method. From the viewpoint of estimation accuracy, it is also an important problem to optimize the detector locations. Considering the cases where estimation is focussed on a specified quantity related to prompt and delayed neutrons, the optimum allocations of two detectors are searched numerically. It is inferred that the optimized allocation has a considerable effect on estimating the shapes of the distributions where higher terms of spatial harmonics cannot be neglected. (auth.)