Application of Kalman filtering techniques in the processing of data on physical experiments

This paper is a survey of a study implemented during the last two years, considering the correction (unfolding) of smearing effects due to instrumental resolution in physical experiments (neutron - and X-ray scattering). In order to obtain as well on-line as interactive situations of treatment of data, sequential methods were studied. Two classes of problems have been treated. In the first one no a-priori physical knowledge about the functions to be estimated was available and simple staircase functions or spline models were developed, so that the application of the Kalman-Bucy Filter equations was advisable. In the second class, analytical functions were given so that the parameters of nonlinear models were to be estimated. This has been done applying the extended Kalman filter equations. Several practical examples have been discussed.