Print Email Facebook Twitter On martingales and recursive optimal state estimation Title On martingales and recursive optimal state estimation Author Moek, G. Institution National Aerospace Laboratory NLR Date 1980-06-26 Abstract This report constitutes the deposit of a study of literature on martingales and estimation theory. Some experimental work concerning the efficiency of an estimation algorithm based on martingales is also described. The investigation has been guided by the intent to investigate martingales in relation to the Kalman and Kalman-Bucy filters and to consider the implications for the practical filtering work at NLR. The optimal estimation problem and the Kalman and Kalman-Bucy filters are recalled. Martingales are defined and some examples are given. A number of theoretical results concerning martingales and linear as well as nonlinear estimation theory is summarized in an innovation and presentation theorem. Based upon this a simple derivation of the Kalman and Kalman-Bucy filters is sketched. Reference is made to more general estimation problems (counting process observations, martingale noise) which can be solved along the same lines. Finally, a wide-sense martingale approach to linear estimation is discussed. For a class of signals,' comprising those studied in the Kalman and Kalman-Bucy problem, recursive estimation equations for the signal based on observations in either white or coloured noise are described. A more general model for coloured noise is given. By means of numerical simulation of some model problems the Kalman filter and the wide-sense martingale approach are compared. Subject Stochastic processesEstimationLinear systemsNonlinear systemsMartingalesLeast squares methodRecursive functionsKalman filterState vectorWhite noiseTheorem provingColoured noiseRepresentation theoremInnovation theorem To reference this document use: http://resolver.tudelft.nl/uuid:d80f8a96-6fa9-4491-9074-9a192085bfaf Publisher Nationaal Lucht- en Ruimtevaartlaboratorium Access restriction Campus only Source NLR-TR 80058 U Part of collection Aerospace Engineering Reports Document type report Rights (c) 1980 National Aerospace Laboratory NLR Files PDF NLR_TR_80058_U.pdf 28.44 MB Close viewer /islandora/object/uuid:d80f8a96-6fa9-4491-9074-9a192085bfaf/datastream/OBJ/view