In this paper, data-compatibility analysis (DCA) problem is investigated with both the measurement noise and input noise considered. The expectation-maximization (EM) algorithm is exploited to deal with the unknown noise statistics. Motivated by the fact that although there exists an excellent EM based estimator for dynamic systems, it cannot be used in the context of DCA due to the presence of non-additive input noises, a generalized EM based estimator is developed to reconstruct the flight path, as well as to estimate the sensor model parameters. Making full use of the special dependencies among the state components and the fact that the associated dynamic system has an affine nonlinear structure, the generalized estimator retains many advantages of the existing EM based one, such as the simple optimization process for the unknowns. Experimental results show that it can give more accurate results than the classical output error method and the existing EM based one in the case of high input noise.
Read full abstract