Lecture notes on state estimation of nonlinear non-Gaussian stochastic systems

Preface These lecture notes are concerned with state estimation problem of linear and particularly nonlinear discrete and continuous-discrete stochastic systems. State estimation has a great variety of applications including The general solution of the state estimation problem is based on the Bayesian recursive relations and the Fokker-Planck equation which generate conditional probability density function of unknown state of the system. An exact solution of the Bayesian recursive solution is known only for linear Gaussian systems and several special cases. In other cases, a certain kind of approximation of the system, solution of the recursive relations or the Fokker-Planck equation must be employed. Development of the nonlinear state estimators was accelerated by the series of annual symposia on nonlinear estimation theory and its applications held in San Diego in 1970 – 1973. In the last forty years a number of state estimators has been proposed that can be classified to two basic classes: the local estimators providing rather point estimates and the global estimators generating probability density function of the state. Both classes will be treated in the lecture notes. As far as the local estimators are considered, the Extended Kalman filter and Kalman-Bucy filter, second order filter, iterated filter, Divided difference filter and Unscented filter will be presented. The global estimators will include the Gaussian sum approach, the point mass approach and the Monte Carlo approach. Also the Cramér Rao bound as a tool for nonlinear filter estimation quality evaluation will be dealt with.