| A dynamical system, often implemented numerically, whose purpose is to estimate unmeasureable states based on available measurements of a dynamical process is called an observer. Novel methods, based on the theory of dynamical systems with sliding modes, are proposed and analyzed for state estimation of uncertain, nonlinear, discrete-time systems. The proposed discrete-time sliding mode observers retain the fundamental property, familiar in continuous-time sliding mode control literature, of robustness to dynamical modelling errors. Design methodologies are proposed for linear or nonlinear, non-redundant or redundant measurement models. Methods for redundant measurements provide an optimal fusion of the available data during the sliding mode through minimization of a squared error cost measure. New methods to obtain exponential stability of nonlinear discrete-time systems are introduced with applications in stability and robustness analysis of the proposed sliding mode observers. For nonlinear measurements, ideal observer forms are represented by systems of nonlinear integral equations which implicitly define the observer output. Practical implementation methodologies are proposed through development and analysis of local iterations at each measurement event. These local iterations for nonredundant or redundant measurements reduce, respectively, to Newton and modified Gauss-Newton methods for which there is a broad literature base. The resulting iterated sliding mode observers can be applied to a broad class of discrete-time state estimation problems. Applications and performance of the various sliding mode observer forms are demonstrated through simulation results in the problem of estimating motion and structure of manoeuvring objects based on feature position measurements in long multiple-camera image sequences. |
