Study On Robust State Estimation Algorithm For Systems With Multiplicative Noise

The state estimation theory of stochastic systems with multiplicative noise is an important developing orientation in modern control theory which can be used in many fields such as oil seismic exploration, communication engineering and underwater remote target detection and tracking. However, in practical engineering there always exist uncertainties in model parameters and/or model structures in that the incomplete system model, model reduction and linearization and aging of electronic components. So the actual system model can not be described accurately. The performance of estimators designed without accounting for these model errors can be severely degraded and sometimes even unacceptable. To solve this problem, the robust estimation theory has been developed and always attracts considerable attention in control theory and application. Studying stochastic systems in presence of both multiplicative noise and uncertainties has profound theoretical and practical significance. Based on previous research works of others, the robust state estimations for systems with multiplicative noise which have the stochastic uncertainties, determinant norm bounded uncertainties and the polytopic uncertainties are studied. The main content of the dissertation can be briefly described as follows:1. Optimal state estimation algorithm and robust variance-constrained state estimation algorithm for systems with multiplicative noise which have stochastic uncertain parameters are studied. First, based on the projection theory, a linear minimum variance recursive optimal estimation algorithm is established. Then the mean-square stability for a linear time-invariant form of these systems is defined based on Lyapunov stability theory. By using properties of mean-square stability and Linear Matrix Inequality, the condition for the existence of robust variance-constrained estimator and a robust optimal variance-constrained estimation algorithm is presented. The difference between these two algorithms and their respective advantage and disadvantage are investigated. The effectiveness and the range of application of these algorithms are tested through simulation.2. Robust variance-constrained state estimation algorithms for systems with multiplicative noise which have norm-bounded uncertain parameters are studied. The quadratic stability for systems of this type is defined based on Lyapunov stability and the properties of the quadratic stability are analyzed. The condition for existence of the robust state estimator and a robust optimal variance-constrained state estimator are derived based on the properties of quadratic stability and Linear Matrix Inequality. Simulation results are given to show the effectiveness of the algorithms.3. Based on parameter-dependent Lyapunov stability theory, systems with multiplicative noise which have polytopic uncertainties are well studied. By constructing a parameter-dependent Lyapunov function, the robust optimal variance-constrained estimation algorithm is established in terms of Linear Matrix Inequalities. The performance of the algorithm is validated by numerical examples.