Kalman Type Filters And Their Application In Joint State-parameter Estimation

Joint state-parameter estimation has been an essential research topic in the academic society.It has a wide variety of applications in both military and civilian aspects.Kalamn type estimators are often used in these joint estimation problems,such as extended Kalman filter,unscented Kalman filter,two-stage Kalman filter and robust Kalman filter.This thesis introduces at length two-stage Kalman filter and robust Kalman filter and their roles in joint state-parameter estimation problems.Two main categories of joint estimation scenarios are discussed in this thesis.In the first category of joint estimation problem,the input term of the linear system is a fix-structure dynamic system with unknown parameters.Two-stage Kalman filter cannot be implemented in such scenario because it need known parameters.Robust Kalman filter is applied for its promising property that without knowing anything of input signal it is still able to produce unbiased state estimates.An input estimator is derived and proved unbiased.From the estimated input sequences,their parameters are estimated through autoregressive identification methods,thereby achieving joint estimation of state and parameter.Simulation results are conducted to show the validity of this algorithm and comparisons have also been made to show advantages of such estimator.The joint estimator is also applied to moving target prediction in radar tracking system.In such case,the model of the moving target is corrected thereby achieving more accurate estimated and predicted states.Also,a simulated real-time moving targeting prediction radar system is built to provide simultaneous target predicted states for the radar system in reaction to the scenario where it needs to recapture the target because the radar system is blocked or mulfunctions.In the second category of joint estimation problem,the transmission matrix of the linear system has some known parameters or the whole matrix is unknown.Normally,estimators cannot be applied in such scenario for lacking crucial information.In the thesis,an optimal condition for input estimator of robust Kalman filter is firstly proved through which the unknown parameters are converted into a special linear function.Many attempts to estimate required parameters in such function have been made.These algorithms are maximum likelihood,matrix inversion,neural network and error-in-variable methods respectively.Also,the advantages and shortcoming of these proposed algorithms are analysed through comparison,which are confirmed by simulation results.No ranking of these algorithms is made because they all operate in different conditions.In addition,for the special linear equation derived for the second type of joint estimation problem,this thesis manages to replace the unknown variable with a known one such that difficulty to design estimators can be reduced.Apparently,the replaced will cause certain replacement error which is larger than some lower bound,e.g.,replacement lower bound.In the meantime,Cramer-rao lower bound is also discussed in such scenario and the relationship among the overall error after the replacement of the variable,the replacement lower bound and Cramer-rao lower bound has been derived.