State and Parameter Estimation for Dynamic Systems: Some Investigations

This dissertation presents the outcome of investigations which envisaged to develop improved state and ?combined state and parameter? estimation algorithms for nonlinear signal models (during the contingent situations) where the complete knowledge of process and/or measurement noise covariance are not available. Variants of ?adaptive nonlinear estimators? capable of providing satisfactory estimation results in the face of unknown noise covariance have been proposed in this dissertation. The proposed adaptive nonlinear estimators incorporate adaptation algorithms with which they can implicitly or explicitly, estimate unknown noise covariances along with estimation of states and parameters. Adaptation algorithms have been mathematically derived following different methods of adaptation which include Maximum Likelihood Estimation (MLE Covariance Matching method and Maximum a Posteriori (MAP) method. The adaptive nonlinear estimators which have been proposed in this dissertation are formulated with the help of a general framework for adaptive nonlinear estimators for both additive and non-additive Gaussian noise. The proposed new algorithms have been formulated and characterized with Monte Carlo simulation using nontrivial plant models. The general framework mentioned as above, is extended to formulate alternative versions of adaptive nonlinear estimators (in the information filter form). Performance of such adaptive nonlinear information filters are demonstrated for multiple sensor fusion. The contribution of this work may be categorized as follows: ? Proposing general frameworks for Q adaptive and R adaptive nonlinear state estimators (for respectively unknown process noise covariance Q and unknown measurement noise covariance R ) and demonstrating applicability of such filters with specific examples. ? Derivation of the nonlinear versions of adaptation algorithms for R-adaptive nonlinear estimators following the Maximum Likelihood Estimation (MLE) method respectively utilizing innovation and residual sequences. The latter version is important as it automatically ensures positive definiteness of the adapted R- matrix. ? Modification of the existing Maximum a Posteriori (MAP) based algorithms for adaptive nonlinear estimators (both R-adaptive and Q-adaptive) with reasonable simplifying assumptions which illustrate that the adaptation algorithms after modification match well with those obtained by the MLE method and the intuitive Covariance Matching method. ? Proposing and characterizing algorithms for different versions of Q-adaptive and Radaptive Divided Difference filter (ADDF). ? Proposing and formulation of algorithms for several new variety of Q and R adaptive nonlinear estimators, viz. Adaptive Gauss Hermite filters (AGHF), Adaptive Cubature Kalman filters (ACKF), Adaptive Cubature Quadrature Kalman filters (ACQKF). ? Extending the algorithms for Adaptive Divided Difference filter to suit signal models with non additive noise. Extension of the general framework for adaptive nonlinear estimators with non-additive noise and its demonstration by formulating Adaptive Cubature Kalman filter. ? Formulation of alternative general framework for adaptive nonlinear estimators (in presence of additive noise) with information filter configuration which are potentially suitable for multiple sensor fusion. Adaptive version of Divided Difference information filter, Gauss Hermite information filter, Cubature information filter, Cubature Quadrature information filter have been formulated from the general framework and validated using multi sensor estimation problems. ? Adopting the square root framework for formulation of adaptive versions of Gauss Hermite filter, Cubature Kalman filter and Cubature Quadrature Kalman filter both in the standard error covariance form and in the information filter form.