State estimation for nonlinear dynamic systems - some contributions

Abstract

This dissertation addresses the problem of state estimation of dynamic systems which remains an active research area. Formally, ‘State Estimation’ may be defined as a technique to estimate the unmeasured states of a dynamic system by using the model of the system and all or some of the measured (output) variables. Observers as state estimators, though have been used fairly extensively, suffer from two shortcomings: firstly, the design methods of observers do not take cognisance of measurement noise; secondly, the accuracy of the (state) estimation may be severely affected if the dynamics of the actual system differs from what has been assumed or some of the excitation inputs are inaccessible. These shortcomings are overcome in stochastic state estimators (of which, the Kalman Filter (KF) is considered to be the most well-known). Stochastic state estimators take care of measurement noise by filtering it out to the extent possible and also admit modeling inaccuracies, which are treated as a different variant of noise, called “process noise”. Kalman filter and its descendants have built-in mechanisms to trade-off components of estimation error due to measurement inaccuracy and due to process model inaccuracy. The present work evaluates Kalman filters and its extensions for nonlinear models as well as their adaptive counterparts for practical problems and also proposes novel extensions. The nonlinear counterparts of KF include Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Central Difference Filter (CDF), Divided Difference Filter (DDF), Gauss Hermite Filter (GHF). The present work also employs variants and extensions of Variable Structure Filter (VSF). In particular, adaptive nonlinear state estimators such as Adaptive Extended Kalman Filter (AEKF), Adaptive Unscented Kalman Filter (AUKF), Adaptive Divided Difference Filter (ADDF) and Adaptive Gauss Hermite Filter (AGHF) have been evaluated for aircraft tracking scenarios under model uncertainty and unknown noise statistics. Evaluations are carried out with fairly extensive Monte Carlo simulation and with a number of numerical metrics like time averaged RMS error, peak RMS error and rms of RMS error. For qualitative appreciation, time plots of RMS errors are also provided. The following modified and improved nonlinear state estimators have been proposed, characterized and evaluated (by cross-comparisons of performance) for civil aircraft tracking scenarios. These are: (i) A sigma point variant of Smooth Variable Structure Filter (SVSF) (ii) An adaptive version of Smooth Variable Structure Filter (ASVSF) (iii) An adaptive version of Interacting Multiple Model Filter (AIMM). Monte Carlo simulation and the metrics mentioned above have been used for evaluating the proposed novel filters. Performance of the proposed enhanced state estimators have been compared with the existing EKF, UKF, DDF, GHF, SVSF and Interacting Multiple Model (IMM) state estimator. Salient contributions of the work of this dissertation are summarised as follows: o A systematic survey of current literature on nonlinear state estimation, including adaptive state estimator and variable structure state estimators were done. Also carried out a systematic study of the estimation of aircraft tracking scenarios which involve mode switching between linear and non-linear models. o The estimation performance of some standard linear and non-linear state estimators have been characterised, evaluated and benchmarked against, for single model adaptive estimator in tracking scenarios. o Evaluation of Adaptive nonlinear state estimators such as AEKF, AUKF, ADDF and AGHF has been carried out for tracking scenarios under model uncertainty and unknown noise statistics. o The following modified, enhanced and improved nonlinear state estimators have been proposed, characterized and evaluated (by cross-comparisons of performance) for civil aircraft tracking scenarios/ These are: i. A sigma point variant of Smooth Variable Structure Filter (SVSF) ii. An adaptive version of Smooth Variable Structure Filter (ASVSF) iii. An adaptive version of Interacting Multiple Model Filter (AIMM)